Preferential Trade Agreements as dynamic farsighted

networks

James Lake∗

Southern Methodist University

September 15, 2012

Abstract

In the presence of multilateral negotiations, are Preferential Trade Agreements

(PTAs) necessary for, or will they prevent, global free trade? This question is ex-

plored using a novel dynamic network theoretic model where countries are farsighted

and asymmetric in terms of market size. I develop a new equilibrium concept that

endogenizes the order of negotiations. When two countries have a PTA, one member's

formation of an additional PTA may create incentives for its original partner to form a

PTA with its new partner. When considering forming an additional PTA, the current

member therefore recognizes the potential for erosion of its preferential access in both

partner markets. This fear of preference erosion undermines its willingness to form the

additional PTA. Thus, global free trade is attained via PTA formation when countries

fear of preference erosion is suciently small. Loosely speaking, PTAs are necessary for

global free trade when there are two small countries and one large country but PTAs

prevent global free trade when there are two large countries and one small country. The

model provides insights into the dynamics of recent trade negotiations involving the

US and suggests ambiguities inherent in GATT Article XXIV may actually promote

global free trade.

JEL: C71, F12, F13

Keywords: Preferential Trade Agreements, preference erosion, multilateralism, free

trade, networks, farsighted

∗E-mail: jlake@smu.edu. I would like to especially thank Pravin Krishna and M. Ali Khan as well asthe editor and three anonymous referees. I would also like to thank Kamal Saggi, Emanuel Ornelas, RayRiezman, Jon Faust, Hulya Eraslan, Han Ozsoylev, Matt Jackson, Martin Richardson, Renee Bowen, KyleBagwell and Sumit Joshi for useful comments and discussion as well as seminar and conference participantsat the 2011 Spring Midwest Economic Trade Meetings, 2011 Public Economic Theory Conference, 2011 AsiaPacic Trade Seminar, 2011 International Trade, Development and Game Theory Workshop at the 22ndStony Brook Game Theory Festival, the 26th Congress of the European Economic Association, SouthernMethodist University, College of William and Mary, University of Memphis and SAIS Bologna.

1

1 Introduction

In recent decades, the number of Preferential Trade Agreements (PTAs) has expanded expo-

nentially. Although sanctioned by GATT Article XXIV, such agreements are discriminatory

by construction and stand in contrast to the central principle of nondiscrimination artic-

ulated in the most favored nation (MFN) principle of GATT Article I.1 The proliferation

of such discriminatory PTAs has stimulated a substantial academic and policy debate on

whether PTAs hinder or facilitate greater liberalization, especially given the lack of multi-

lateral liberalization since the 1994 Uruguay Round. In the phrasing of Bhagwati (1991,

1993) are PTAs building blocs or stumbling blocs on the path to global free trade?

Various approaches in the academic literature have investigated the interplay between

PTAs and nondiscriminatory multilateral liberalization. In essence, this is a dynamic

question concerning the evolution of trade agreements over time, yet much of the previous

analysis has used static threecountry models. These models ask whether an arbitrarily

chosen pair of countries want to form a bilateral agreement (BA) and, if so, how this

aects the incentives for expansion of the agreement to include the third country, thus

achieving global free trade (see, for instance, Levy (1997), Krishna (1998), Ornelas (2005b)).2

3 Building a dynamic model to analyze the building blocstumbling bloc issue faces the

important challenge that a dynamic framework requires specifying the order of negotiations.

That is, which country is initially left out and how, if at all, will it be included later?

Specifying an arbitrary order of negotiations (as in Mukunoki and Tachi (2006) and Aghion

et al. (2007)) creates diculties because the equilibrium of sequential move games is often

sensitive to the order of negotiations (Ludema (1991), Ray and Vohra (1997), Jackson

(2008)) especially since asymmetries in country characteristics are likely to endogenously

determine the order.4 5

To alleviate this problem, this paper develops a novel dynamic network model in which

countries are farsighted and asymmetric in terms of market size.6 The novelty arises because

1While GATT Article I requires any tari reductions aorded to one country are aorded to all, GATTArticle XXIV provides an escape clause whereby PTA members can eliminate taris between themselves aslong as they do not raise taris or other non tari barriers on other countries.

2Alternatively, Ornelas (2005a) views multilateral liberalization as tari reductions on nonPTA mem-bers. Bagwell and Staiger (1999), Freund (2000), Bond et al. (2001) and Saggi (2006) also take this approachbut view determination of taris on nonPTA members as a self enforcing outcome of a repeated game. Incontrast, taking the stalled nature of MFN liberalization as exogenous, Baldwin (1996) shows the possibilityof a PTA domino eect in a static n country model.

3This twostep approach is eectively static because countries do not consider that the initial BA maycreate incentives for formation of further BAs.

4The inuential work of Aghion et al. (2007) assumes a leader country makes sequential take it or leave itoers to two following countries who never negotiate between themselves. In contrast, Mukunoki and Tachi(2006) assume an ordering in which each pair of countries has an opportunity to negotiate.

5Jackson (2008, p. 372) states that ... the ordering of links can have a substantial impact on whichnetworks emerge, and it is not clear what a natural ordering is.

6See Goyal and Joshi (2006) and Furusawa and Konishi (2007) for the rst applications of network theoryto the PTA literature. They use the Jackson and Wolinsky (1996) static network equilibrium concept ofpairwise stability which is a myopic best response concept. For alternative network theoretic approaches

2

the model embeds a coalitional simultaneous move game in each period of the dynamic

game to endogenously determine the order of negotiations. The new equilibrium concept

that emerges, called a farsighted dynamic network equilibrium (FDNE), is intuitively similar

to a subgame perfect equilibrium. However, rather than requiring a Nash equilibrium in

every subgame, an FDNE requires an Equilibrium Binding Agreement, a solution concept

introduced by Ray and Vohra (1997) and Diamantoudi (2003), in every subgame. The

dynamics arise because countries form agreements sequentially, at most one per period.7

Countries are farsighted because they anticipate the equilibrium evolution of the global

trade network conditional upon forming and not forming a potential agreement, and compare

the two discounted payos. Because countries are farsighted, the presence of market size

asymmetry and an endogenous order of negotiations leads to a rich environment of strategic

interaction and equilibrium dynamics.

The dynamic network model developed provides an opportunity to capture the equilib-

rium eect of BAs in a three country setting. Loosely, this eect translates into the idea of

whether BAs are building blocs or stumbling blocs. However, the important work of Saggi

and Yildiz (2010, 2011) emphasizes that capturing the equilibrium eect requires comparing

the equilibrium in which only the MFN principle exists to the equilibrium in which BAs

also exist.8 In contrast, much of the earlier literature draws implications from formation

of a single BA. By comparing the dierent equilibria, Saggi and Yildiz (2011) dene BAs

as strong building blocs if global free trade is only attained in the presence of BAs. In

contrast, this paper refers to BAs as strong stumbling blocs if global free trade is only

attained in their absence.9 10

The farsighted and dynamic aspects of the FDNE shed new light on the strong building

blocstrong stumbling bloc question with the notion of preference erosion central to the

analysis. Suppose two countries have the sole BA. These countries are insiders and the

other country is the outsider. If an insider forms an additional BA, it becomes the hub

while the other countries become spokes. Now the hub has sole preferential access in

each spoke market. However, when contemplating such a move, the insider recognizes the

see Zhang et al. (2009) for a farsighted static framework and Zhang et al. (2011) for implementation in asymmetric sequential move setting.

7Despite the recent dramatic acceleration in PTA formation, individual trade agreements still form slowlyover time. For example, NAFTA was not implemented until 1994 despite negotiations beginning as early as1986, and two to three years between commencement of negotiations and implementation of an agreementis common.

8This approach was rst adopted by Riezman (1999) and Aghion et al. (2007). However, unlike Aghionet al. (2007) who use an extensive form game where a leader makes sequential take it or leave it oers to twofollower countries, Saggi and Yildiz (2010, 2011) allow the follower countries to form an agreement betweenthemselves. Unlike Riezman (1999), Saggi and Yildiz (2010, 2011) solve the model analytically.

9The new terminology of Saggi and Yildiz (2011) reects the varied usage of the building blocstumblingbloc terminology (e.g. Bhagwati and Panagariya (1996), Saggi (2006), Aghion et al. (2007) and Furusawaand Konishi (2007)).10When global free trade is only attained in the absence of BAs, Saggi and Yildiz (2011) refer to BAs as

weak stumbling blocs if some BAs form but they refer to BAs as strong stumbling blocs if no BAs form.This paper makes no such distinction, referring to BAs as strong stumbling blocs in both situations.

3

spokes may form their own subsequent BA, which erodes the value of preferential access in

each spoke market. When the discount factor is suciently large, the eect of preference

erosion dominates the immediate hub benets and the insiders nd it Pareto dominant

to remain insiders. Thus, the fear of preference erosion prevents BA formation leading

to global free trade.11 Because sequential BA formation creates rents on the equilibrium

path, sequential BA formation arises in equilibrium even when countries have the option to

form MFN agreements. Moreover, the preference erosion logic applies regardless of whether

MFN agreements, by themselves, lead to global free trade. Thus, BAs can be either strong

building blocs or strong stumbling blocs.

Market size asymmetry and the discount factor drive the fear of preference erosion. Even

when countries are symmetric, a suciently large discount factor means the fear of preference

erosion prevents additional BA formation and undermines global free trade. Initially, greater

asymmetry between the insiders and the outsider increases insider rents by increasing the

value of preferential access protected by insiders. This makes preference erosion more costly.

In turn, since preference erosion arises in the future, attainment of global free trade requires

greater insider impatience. Thus, the extent to which BAs lead to global free trade falls. In

terms of the equilibrium when only MFN agreements exist, the largest country blocks the

move to global free trade when it is suciently large relative to the medium sized country.

This has two implications for the strong building blocstrong stumbling bloc issue. First,

loosely speaking, BAs are strong building blocs when there is one larger and two smaller

countries. When only MFN agreements exist, the largest country blocks a direct move to

global free trade because the medium country is suciently small. But, unless the discount

factor is very high, the relatively small insider rents protected by the largest and medium

countries mean the fear of preference erosion does not prevent BA formation leading to

global free trade.12 Second, loosely speaking, BAs are strong stumbling blocs when there

is one smaller and two larger countries. When only MFN agreements exist, the largest

country does not block a direct move to global free trade because the medium country is

suciently large. But, unless the discount factor is very low, the large insider rents protected

by the largest and medium countries means the fear of preference erosion prevents further

BA formation.

While greater asymmetry initially makes preference erosion more costly, the fear of

preference erosion eventually disappears for some countries. When suciently large, the

largest country no longer forms the nal spokespoke BA with the smallest country. Thus,

the medium country no longer fears preference erosion and, thus, no longer hesitates in

becoming the hub. In turn, the largest country exercises far less restraint in becoming the

11Because least developed countries have privileged access to the EU market through the Everything ButArms agreement, recent work in the policy literature has investigated the cost of preference erosion theyface if the EU grants large scale MFN tari reductions (see Hoekman (2006), Lawrence and Rosito (2006),Limão and Olarreaga (2006)).12The dependence on the discount factor which underlies the loosely speaking qualication.

4

hub. Hence, regardless of whether global free trade is attained when only MFN agreements

exist, the role of BAs becomes much more constructive. The key implication is a non

monotonic relationship between market size asymmetry and the role of BAs: greater levels

of asymmetry initially decrease (increase) the extent to which BAs are strong building

(stumbling) blocs but crossing the threshold level of asymmetry provides a dramatic reversal.

While the question asked in this paper is the same as Aghion et al. (2007) and Saggi and

Yildiz (2010, 2011), the answers are dierent. In addition to developing a dynamic model

that endogenizes the order of negotiations, the results dier from Aghion et al. (2007)

because BAs can be strong stumbling blocs even if the aggregate world payo is maximized

under global free trade.13 Relative to Saggi and Yildiz (2010), the most important dierence

is that BAs can be strong stumbling blocs. The presence of dynamics and farsightedness

underlie this dierence. Even when all countries would willingly move to global free trade

if MFN agreements were the only form of liberalization, a suciently large discount factor

means fears of preference erosion dominate temporary hub rents. In this case, the presence of

BAs prevent global free trade. However, this dynamic farsighted logic of preference erosion

is nonexistent for Saggi and Yildiz (2010). There, an insider does not contemplate that the

spokes may subsequently form their own BA if it becomes the hub. Since the spokespoke

BA underlies the fear of preference erosion, Saggi and Yildiz (2010) nd that BAs cannot

be strong stumbling blocs.

An obvious corollary is that the rationale behind BAs being strong building blocs, i.e.

necessary for global free trade, is dierent to Saggi and Yildiz (2010, 2011). There, the

discrimination faced by an outsider when insiders form a BA can induce the outsider's

participation in an MFN agreement leading directly to global free trade. Here, in contrast,

insider incentives drive the strong building bloc result. When the fear of preference erosion

is suciently small, BAs lead to global free trade because an insider willingly forms a BA

with the outsider to become the hub. Moreover, for Saggi and Yildiz (2010, footnote 24),

the outsider's discrimination fear is general enough that analogous results hold under the

case of one larger and two smaller countries in addition to the case they present which is one

smaller and two larger countries. However, in this paper, these two cases deliver dierent

results in terms of the strong building blocstrong stumbling bloc dichotomy because the

value of insider rents, and thus the fear of preference erosion, depend on the joint size of

insider markets.

The dynamic role of preference erosion underlying the results of this paper is identied

by Mukunoki and Tachi (2006).14 Their main result shows a constructive role for BAs: when

insiders have a BA, sequential BA formation can yield global free trade when a Customs

13More specically, given government payo functions, BAs can be strong stumbling blocs if the worldpayo is maximized under global free trade. The main text considers rm prots as the government payofunction but Appendix D shows the main results are robust to using national welfare instead.14Indeed, Proposition 1 closely resembles the equilibrium characterization described by Mukunoki and

Tachi (2006).

5

Union (CU) would not. Thus, they do not focus on the destructive impact that preference

erosion can have on BA formation which is the focus of this paper. Moreover, since their

focus is the relative merits of BAs versus CUs, they do not consider MFN agreements

and thus they do not consider the question of this paper: the strong building blocstrong

stumbling bloc question. Additionally, they do not endogenize the order of negotiations or

consider country asymmetries which are important features of this paper.

In a related strand of the literature, Krueger (1999) describes how the MFN principle

emerged in the 1800s and early 1900s as a mechanism to protect the value of preexisting

trade concessions. Indeed, Schwartz and Sykes (1997) argue this is the main benet of the

MFN principle. This may appear to contrast with the result that, despite the presence of

the MFN principle, preference erosion allows a destructive role for BAs as strong stumbling

blocs. However, this result merely emphasizes a key point of Bagwell and Staiger (2005):

while the MFN principle can help protect preexistingMFN concessions, it cannot, in general,

protect preexisting discriminatory concessions (i.e those won via PTAs).

In summary, this paper develops a dynamic farsighted network model that endogenously

determines the order in which countries negotiate. The dynamic and farsighted behavior of

countries imply that, unlike earlier work, BAs can be strong stumbling blocs, thus preventing

global free trade, even if the world payo is maximized under global free trade. Moreover,

asymmetry and an endogenous order of negotiations lead to rich equilibrium dynamics that

have observable implications for PTA negotiations. Indeed, these implications are consistent

with actual PTA negotiations.

The model predicts a relationship between the order that negotiations commence and

the order they conclude: the smaller insider begins negotiations with the outsider before the

larger insider but, in equilibrium, this induces the larger insider to become the hub. Recent

BA negotiations between the US, Canada and Colombia as well as the US, Canada and Korea

and, to a lesser extent, the US, Australia and Korea support this sequence of events.15 While

sequential negotiations like these are the most common type of equilibrium that leads to

global free trade, the model does predict that NAFTA style negotiations, where a single

BA expands into a three country PTA, can occur. The model also suggests that preference

erosion underlies why BAs do not form. While the reason behind BA nonformation is

inherently unobservable, spokespoke BAs do not suer from the fear of preference erosion

that insideroutsider BAs suer. Indeed, the observable implication that spokespoke BAs

should have a higher probability of formation than insideroutsider BAs receives empirical

support from Chen and Joshi (2010).16

While the theoretical literature abstracts away from the ambiguities inherent in GATT

Article XXIV, these ambiguities are generally seen as problematic. The ambiguities lie in the

15The exact timing of these events is discussed in Section 5.3.16Specically, they nd that the conditional probability of a spokespoke BA exceeds that of an insider

outsider BA by a factor of four.

6

reality that GATT Article XXIV only requires PTA members remove taris on substantially

all trade and allows removal to be phased out over time. However, the model suggests these

ambiguities may actually promote achievement of global free trade. Taking advantage of

these ambiguities increases hub benets. Indeed, they may rise suciently that the fear of

preference erosion no longer prevents the insider from becoming the hub. In this sense, the

ambiguities are productive in promoting global free trade.

The rest of the paper proceeds as follows. Section 2 develops the network terminol-

ogy and equilibrium concepts. Section 3 presents the underlying trade model. Section 4

begins by analyzing the equilibrium when symmetric countries choose between BAs and

MFN agreements. It then compares the resulting equilibrium with that when only MFN

agreements exist, which underlies the strong building blocstrong stumbling bloc question.

Sections 5 and 6 perform similar exercises under asymmetric market size, rst assuming

all countries fear preference erosion and then relaxing this assumption. Finally, Section 7

concludes. Appendix B collects proofs not given in the text.

2 Network formation games and equilibrium

2.1 Overview

Following Saggi and Yildiz (2010, 2011), this paper considers two threeplayer games: a

multilateralism game where only MFN agreements exist and a bilateralism game where

countries choose between MFN agreements and BAs. However, unlike Saggi and Yildiz

(2010, 2011), each game is a farsighted dynamic innite horizon game where at most one

agreement can form per period. Figure 1 depicts the possible networks where the countries

are generically labeled i, j and k. An edge between two countries represents a BA. The free

trade network can arise because of the three country MFN agreement or three individual

BAs. Three features of the model warrant explicit discussion.

First, the assumption of one agreement per period is not crucial to the strong building

blocstrong stumbling bloc results. Because a direct move to global free trade is always

an option, the assumption only rules out a direct move from the empty network to a hub

spoke network. BAs can be strong stumbling blocs when the insiders prefer to remain

insiders rather than become the hub on the path to free trade. But then, by construction,

they prefer a permanent move to the insideroutsider network rather than jumping to the

hubspoke network from the empty network. Conversely, when BAs are strong building

blocs, global free trade arises because the spokes benet from forming their own BA. But,

this does not depend on how the hubspoke network emerged. Despite the nonessential

nature of the assumption, it increases analytical tractability of the model. Indeed, dening

a period as the time required to complete a PTA is not inconsistent with history in that

PTA formation takes a number of years (see footnote 7).

7

Figure 1: Network positions

Second, BAs formed in previous periods are assumed binding. Nevertheless, naturally,

when checking whether an agreement formed in the current period is an equilibrium, de-

viations that involve severing this agreement are considered. Imagining networks as nodes

of a game tree, binding agreements mean players cannot move backwards in the game tree.

Together with an assumption of Markov behavior, this implies the status quo remains for-

ever once global free trade is reached or no BA forms in a given period.17 Since there are

only three possible BAs, the network remains unchanged after, at most, three periods. This

property preserves analytical tractability.

Ornelas (2008) explains that the implicit or explicit assumption of binding PTAs is

very common in the literature (see, for example, Bagwell and Staiger (1997), Bond and

Syropoulos (1996), Maggi and Rodriguez-Clare (1998), Bond et al. (2001), Mitra (2002),

Mukunoki and Tachi (2006), Ornelas (2007) and Ornelas (2008)) and consistent with history.

Indeed, Ornelas and Liu (2012) note that the the only PTA violating the assumption is

the 2005 Venezuelan withdrawal from the Andean Pact. McLaren (2002) provides strong

theoretic justication for the assumption. In his model, initial expenditure on sunk costs

ensure a PTA remains in place even though, absent sunk cost expenditures, countries would

prefer an MFN agreement. The sunk costs justication also has empirical support (e.g.

Roberts and Tybout (1997), Eichengreen and Irwin (1998) and Freund and McLaren (1999)).

Additionally, Baldwin (2008) explains that the costs of severing BAs far exceed lost exports

because taris are merely one element of a large and varied set of retaliation instruments.18

Third, backward induction can be used to solve the equilibrium. To begin, consider each

hubspoke network and solve for the Equilibrium Binding Agreement (EBA; explained in

Section 2.2.3), given global free trade remains forever once attained. Then, consider each

insideroutsider network and solve for the EBA given how the network evolves from any

hubspoke network. Finally, consider the empty network and solve for the EBA given how

the network evolves from any insideroutsider network. The sequence of networks on the

17Suppose no link forms in the current period. Markov behavior then rules out the possibility that aplayer would form a link in the following period given refusal to form this link in the current period.18Retaliation instruments include the whole host of non tari trade barriers as well as development aid,

military aid and political support in various international political issues. A breakdown in internationalcooperation could imply costs via less progress in issues such as climate change, human rights, moneylaundering or illegal drugs.

8

equilibrium path is the farsighted dynamic network equilibrium (FDNE). Thus, an FDNE

is intuitively similar to a subgame perfect equilibrium. However, it requires an Equilibrium

Binding Agreement, rather than a Nash equilibrium, in every subgame.

2.2 Network formation games

2.2.1 Networks and payos

The set of players is N = s,m, l; the small, medium and large countries. Generically, they

are denoted i, j and k. The game is an innite horizon game where a network link represents

a trade agreement. Agreements formed in previous periods cannot be severed and, at most,

one agreement can form per period. Thus, denoting the trade agreement formed in period

t by `t, the network in existence at the end of period t is gt = (`1, `2, ..., `t).

Given a network g, the one period payo to player i is πi (g). Given a path of networks

(gt0 , gt0+1, ...) from period t0 onwards, player i's continuation payo is∑∞t=t0

βt−t0πi (gt).

For any coalition S ⊆ N , (gt0 , gt0+1, ...) S(g′t0 , g

′t0+1, ...

)denotes that the coalition S

prefers the former path over the latter. When the context makes clear the network path

following from gt0and g′t0 then gt0 S g′t0 and (gt0 , gt0+1, ...) S(g′t0 , g

′t0+1, ...

)are used

interchangeably.

2.2.2 Actions, strategies and equilibrium

Given a network g, Ai (g) and ai (g) ∈ Ai (g) denote, respectively, the action space and an

action for player i. Similarly, AS (g) =∏i∈S Ai (g) and aS (g) ∈ AS (g) denote the action

space and an action for a coalition S ⊆ N . Ai (g) is the set of announcements i can make

given the network at the beginning of the period is g. When i does not have BAs with j

and k in the bilateralism game, i can make the following announcements: i) it wants to

form no agreement, denoted φ, ii) it wants to move to free trade, denoted FT , or iii) the

country name (j or k) with whom it wants to form a BA but has not yet done so. Table

1 summarizes the action space for each player and network type where Ø and FT denote,

respectively, the empty and free trade networks. A proposed agreement forms when all

members of the proposed agreement announce in favor.

In the multilateralism game, only MFN consistent agreements are allowed meaning any

tari concessions must be given to all countries. This requirement rules out BAs. In this

paper, subject to members WTO commitment of not raising taris, the two country jointly

optimal MFN tari is the initial common tari.19 Thus, only the three country MFN

agreement is considered. Moreover, since the three country joint optimal tari is zero, this

agreement is equivalent to a direct move to free trade.20 Hence, the only possible networks

19Saggi and Yildiz (2010) allow two country MFN agreements. There, the jointly optimal tari diersfrom the initial tari.20See footnote 31

9

NetworkPlayer action space

Ai (g) Aj (g) Ak (g)

Ø φ, j, k, FT φ, i, k, FT φ, i, j, FT(ij) φ, k, FT φ, k, FT φ, i, j, FT

(ij, ik) Empty φ, k φ, jFT Empty Empty Empty

Table 1: Action space for the bilateralism game

in the multilateralism game are the empty network, with Ai (Ø) = φ, FT for each countryi, and the free trade network.

Given the action space for each network, a Markov strategy for player i is a function σi

that assigns an action ai (g) for every network g. Since a strategy prole σ = (σi, σj , σk)

induces a unique network path (gt0 , gt0+1, ...) from any initial network gt0 , σ induces the

continuation payo for player i of∑∞t=t0

βt−t0πi (gt). A farsighted dynamic network equi-

librium (FDNE) is simply dened as the equilibrium path of networks that emerges by

using backward induction to solve for a strategy prole σ such that the action prole

a (g) = (ai (g) , aj (g) , ak (g)) is an EBA for every network g or, equivalently, is an EBA

in every subgame.21 22

2.2.3 Equilibrium Binding Agreements

Ray and Vohra (1997) introduced the equilibrium concept of an Equilibrium Binding Agree-

ment (EBA). This paper uses a slight variation introduced by Diamantoudi (2003) and

discusses this variation below.

An EBA is similar to a coalition proof Nash equilibrium (CPNE), recently used by Saggi

and Yildiz (2010, 2011) and Saggi et al. (2011). Each concept begins by only considering

Pareto optimal action proles and restricts attention to protable deviations that are self

enforcing. A deviation is self enforcing if the deviation results in an action prole that is

itself an equilibrium. Thus, both concepts require coalition deviations be robust to subse-

quent deviation by coalition members. Hence, both concepts are, to some extent, farsighted.

However, the key dierence is that deviating players in a CPNE assume other players ac-

tions remain xed following their deviation while deviating players in an EBA assume other

players actions adjust in response to their own deviation.

Central to an EBA is the idea of a coalition structure. A coalition structure, denoted P ,

21An FDNE can be seen as an extension of the Dutta et al. (2005) dynamic network formation model.Unlike here, the Dutta et al. (2005) notion of an equilibrium process of network formation (EPNF) assumesthe pair of players who negotiate in any given period, the active pair, is exogenous. However, unlikean FDNE, an EPNF allows each player in the active pair to sever any of its agreements. Nevertheless,unfortunately from the perspective of BAs, an EPNF does not allow players other than the active pair tosever existing agreements.22Indeed, Bernheim et al. (1987) not only introduce coalition proof Nash equilibrium (CPNE) to the game

theoretic literature they also introduce perfectly CPNE which solves for a CPNE in each subgame.

10

is a partition on the set of players N . Each element of the coalition structure is a coalition.

For the three player game where N = i, j, k, the set of coalition structures consist of i)

the grand coalition N , ii) the set of singleton coalitions, denoted P ∗, and iii) each coalition

structure i, j , k that has a two player coalition and a singleton coalition, denoted by

PS where S is one coalition and N \ S is the other coalition.23 Loosely, a Pareto optimal

action prole is an EBA if there is no self enforcing deviation by any coalition S ⊂ N . A

deviation by S from aS to a′S is self enforcing if there exists a′−S such that(a′S , a

′−S)is an

EBA for the induced coalition structure PS and each coalition member prefers any such

EBA to a. Since the notion of EBA appears in its denition, the formal denition of an

EBA (and CPNE) proceeds recursively.

The recursion begins by dening an EBA for the singletons coalition structure P ∗. This

allows computation of EBAs for coalition structures of the form PS which in turn allows

computation of EBAs for the coalition structure N which, if nonempty, is the set of EBAs

for the game itself.24 Before outlining the recursion, let β (P, g) denote the set of Nash

equilibrium, given network g, where each coalition in the coalition structure P is treated as

an individual player.25 Given a network g, the recursion proceeds as follows:

1. Dene B (P ∗, g) = β (P ∗, g) as the EBAs for P ∗.

2. a (g) ∈ β (Pij , g) is an EBA for Pij , denoted a (g) ∈ B (Pij , g), if there is no self

enforcing deviation for i or j. A deviation by i from ai (g) to a′i (g) is self enforcing if

there exists a′−i (g) such that i) a′ (g) =(a′i (g) , a′−i (g)

)∈ B (P ∗, g) and ii) i prefers

any such a′ (g) to a (g).

3. a ∈ β (N, g) is an EBA for N , denoted a (g) ∈ B (N, g), if there is no self enforcing

deviation by any coalition S ⊂ N . A deviation by S from aS (g) to a′S (g) is self

enforcing if there exists a′−S (g) such that i) a′ (g) =(a′S (g) , a′−S (g)

)∈ B (PS , g) or,

if S = i and B (PS , g) is empty, a′ (g) ∈ B (P ∗, g), and ii) every player i ∈ S prefers

any such a′ (g) to a (g).26

The set of EBAs, given network g, is then dened as the set of EBAs for the coarsest

coalition structure such that an EBA exists. So the set of EBAs is: i) B (N, g) if nonempty,

ii) if B (N, g) empty, the sets B (Pij , g) and iii) if B (Pij , g) empty for all ij, the set of Nash

equilibrium B (P ∗, g).

Saggi and Yildiz (2010) note that while deviations by players are changes in action

proles, it proves far more convenient to refer to these deviations as changes in the network

23Pij = i, j , k and Pk = i, j , k are the same coalition structure.24The recursion procedure for CPNE works similarly.25β (P ∗, g) is the usual set of Nash equilibrium (i.e. each player is treated as an individual player) while

β (N, g) is the set of Pareto optimal action proles for the set of players N .26aS (g) = a′S (g) is permitted to allow S to break away from the coalition N . Similarly, ai (g) = a′i (g)

allows i to break away from ij in step 2.

11

structure. This paper follows the same approach. For example, given ai (Ø) = j and

aj (Ø) = i, the unilateral deviation by player i to ai (ij) = φ yields Ø rather than (ij).

As such, this is referred to as i deviating from (ij) to the empty network. To this end,

let G (P, g) denote the networks induced by the EBAs B (P, g) and let γ (P, g) denote the

networks induced by β (P, g). A network induced by a Nash equilibrium is referred to as

a Nash equilibrium network. Also, an EBA of the game, most commonly g′ ∈ G (N, g), is

referred to as an EBA network.

EBAs possess at least two advantages relative to CPNE. The rst advantage is technical.

While nonexistence is a well known problem for CPNE, Nash equilibrium existence ensures

EBA existence. For example, a situation arising in this paper causing CPNE nonexistence

is the classic Condorcet paradox. The second advantage is substantive: unlike a CPNE,

deviating players in an EBA assume other players react to their deviation. To illustrate rel-

evance, take a preexisting USCanada BA and consider whether a subsequent USColombia

BA occurs in equilibrium. If the US prefers the status quo, then a USColombia BA is not

a CPNE because the US has a protable unilateral deviation. Notice, this US deviation

does not consider potential formation of a CanadaColombia BA. However, in an EBA, the

US takes this possibility into account meaning fear of a CanadaColombia BA can induce

a USColombia BA.

A potential problem emerges when deviating players consider other players reactions:

what if a Pareto dominant reaction does not exist for the other players? In the recursion

notice that, when combined with the deviating players action prole, there could be many

action proles of the non deviating players that constitute an EBA of the induced coalition

structure. The recursion specied above requires that the deviating coalition prefer every

such EBA a′ to the action prole a under consideration.27 This is the key dierence between

Ray and Vohra (1997) and Diamantoudi (2003). Diamantoudi (2003) requires the deviating

coalition prefer every such EBA a′ to a while Ray and Vohra (1997) only require it prefer

some a′ to a. Essentially, Ray and Vohra (1997) allow the deviating coalition to choose the

resulting EBA.

This section concludes with a useful lemma: Pareto dominant networks that can be

sustained by coalitions are EBA networks.

Lemma 1. Suppose the network at the beginning of period t is g. If g′ = g+ ij or g′ = g is

Pareto dominant for i and j then g′ is an EBA network in period t. If Pareto dominance

is strict, then g′ is unique.

Proof. The only protable deviation from g′ is the unilateral deviation by k. However,

g′ ∈ G (Pij , g) because g′ is Pareto dominant for i and j and the only outcomes consistent

27Notice the deviating players S do not assume the non deviating players N \ S take actions that hurt Sat the expense of N \ S. This is captured by requiring a′ is an EBA of the induced coalition structure PSwhich in turn requires that the action prole of each coalition in PS is Pareto optimal for the given coalition.

12

with i) ai = j and aj = i and ii) ai = aj = φ are, respectively, g′ = g + ij and g′ = g.

Thus, k has no self enforcing unilateral deviation to any g ∈ G (Pij , g) and so g′ ∈ G (N, g).

Moreover, if Pareto dominance is strict, the deviation by i and j from any g 6= g′ to

g′ ∈ G (Pij , g) is self enforcing and thus g′ = G (N, g).

3 Underlying trade model

The underlying trade model is a three country oligopolistic intra industry trade model.

Krishna (1998), Ornelas (2005b, 2008), Goyal and Joshi (2006), Mukunoki and Tachi (2006)

and Saggi and Yildiz (2011) use slight variations of this. While Saggi and Yildiz (2011)

model marginal cost asymmetry, this paper models market size asymmetry. As shown later,

emergence of an insideroutsider network as the unique FDNE under market size asymmetry

implies the largest countries are insiders. In contrast, for Saggi and Yildiz (2011), the lower

cost countries are insiders. However, Chen and Joshi (2010) present empirical evidence that

when PTAs form sequentially, high cost countries and countries with a large market size are

insiders. Moreover, as discussed in Section 5.3, market size asymmetry yields interpretations

consistent with recent real world negotiations. It is also worth noting that Saggi and Yildiz

(2010) use the competing exporters model of Bagwell and Staiger (1999). However, the fear

of preference erosion cannot play the crucial dynamic role in a competing exporters model

that it plays in this paper. For preference erosion to play an important dynamic role, free

trade must leave a country worse o than as an insider. But, Saggi and Yildiz (2010) show

this cannot happen in the competing exporters model.

The economic structure of the model is simple. A single rm from each country produces

an oligopolistic good, Q, under a common and constant marginal cost which, without loss

of generality, is assumed to be zero.28 These rms compete under oligopolistic competition

in segmented international markets. Single period payos are realized at the end of each

period through CournotNash competition. This paper takes a political economy approach,

so government incentives for trade agreement formation depend only on rm prots. While

extreme, the assumption sharpens the intuition behind preference erosion and signicantly

increases analytical tractability of the model. Moreover, as discussed at the end of this

section, it is not essential.

The inverse demand function in country j is P j = αj −Qj where Qj =∑k∈N q

jk is the

total quantity produced in country j and αj captures market size asymmetry. A common

non prohibitive tari, τ ji (g) = τ ≤ τ , is implemented by country j on country i if ij /∈ gwhere g represents the set of trade agreements in existence.29 Otherwise τ ji (g) = 0. The

28With a constant but nonzero marginal cost c > 0, the linear demand curve given below can be rewrittenwith the intercept α = α− c. The resulting model would be equivalent.29τ being non prohibitive means that, in any network g, each rm makes non negative prots by exporting

to any other country when τ ≤ τ . Given the optimal quantity formula qj∗i (g) (derived below), the lower

13

common non prohibitive tari and segmented markets ensure each rm participates in each

market. However, without the non prohibitive tari assumption, the optimal unilateral

tari is the prohibitive tari because the governments objective function is rm prots.

This paper focuses on the dynamics of trade agreement formation, so the model presented

in the text abstracts from optimal taris.30

Given g, the rm from country i maximizes prots by solving the following problem in

each country j:max

qjiqji

[αj −Qj − τ ji (g)

].

Equilibrium quantity and prot for this rm are qj∗i (g) = 14

[αj +

(3− pj (g)

)τ − 4τ ji (g)

]and πji (g) =

(qj∗i (g)

)2

, where pj is the number of countries that have a BA with country

j, including country j itself, in network g. The payo for the country j rm is then πi (g) =∑j∈N π

ji (g).31

The net benet of BA formation and the associated negative third party externalities

drive the model's static incentives. A BA between countries i and j eliminates discrimination

faced by i in j. Thus, i's prots in j rise by 3τ16

(8qj∗i (g) + 3τ

). This is the benet of

preferential access for country i which, given∂qj∗i (g)

∂αj > 0, increases with the market size of

country j. However, the preferential access given by country i to country j lowers the prots

of countries i and k in market i by τ16

(8qi∗ι (g)− τ

)for ι = i, k. For country i, this diversion

of prots, or trade diversion, is the cost of preferential access incurred when entering a BA

with country j. For country k, this represents preference erosion if it already has a BA with

country i. In any case, the cost increases with the market size of country i since∂qi∗ι (g)∂αi > 0.

These static incentives directly imply that, as recorded in Lemma 2, a country prefers to

form a BA a larger partner.

Lemma 2. The one period change in prots for country i when forming a BA with country

j is increasing in αj − αi.

More generally, country i's net benet from a BA with country j is ∆πji (g) = 3τ16

(8qj∗i (g) + 3τ

)−

bound on qj∗i (g) occurs when j and k have a BA. In this case qj∗i (g) = 14

[aj − 3τ

]and, thus, τ = αs

3.

Note, τ ∈[τ , α

s

2

]ensures non negative prots in the empty network so τ ≤ τ implies rms make positive

prots in each market in the empty network. I thank the editor for bringing the importance of this subtletyto my attention.30Appendix D numerically explores the case of optimal taris and shows there exists regions of the

parameter space where the main results still hold.31Network dependent one period payos are derived in Appendix A. Moreover, given qj∗i (g),

it is simple to verify that the three country joint optimal tari is zero. In the empty net-

work, πi (Ø) = 116

[∑j∈N

(αj)2

+ 4τ(αi − αj − αk

)+ 12τ2

]. Thus, world prots are πW (Ø, τ) =

116

[3∑j∈N

(αj)2

+ 4τ∑j∈N αj + 36τ2

]. Further,

∂πW (Ø,τ)∂τ

><

0 when τ ><τ =

∑j∈N αj

18meaning

πW (Ø, τ) is minimized at τ . Since πW (Ø, 0) ≥ πW (Ø, τ) reduces to∑j∈N αj ≥ 3αs which is true

by denition, then πW (Ø, 0) ≥ πW (Ø, τ) for any τ ≤ τ .

14

τ16

(8qi∗i (g)− τ

). This reduces to ∆πji (g) ∝ 8qj∗i (g) + τ +

(αj − αi

)+ τ

(pi (g)− pj (g)

).

Importantly, ∆πji (g) is increasing in pi (g) − pj (g). A higher pi (g) reduces the rents, and

thus the cost of preferential access, in i's market while a lower pj (g) increases the rents, and

thus the benets of preferential access, in market j. This yields the following implication,

the rst part of which is known, for example, from Lemma 2 of Mukunoki and Tachi (2006).

Lemma 3. For any network g, a BA between two symmetric countries is mutually protable

and, regardless of asymmetry, a BA is always protable for the smaller country.

Proof. When αi = αj , the lower bound of ∆πji (g) occurs for pj (g) = 2 and pi (g) = 1. This

lower bound is ∆πji (g) ∝ 8qj∗i (g) > 0. Application of Lemma 2 now yields ∆πji (g) > 0

when αj > αi.

As mentioned above, the non prohibitive tari assumption and the restrictive government

objective function are not essential to the results. To expand, let πn,ji denotes country i's

payo given occupation of network position n with country j, where dependence on the

parameters of the model, θ ≡(αs, αm, αl, τ

), is suppressed. Figure 1 shows each network

position and its notation. What is essential to the main results is that i) πHl > πI,ml , ii)

πI,ml > πFTl , iii) πFTl><π

K,sl depends on θ, iv) πI,ml > πNl , and v) πFTl

><π

Nl depends on

θ. As shown later, i) and ii) generate the fear of preference erosion while iii) allows for

existence or nonexistence of preference erosion. iv) allows an insideroutsider FDNE while

v) ensures global free trade may or may not emerge in the absence of BAs. Importantly,

as discussed in Appendix D, these payo rankings exist even if the government cares about

national welfare and sets optimal taris.

4 Symmetric market size

4.1 Bilateralism game

The symmetric case helps build the basic intuition guiding BA formation: the insiders'

fear of preference erosion. Symmetry is also a useful starting point because, from a static

perspective, Lemma 3 implies any BA is mutually protable. In terms of preference erosion,

Lemma 3 yields two implications. First, πHi > πI,ji because, as the hub, an insider earns

additional rents via preferential access to the outsider's market. However, second, the insider

recognizes the spokes will subsequently form their own BA since πFTj > πK,kj . Indeed, free

trade not only erodes the value of preferential access enjoyed by the hub in each spoke

market, but this preference erosion is suciently large that πI,ji > πFTi .32 Thus, an insider

may prefer to remain an insider because of preference erosion.

32In general, as shown in Appendix A, πI,ji −πFTi ∝ αi+αj −2αk + 3τ . This is positive under symmetry

and always positive when l and m are insiders.

15

Formally, an insider, say country i, prefers to become the hub rather than remain an

insider with j when πHi + β1−βπ

FTi ≥ 1

1−βπI,ji . This yields the Free TradeInsider (FTI)

condition:

β ≤ βFT−Ii,j (θ) ≡ πHi − πI,ji

πHi − πFTi=−αi + 3αk − 2τ

αj + αk + τ, (1)

which reduces to βFT−I (τ) under symmetry. (1) is intuitive because sucient impatience

places relatively low (high) weight on preference erosion (additional hub rents). As insiders,

Lemma 4 shows that the FTI condition, and insiders' underlying fear of preference erosion,

drive the EBA network.

Lemma 4. Assume countries are symmetric and consider an insideroutsider network (ij).

The EBA networks are: i) (ij) when β > βFT−I (τ), and ii) the hubspoke networks (ij, ik)

and (ij, jk) when β ≤ βFT−I (τ).

When the FTI condition is violated, β ≥ βFT−I (τ), both insiders prefer remaining

insiders over becoming the hub on a path to free trade. By Lemma 1, this mutual fear of

preference erosion allows the insiders to remain insiders. However, when the FTI condition

is satised, the fear of preference erosion is suciently small that each insider wants to

become the hub. Multiplicity arises because the outsider is indierent as to its BA partner.

A direct move to free trade is not an EBA network because the insiders can jointly deviate

and remain insiders. This deviation is self enforcing because the fear of becoming a spoke

prevents an insider from a subsequent attempt to become the hub.

Given the intuition behind preference erosion and the FTI condition, Proposition 1

is intuitive and formally characterizes the FDNE. Note, the critical value β (τ) is dened

such that β > β (τ) implies a country prefers a direct move to free trade over being an

insiderturnedspoke on the path to free trade.

Proposition 1. Assume countries are symmetric. The FDNE are: i) any insideroutsider

network (ij) when β > βFT−I (τ), ii) a direct move to free trade when β ∈(β (τ) , βFT−I (τ)

]and iii) any path of BAs that lead to free trade when β ≤ β (τ).

Proposition 1 is depicted in Figure 2. Henceforth, to simplify notational clutter, (ij, ik, jk)

is used to represent not only the network itself but also the network path obtained by i and

j forming the BA in period one, i and k in period two and j and k in period three.33 The

context should avoid confusion. Violation of the FTI condition implies the mutual fear of

preference erosion is suciently large that remaining insiders is Pareto dominant for any

pair of insiders. However, using Lemma 1, any insideroutsider network can emerge because

of symmetry with ΩI−O denoting this set in Figure 2.

33Similarly, (ij, ik) can represent the network path where i and j form a link in period one followed by iand k in period two and no further links in subsequent periods. Finally, (ij) can represent the network pathwhere the only link formed is i and j in period one.

16

When the FTI condition holds, the fear of preference erosion is suciently small that

any insider wants to be the hub on the path to free trade. Due to symmetry, suppose

that, without loss of generality, each insider is the hub on a path to free trade.34 Lemma 3

and the trade diversion suered by nonmembers imply a country prefers to be an insider

turnedhub rather than an insiderturnedspoke rather than an outsiderturnedspoke.

However, this creates a Condorcet paradox situation across the insideroutsider networks:

from any such network, the insiderturnedspoke and outsiderturnedspoke can jointly

deviate and become insiders with the former being the hub. Moreover, this joint deviation is

self enforcing because the fear of becoming an outsider deters the new insiderturnedspoke

from subsequently deviating and attempting to become the hub. Thus, no insideroutsider

network is an EBA network for the grand coalition N in the rst period; (ij) /∈ G (N,Ø) for

any (ij). Additionally, Ø /∈ G (N,Ø) since a country prefers being an insiderturnedspoke

or an insiderturnedhub over the empty network and so any i and j have a self enforcing

deviation to (ij). However, it is useful to note that these self enforcing deviations imply any

insideroutsider network, but not the empty network, is an EBA network for the coalition

structure Pij , i.e. (ij) ∈ G (Pij ,Ø).

Given no insideroutsider network nor the empty network is an EBA network for the

grand coalition, a direct move to free trade is the unique EBA network, G (N,Ø) = FT ,

and unique FDNE if there is no self enforcing deviation from FT . Otherwise, ΩI−O are

EBA networks and any path of BAs that lead to free trade is an FDNE (this set is denoted

ΩFT in Figure 2). In any self enforcing joint deviation from FT , the insiderturnedspoke is

the critical player. On one hand, the outsiderturnedspoke will not jointly deviate because

Lemma 3 implies πFTi > πKi > πOi . On the other hand, the insiderturnedhub will jointly

deviate because of the insider and hub rents. Because a spoke faces discrimination in the

other spoke market, the insiderturnedspoke deviates jointly with the insiderturnedhub

when there is sucient weight on the insider rents, β ≤ β (τ). Moreover, β ≤ β (τ) not

only implies there is a self enforcing deviation from FT but also that FT is not Pareto

optimal for any pair of insiders meaning FT /∈ G (Pij ,Ø). Hence, the FDNE are ΩFT when

β ≤ β (τ).35 In contrast, FT is the unique FDNE when β ∈(β (τ) , βFT−I (τ)

].

Figure 2: FDNE symmetry

The FDNE characterized by Proposition 1 closely resembles the equilibrium described

by Mukunoki and Tachi (2006). However, there are two important dierences. First, (ij) is

34Note, free trade can emerge from any one of the three insideroutsider networks.35Indeed, τ & .216αs implies β (τ) > βFT−I (τ) meaning that β ≤ βFT−I (τ) implies β ≤ β (τ). In this

case,(β (τ) , βFT−I (τ)

]is empty and a direct move to free trade is never an FDNE.

17

Attainment of global free trade

Multilateralism game Bilateralism game

Strong Building Blocs (SBB) No YesStrong Stumbling Blocs (SSB) Yes NoWeak Building Blocs (WBB) Yes YesWeak Stumbling Blocs (WSB) No No

Table 2: Classifying the role of BAs

the unique FDNE here when β > βFT−I (τ) while ΩFT are also FDNE for Mukunoki and

Tachi (2006). The dierence arises because, unlike a Markov Perfect Equilibrium used by

Mukunoki and Tachi (2006), an FDNE has a coalitional aspect built in via solving for an

EBA in every subgame. This ensures insiders can coordinate and not form a BA with the

outsider if this coordination raises the continuation payo of each insider. Second, Mukunoki

and Tachi (2006) do not allow MFN agreements meaning a direct move to free trade, FT ,

cannot be an equilibrium. Indeed, this highlights their focus on the relative merits of BAs

and CUs rather than the strong building blocstrong stumbling bloc issue, which is now

tackled in the following subsection.

4.2 Role of BAs as strong building blocs and strong stumbling blocs

To isolate the equilibrium eect of BAs in a world where countries choose between BAs

and MFN agreements, this section follows Saggi and Yildiz (2010, 2011) by comparing the

equilibrium outcomes of two games: the bilateralism game where countries choose between

MFN agreements and BAs, and the multilateralism game where only MFN agreements exist.

Table 2 classies the role of BAs.

Carrying out this comparison requires characterization of the equilibrium in the multi-

lateralism game. Remember, the only possible agreement is a three country MFN agreement

that takes the world to free trade. Thus, since any country has veto power, characterization

of the FDNE, even under asymmetric market size, is simple. For s and m, the preferential

access to l's market outweighs the cost of lost domestic preferential access and ensures they

do not block free trade. However, as the largest export market, l incurs the largest cost of

preferential access via lost domestic prots while it gains the smallest benet of preferential

access via prots gained in its smaller partner markets. Indeed, Proposition 2 shows that

l vetoes global free trade when it is too large relative to the other smaller countries. To

this end, αls = αl/αs and αms = αm/αs denote the market sizes of the large and medium

countries relative to the small country and, abusing notation, τ now denotes the original

tari normalized by αs.

Proposition 2. In the multilateralism game, a direct move to global free trade is the unique

FDNE i l does not block this agreement. l blocks this agreement i αms < αMFNls (θ) ≡

18

αls − 1 + 3τ . Otherwise, the empty network is the unique FDNE.

An immediate implication of Proposition 2 is that global free trade is the unique FDNE of

the multilateralism game under symmetry.

With an understanding of the FDNE under the bilateralism and multilateralism games,

Corollary 1 follows directly from Propositions 1 and 2 and summarizes the role of BAs under

symmetry.

Corollary 1. Under symmetry, BAs are strong stumbling blocs when β > βFT−I (τ) but

weak building blocs when β ≤ βFT−I (τ).

Interestingly, in contrast to the strong stumbling bloc role of BAs in Corollary 1, Saggi and

Yildiz (2010, 2011) nd that, under symmetry, global free trade is attained in the bilater-

alism and multilateralism games; that is, regardless of whether BAs exist. The destructive

role of BAs here occurs when β > βFT−I (τ) because this implies insiders' mutual fear

of preference erosion dominate the temporary hub rents. However, like Saggi and Yildiz

(2010, 2011), global free trade is attained in the bilateralism and multilateralism games

when β ≤ βFT−I (τ) and the temporary hub rents dominate. In this case, BAs are weak

building blocs.

5 Asymmetric market size: all countries fear preference

erosion

5.1 Bilateralism game

This section introduces a moderate amount of market size asymmetry by assuming αls >

αms > 1. The degree of asymmetry is restricted so that all countries still fear preference

erosion. Since this fear rests on formation of spokespoke BAs, Condition 1 states the

conditions that ensure spokes form their own BAs.

Condition 1. Assume, i) πFTi ≥ πK,ji for any i, j and ii) πK,sl ≥ πOl . These conditions

reduce to αls ≤ 3− 5τ , αms ≤ 3− 5τ and αls ≤ 3αms − 6τ .

Part ii) of Condition 1 implies that, myopically, l prefers to form a BA with m and become

a spoke rather than remain an outsider. This ensures that, in equilibrium, global free trade

can be attained conditional on s and m being insiders.36

Unlike the symmetric case, the FTI condition now depends on the insiders' identity.

Indeed, this dependence implies that attainment of global free trade can depend on which

36Condition 1 also implies that all BAs are mutually protable except, potentially, BAs between s and l(m) when l (m) is the outsider.

19

countries are insiders and, thus, shows how arbitrary assumptions about the order of nego-

tiations can substantively aect equilibrium predictions. Using (1), two observations imply

that market size asymmetry drives a wedge between βFT−Ij,i (θ) and βFT−Ii,j (θ). First, be-

cause of the same degree of preferential access among member countries, πI,ij = πI,ji and

πFTi = πFTj . However, second, πHj > πHi when αj < αi because, through protecting a

larger market and larger rents, becoming the hub is more costly for a larger country. Thus,

βFT−Ij,i (θ) > βFT−Ii,j (θ) because the larger hub rents allow the smaller insider to place a

larger weight on preference erosion. That is, the smaller insider has a greater incentive to

become the hub. Lemma 5 now extends Lemma 4 to the case of asymmetry.

Lemma 5. Assume Condition 1 holds and consider an insideroutsider network (ij) where

αi > αj. The EBA networks are: i) (ij) when β > βFT−Ij,i (θ), ii) (ij, ik) and (ij, FT ) when

β < 1 < βFT−Ii,j (θ) or β ∈(βFT−Ii,j (θ) , βFT−Ij,i (θ)

], and iii) (ij, ik) when β ≤ βFT−Ii,j (θ) ≤ 1.

Like the symmetric case, the insiders remain insiders when the FTI condition of both

insiders is violated, β > βFT−Ij,i (θ), while free trade is attained when the FTI condition

of both insiders is satised, β ≤ βFT−Ii,j (θ). Thus, the role of preference erosion embodied

in the FTI condition remains central to the analysis. However, two new features emerge

under asymmetry. First, there is an intermediate range, β ∈(βFT−Ii,j (θ) , βFT−Ij,i (θ)

], where

only the FTI condition of the smaller insider j is satised. Second, a direct move to free

trade, (ij, FT ), emerges as an EBA network.

Consider this intermediate range β ∈(βFT−Ii,j (θ) , βFT−Ij,i (θ)

]. In particular, consider

the EBA network that emerges from the insideroutsider network (ij) noting that free

trade emerges from any hubspoke network. Interestingly, despite protable deviations

from (ij, ik), no self enforcing deviation exists meaning (ij, ik) is an EBA network. Even

though i prefers to remain an insider, implying (ij, ik) is not a Nash equilibrium network, i

anticipates that backing out of the BA with k does not lead to (ij) but actually induces a

BA between j and k and, thus, (ij, jk). This fear deters i's deviation.37 Additionally, while

the insiderturnedspoke j also prefers remaining an insider, given πI,ij > πFTj > πK,kj , the

joint deviation by i and j to (ij) is not self enforcing. Since (ij, ik) is not a Nash equilibrium

network, j can then unilaterally deviate from aj = φ to aj = k expecting (ij, jk) will result.

Finally, by Condition 1, j and k also prefer (ij, FT ) over (ij, ik). However, their joint

deviation to aj = ak = FT is not self enforcing because (ij, FT ) is not a Nash equilibrium

network between S = jk and i, (ij, FT ) /∈ γ (Pjk, (ij)), since i can protably deviate

to (ij) by responding with ai 6= FT . Thus, (ij, ik) is an EBA network. In addition to

(ij, ik), (ij, FT ) is also an EBA network because, again, the unilateral deviation by i or

joint deviation by i and j to (ij) is not self enforcing.

Once β < βFT−Ii,j (θ) < 1, the key implication is that i now prefers to become the hub

37This logic is the most important example of the dierence between an EBA and a CPNE. In a CPNE,i does not consider that j and k will form a BA if i backs out of the BA with k.

20

rather than remain an insider. As a result, (ij, ik) is a Nash equilibrium network because the

joint deviation by i and j from (ij, FT ) to (ij) is now self enforcing since the fear of becoming

a spoke deters j from deviating further. Thus, (ij, FT ) is no longer an EBA network. Absent

(ij, FT ), (ij, ik) is Pareto dominant for i and k and is now the unique EBA network. The

importance of βFT−Ii,j (θ) < 1 is that this condition holds i πI,ji > πFTi and πI,ij > πFTj .

Hence, βFT−Ii,j (θ) ≥ 1 has two implications. First, the joint deviation by j and k from (ij, ik)

to (ij, FT ) is self enforcing because i's best response to aj = ak = FT is now ai = FT .

Second, the joint deviation from (ij, FT ) to (ij) is no longer protable. Nevertheless, as

shown in the proof, i has a self enforcing unilateral deviation, given πHi > πFTi , from (ij, FT )

to (ij, ik). Thus, (ij, ik) nor (ij, FT ) are EBA networks for the grand coalition. Indeed,

G (N,Ø) is empty. But, the presence of self enforcing deviations by j and k to (ij, FT )

and by i to (ij, ik) imply these networks are EBA networks for, respectively, the coalition

structures Pjk and Pij and so they are EBA networks.

Multiple equilibria complicate matters for two reasons. First, for any given θ, many

combinations of paths could arise from the three insideroutsider networks. To streamline

the analysis when free trade is attained in equilibrium, Proposition 3 below focuses on two

cases. Players have either bilateral beliefs or multilateral beliefs meaning they believe

that, respectively, (ij, ik) or (ij, FT ) emerges from any (ij). Thus, bilateral beliefs occur for

β ≤ βFT−Im,l (θ). However, if (ij, FT ) emerges from any (ij) then, letting αi > αj , Lemma

5 implies either β ∈(βFT−Ii,j (θ) , βFT−Ij,i (θ)

]or βFT−Ii,j (θ) > 1 for any i, j ∈ N . Given

the value of preferential access protected is larger for larger insiders then βFT−Im,l (θ) <

βFT−Is,l (θ) < βFT−Is,m (θ). Thus, multilateral beliefs require βFT−Im,s (θ) > 1 and either i)

β ∈(βFT−Il,s (θ) , βFT−Im,l (θ)

]or ii) β ∈

(βFT−Il,m (θ) , βFT−Im,l (θ)

]and βFT−Il,s (θ) > 1.

The second complication due to multiple equilibria is that the FTI condition depends

on insider identities. Nevertheless, the primacy of m's FTI condition with l underlies the

FDNE. The reason is simple: m and l protect the largest insider rents, so if they prefer to

remain insiders rather than become the hub then they prefer remaining insiders over any

path on which they are an insider with s. Before presenting Proposition 3, an assumption

and a condition that simplify presentation of the results are introduced.38

Assumption 1. (ml, sm, sl) m (FT, FT, FT ) and (sl,ml, sm) l (Ø,Ø,Ø) whenever

β ≤ βFT−Im,l (θ).

Condition 2. Either i) FT s (sl) or ii) FT s (sm) and FT l Ø.

Proposition 3 now formally characterizes the FDNE when all countries fear preference ero-

sion. To this end, let ΩFT denote the set of BA paths leading to free trade on which the

larger insider is the hub.

38Under Condition 1, the assumption is violated only in a very small range of the parameter space. Whenτ and αms are very low, the rst (second) part of the assumption is violated when αls is very low (high).The FDNE that result when the assumption is violated are considered in Proposition 5.

21

Proposition 3. Assume Condition 1 and Assumption 1 hold. The unique FDNE is (ml)

when β > βFT−Im,l (θ). Now suppose β ≤ βFT−Im,l (θ). Under bilateral beliefs, the FDNE are

i) if β ≤ βm (θ), then (ml, sl, sm), and ii) if β > βm (θ), then ΩFT and, unless Condition 2

fails, FT . Under multilateral beliefs, the unique FDNE is (ml, FT ).

Figure 3 illustrates the FDNE. When m and l prefer to remain insiders because of a

mutual fear of preference erosion, Lemma 1 implies this is the unique FDNE. However, once

m's fear of preference erosion is suciently small that it prefers to become the hub, global

free trade is attained. Moreover, given βFT−Im,l (θ) < βFT−Is,l (θ) < βFT−Is,m (θ), global free

trade emerges from any insideroutsider network via a path of BAs once β < βFT−Im,l (θ).

m faces an important tradeo when comparing (ml, sl, sm) and (sm,ml, sl). While the

value of preferential access as an insider with l exceeds that as an insider with s, m must be

an insider with s to become the hub. The former eect outweighs the latter when β < βm (θ)

and (ml, sl, sm) is the unique FDNE.

Figure 3: FDNE asymmetry but all countries fear preference erosion

Multiple equilibria again arise under asymmetry, specically for β ∈(βm (θ) , βFT−Im,l (θ)

].

While Figure 3 depicts βm (θ) < βFT−Im,l (θ) for illustrative purposes, βm (θ) > βFT−Im,l (θ)

often holds meaning that (ml, sl, sm) can be the unique FDNE under bilateral beliefs.

Nevertheless, multiplicity again stems from the same Condorcet paradox situation across

the three insideroutsider networks: there is always a pair of countries who benet from

the self enforcing deviation to install themselves as insiders. Also, given Assumption 1,

m and l have a self enforcing deviation from both the empty network and FT because i)

(ml, sl, sm) ml FT and ii)m fears being an outsider if it attempts to deviate to (sm,ml, sl).

Thus, like Proposition 1, there is no EBA network for the grand coalition (i.e. G (N,Ø)

is empty), but the self enforcing deviations to the various insideroutsider networks imply

ΩI−O are EBA networks and, thus, ΩFT are FDNE.

Additionally, FT is an FDNE if FT ∈ G (PS ,Ø) for some S = ij. While FT /∈ G (Pml,Ø)

because (ml, sl, sm) ml FT , parts i) and ii) of Condition 2 ensure, respectively, FT ∈G (Psl,Ø) and FT ∈ G (Psm,Ø). Part i) (part ii)) ensures FT is a Nash equilibrium network

between S = sl (S = sm) and m (l) while the fear of being an outsiderturnedspoke deters

the deviation by l (m).

22

Unlike bilateral beliefs, Lemma 1 yields a unique FDNE under multilateral beliefs. Be-

cause free trade is attained directly from any insideroutsider network, insiders cannot enjoy

hub rents. Hence, becoming insiders is Pareto dominant for m and l. The cases of bilateral

and multilateral beliefs have interesting real world analogs that are discussed in Section 5.3.

Given a formal characterization of the FDNE, Proposition 4 characterizes how the FDNE

depends on asymmetry and follows from inspection of βFT−Im,l (θ).

Proposition 4. Suppose Condition 1 and Assumption 1 hold. Then,∂βFT−Im,l (θ)

∂αls< 0 and

∂βFT−Im,l (θ)

∂αms< 0. That is, greater asymmetry increases the extent to which m and l remain

insiders and reduces the extent to which global free trade is attained.

Without loss of generality, Figure 4 illustrates Proposition 4. Here, τ = 14 and αms and

αls are the relative market sizes. The αms curves show how βFT−Im,l (θ) depends on αls for

a given αms. The curve labeled αms = αms (θ) represents the constraint that ensures part

ii) of Condition 1: αms > αms (θ) ≡ max

1, 13αls + 2τ

. For any αms ∈ [1, αls), an αms

contour curve lies between the αms = αms (θ) and αms = αls curves. The contour curves

are downward sloping because∂βFT−Im,l (θ)

∂αls< 0. Lower contour curves are associated with

higher values of αms because∂βFT−Im,l (θ)

∂αms< 0. Thus, greater asymmetry through a higher αls

or αms reduce the range of β for which m's FTI condition with l holds. Intuitively, greater

asymmetry has two eects. First, it makes preference erosion more costly by increasing the

value of preferential access that m and l protect as insiders. Second, it reduces the value

of temporary hub rents in the outsider's market. These eects strengthen the incentive to

remain insiders and reduce the extent that BAs lead to free trade.

This section showed that the fear of preference erosion drives the extent to which BAs

lead to free trade and that greater asymmetry strengthens this fear. The following section

reconsiders the strong building blocstrong stumbling bloc issue by allowing market size

asymmetry. Section 5.3 then discusses how recent real world negotiations are consistent

with the model's predictions.

5.2 Role of BAs as strong building blocs and strong stumbling blocs

This section analyzes the role of BAs when all countries fear preference erosion. Corollary

2 summarizes, following directly from Propositions 2 and 3.

Corollary 2. Suppose Condition 1 holds. BAs are strong stumbling blocs when the market

sizes of l and m are suciently similar but suciently larger than s (i.e. two larger

and one smaller country). BAs are strong building blocs when the market sizes of l and

m are suciently dierent but those of m and s are suciently similar (i.e. one larger

and two smaller countries). The former (latter) corresponds to αms≥

(<) αMFNls (θ) and

β >(≤) β

FT−Im,l (θ).

23

Figure 4: Eect of asymmetry on extent that BAs lead to global free trade when all countriesfear preference erosion

Figure 5 illustrates Corollary 2 for τ = 14 . To begin, consider the multilateralism game.

Using Proposition 2, l does not block the three country MFN agreement in the band between

the αms = αls and αms = αMFNls (θ) lines. Thus, FT is the unique FDNE. Outside this band,

l blocks the three country MFN agreement and the empty network is the unique FDNE.

Thus, free trade is attained (not attained) when there are two (one) larger countries and

one (two) smaller country.

Now consider the bilateralism game. The downward sloping bold lines are contour curves

along which βFT−Im,l (θ) is constant. By Proposition 3, global free trade is attained i β ≤βFT−Im,l (θ). The move from A to A′ and B to B′ depicts how greater asymmetry aects

these contour curves: βFT−Im,l (θ) falls from .47 to .4. The logic from Proposition 4 and

Figure 4 explain this eect. Greater asymmetry increases the rents protected by m and l as

insiders which increases the value of preferential access and makes preference erosion more

costly. Compounded by the reduced hub benets, becoming the hub requires insiders place

additional weight on the higher hub prots compared to the lower free trade prots. This

translates into increased impatience as captured by the lower value of βFT−Im,l (θ) meaning

greater asymmetry undermines global free trade. Thus, free trade is attained (not attained)

in the bilateralism game when there are two (one) smaller countries and one (two) larger

country. Together with the previous paragraph, this captures Corollary 2.

More generally, the change in the FTI condition at these dierent degrees of asymmetry

has important implications for the role of BAs as strong building blocs and strong stumbling

blocs. At A′, BAs are now strong stumbling blocs for β > βFT−Im,l (θ) = .4 rather than

β > βFT−Im,l (θ) = .47 at A. Thus, when global free trade is attained in the multilateralism

24

Figure 5: Eect of asymmetry on role of BAs as SSBs and SBBs when all countries fearpreference erosion

game, greater asymmetry increases the extent to which BAs are strong stumbling blocs

and, thus, the extent to which BAs prevent global free trade. Additionally, the move from

A to A′ also means BAs are now only weak building blocs for β ≤ βFT−Im,l (θ) = .4 rather

than β ≤ βFT−Im,l (θ) = .47. Similarly, at B′, BAs are now strong building blocs only for

β ≤ βFT−Im,l (θ) = .4 rather than β ≤ βFT−Im,l (θ) = .47 at B. Thus, when global free trade is

not attained in the multilateralism game, greater asymmetry decreases the extent to which

BAs are strong building blocs and, thus, the extent to which BAs are necessary for global

free trade. Additionally, the move from B to B′ also means BAs are now weak stumbling

blocs for β > βFT−Im,l (θ) = .4 rather than β > βFT−Im,l (θ) = .47. Thus, regardless of whether

global free trade is attained in the multilateralism game, greater asymmetry enhances the

destructive role of BAs.

Figure 5 provides a dierent interpretation of the βFT−Im,l (θ) contour curves. The ap-

proach thus far xes the level of asymmetry, which xes βFT−Im,l (θ), and then determines the

range of the discount factor such that β>< βFT−Im,l (θ). However, the opposite approach is also

possible and depicted in Figure 6; that is, x the discount factor, say β, and determine the

range of asymmetry such that β>< βFT−Im,l (θ). From this perspective, assume β = .47. Points

A and B in Figure 5 lie on the contour curve in Figure 6 such that β = .47 = βFT−Im,l (θ).

Since increasing the level of asymmetry to A′ or B′ implies β = .47 > βFT−Im,l (θ) = .4,

then, in Figure 6, global free trade is not attainable in the bilateralism game above the

β = .47 contour curve. Thus, in Figure 6, BAs are strong stumbling blocs above the β = .47

contour curve in the band that would contain A′. Conversely, Figure 6 shows BAs are weak

stumbling blocs in the region that would contain B′. Figure 6 also extends this analysis to

25

Figure 6: Bilateralism versus multilateralism FDNE. Bilateral beliefs and all countries fearpreference erosion.

classify the role of BAs in all areas of the parameter space when all countries fear preference

erosion and have bilateral beliefs.39

5.3 Application to real world negotiations

Recent real world negotiations involving the US are consistent with equilibrium predictions

of the model and the eects of greater asymmetry. Under multilateral beliefs, (ml, FT ) is

the unique FDNE which represents a BA between the two largest countries followed by a

direct move to a three country PTA. Conversely, (ml, sl, sm) also leads to an eective three

country PTA under bilateral beliefs, but via a sequence of BAs where the largest countries

form the rst BA followed by the larger insider becoming the hub. The former is consistent

with NAFTA: the 1987 USCanada BA expanded into NAFTA in 1994 with the inclusion

of Mexico who, in the model, would be the small country. The latter is consistent with

recent negotiations between, for example, the US, Canada and Colombia. Again, the US

and Canada were the largest countries and insiders since 1987. The US, the largest country,

then became the hub via the 2006 USColombia BA before the 2008 CanadaColombia BA.

Interestingly, the three country NAFTA style agreement only occurs in a small section of

the parameter space relative to the USCanadaColombia style path of BAs. This matches

the observation that BAs are by far the most pervasive form of PTAs.40

In terms of how asymmetry aects the equilibrium, Figure 4 provides an interpretation

39ΩFT denotes the paths to free trade in Proposition 3.40BAs account for 90% of all free trade agreements and 80% of all PTAs (Free Trade Agreements and

Customs Unions) notied to the WTO under GATT Article XXIV.

26

of the relationship between the order that negotiations commence and the order that agree-

ments conclude: while the outsider begins negotiations with the smaller insider before the

larger insider, the larger insider concludes the rst BA with the outsider. To illustrate,

consider USCanadaColombia negotiations. As discussed, Canada and the US have been

insiders since 1987 with the US the largest insider. Pre 2002, Colombia was the outsider.

This is consistent with the model when β > βFT−Im,l (θ), for example at point A with β = .35

and βFT−Im,l (θ) = .3, because the unique FDNE is that the largest countries remain insid-

ers. Intuitively, the model suggests US and Canadian fears of preference erosion could have

driven the absence of BAs with Colombia. Indeed, since the US is Canada's largest export

market, the fear of preference erosion in terms of a USColombia spokespoke BA could

have plausibly been a concern for Canada.

It is also plausible that the Colombian market became more attractive relative to the

larger insider markets in the 1990s and early 2000s due to economic liberalization. A lower

αms and αls captures this in the model; for example, moving from A to B in Figure 4. With

βFT−Im,l (θ) > β at B, Canada now views the temporary hub benets of sole preferential access

to the Colombian market as more than compensating for subsequent preference erosion. An

interpretation is that Canada begins negotiations with Colombia, which actually happened

in 2002. Assuming β > βFT−Il,m (θ), the US has no incentive to initiate negotiations with

Colombia before Canada does so. Nevertheless, given bilateral beliefs and a pre existing

USCanada BA, the unique FDNE is that the US becomes the hub because, otherwise, it

fears a CanadaColombia BA. Indeed, this is consistent with history. Following Canada

Colombia negotiations in 2002, the US initiated discussions with Colombia in 2004 which

led to the 2006 USColombia BA prior to the 2008 CanadaColombia BA.

Similar interpretations apply to US, Canada, Australia and Korea negotiations. Canada

Korea exploratory talks began in 2004 and formal negotiations in 2005 before the 2006

USKorea negotiations. Korea, an Asian tiger, rapidly became more attractive relative to

the larger insider markets through 1990-2005. Thus, the previous interpretation of Figure 4

applies again and matches history; the USKorea BA was concluded in 2007 while Canada

is yet to conclude their agreement with Korea. Similarly, the 2005 USAustralia BA makes

the US and Australia insiders and Australia-Korea negotiations began in early 2009. Once

again, the interpretation of Figure 4 is consistent with history. While the USKorea BA

was concluded in 2007, it lay dormant in the US Congress until the Obama administration

began renegotiations in mid 2010 which then passed through Congress in 2011. In contrast,

Australia has yet to conclude their agreement with Korea.

27

6 Asymmetric market size: not all countries fear prefer-

ence erosion

6.1 Bilateralism game

The fear of preference erosion underlying the FTI conditions in Section 4 assumes the

spokes form their own BA. This assumption is now relaxed.

Condition 3. Suppose Condition 1 holds except that πK,sl > πFTl . Thus, αls ∈ (3− 5τ, 3− 2τ ]

where αls ≤ 3− 2τ ensures πHl ≥ πI,ml .

The key implication of Condition 3 is that, since l won't form a spokespoke BA with

s, m no longer fears preference erosion: m knows it can remain the hub forever.41 Thus,

unlike Section 4, m exercises no restraint in becoming the hub. Hence, conditional on s and

m being insiders, Condition 3 implies m and l form a BA but no further BAs after (sm,ml).

However, conditional on m and l being insiders, l faces a stark tradeo: let m become the

hub and remain a spoke forever or become the hub knowing free trade will follow. l prefers

to become the hub when πHl + β1−βπ

FTl ≥ 1

1−βπK,sl . This reduces to the Free TradeSpoke

(FTK) condition:

β ≤ βFT−K (θ) ≡πHl − π

K,sl

πHl − πFTl=−αls + 4 + αms − 4τ

αms + 1 + τ.

Like the FTI condition, the FTK condition captures that l must be suciently impatient

for the hub benet to dominate.

When m and l had a mutual fear of preference erosion, l preferred to be an insider with

m rather than s because larger insiders protect larger rents. However, now l may prefer to be

an insider with s rather than m when β > βFT−Is,l (θ). While l forgoes the temporary higher

rents associated with m as its fellow insider, the mutual fear of preference erosion allows s

and l to remain insiders unlike when m and l are insiders. Nevertheless, once β ≤ βFT−Is,l (θ)

and s wants to become the hub, l always prefers to be an insider with m because of the

larger insider rents. Thus, for β ≤ βmin (θ) ≡ minβFT−K (θ) , βFT−Is,l (θ)

, l becomes the

hub on the path to free trade if it is an insider with s or m.

Together with βmin (θ), two further critical values help characterize the FDNE. Like

before, m prefers to be an insider with l rather than s when β ≤ βm (θ). However, as

discussed, the equilibrium path conditional on s and m being insiders is now (sm,ml)

rather than (sm,ml, sl). Moreover, because s is stuck as a spoke if it becomes an insider

with m while (ml, sl, sm) yields free trade, (ml, sl, sm) s (sm,ml) when s is suciently

41While Assumption 1 ensured that m preferred (ml, sl, sm) over FT under Condition 1, this always holdsunder Condition 3.

28

patient, i.e. β > βs (θ). Letting Ω = (ml, sl, sm) , (sl,ml, sm) , (sm,ml), the following

proposition characterizes when BAs lead to free trade.

Proposition 5. Suppose Condition 3 holds and β ≤ βmin (θ). For β ≤ βm (θ), (ml, sl, sm)

is the unique FDNE. For β ∈(βm (θ) , βs (θ)

], the following are FDNE: i) if (sl) l Ø, then

Ω and, unless Condition 2 fails, FT but ii) if Ø l (sl), then (sl,ml, sm) and, unless there

is a self enforcing deviation, FT . For β ∈(βs (θ) , βmin (θ)

], the following are FDNE: i) if

(sl) l Ø, then (ml, sl, sm) but ii) if Ø l (sl), then Ω \ (sm,ml) and, unless there is a self

enforcing deviation, FT .

Proposition 5 yields similar results to Proposition 3. Most importantly, global free

trade is attained when the discount factor is suciently small, β ≤ βmin (θ). When β ∈(βm (θ) , βs (θ)

]and (sl) l Ø, multiple equilibria arise because of the same Condorcet

paradox across across the various paths induced by the dierent insideroutsider networks

with Condition 2 again determining whether FT is an FDNE.42 Once β ≤ βm (θ), m and

l ensure (ml, sl, sm) is the unique FDNE because m no longer wants to deviate with s to

(sm,ml). In contrast, (ml, sl, sm) is an FDNE when β ∈(βs (θ) , βmin (θ)

]because s no

longer wants to deviate with m to (sm,ml).

A noticeable dierence compared to Proposition 3 is that (sl,ml, sm) can be the unique

FDNE. When β ∈(βm (θ) , βs (θ)

]and Ø l (sl), then (sl) is not a Nash equilibrium

network in period 1. This alters the Condorcet paradox logic. Earlier, the deviation by

m and l from (sl,ml, sm) to (ml, sl, sm) was self enforcing because m's fear of becoming

an outsiderturnedspoke in (sl,ml, sm) prevented m's subsequent attempted deviation to

become an insiderturnedhub with s. However, m no longer holds this fear once (sl) is not

a Nash equilibrium network. Thus, G (N,Ø) = (sl) and (sl) is the unique EBA network in

period 1. Similar logic implies (sl,ml, sm) can also be an FDNE in addition to (ml, sl, sm)

for β ∈(βs (θ) , βmin (θ)

].

FT can also be an FDNE when Ø l (sl). However, Condition 2 does not determine

whether FT is an FDNE. Unlike Proposition 3 when FT is an FDNE, an EBA exists here

for the grand coalition since G (N,Ø) = (sl). Thus, FT is an FDNE unless there is a self

enforcing deviation from FT by some coalition S ⊂ N . If s prefers (sl,ml, sm) over FT ,

the deviation by s and l to (sl,ml, sm) is self enforcing because l's fear of becoming an

outsiderturnedspoke in (sm,ml) prevents it from deviating further.

That m no longer fears preference erosion dramatically increases the extent that BAs

lead to free trade. Letting θ ≡ (αms, αls = 3− 5τ , τ) for some αms ≤ 3 − 5τ and τ ≤ τ ,

Proposition 6 formalizes this result.

Proposition 6. βmin(θ)> βFT−Im,l

(θ)for any θ = (αms, αls, τ) satisfying Condition 3.

42To be clear, (sl) l Ø means that (sl,ml, sm) l Ø given β ≤ βmin (θ) implies (sl,ml, sm) is theequilibrium network path conditional on (sl).

29

Figure 7: Non monotonic aect of asymmetry on extent that BAs lead to global free trade

That is, at the threshold level of asymmetry αls = 3− 5τ , the extent that BAs lead to global

free trade jumps. Additionally, ∂βmin(θ)∂αls

< 0 and ∂βmin(θ)∂αms

> 0.

Underlying Proposition 6 is that the FTK condition, rather than the FTI condition,

governs the dynamic incentives facing m and l as insiders. The mutual fear of preference

erosion under the FTI condition allowed m and l to exercise mutual restraint in becoming

the hub. However, now m exercises no restraint in becoming the hub. Thus, in turn, l

exercises far less restraint. Figure 7 illustrates the basic result where τ = 14 . The threshold

level of asymmetry αls = 3 − 5τ = 1.75 is such that m no longer fears preference erosion

because l and s don't form a BA as spokes. For αls > αls, the αms contour curves depict

the critical value βmin (θ) below which global free trade is attainable. Like before, the

αms = αms (θ) curve represents part ii) of Condition 1. Notice that, for any αls ≥ αls, all ofthe new contour curves lie above all of the old contour curves at αls = αls. This emphasizes

the dramatic increase in the extent that BAs lead to global free trade.

Conditional on αls > αls, Figure 7 clearly illustrates the eect of asymmetry. A higher

αls is a movement down an αms contour curve for two reasons: i) the value s places on

insider rents with l rises, and ii) the cost of preferential access incurred by l when becoming

the hub rises. Respectively, these lower s and l's incentive to become the hub which reduces

βFT−Is,l (θ) and βFT−K (θ). Thus, since∂βFT−Im,l (θ)

∂αls< 0, a higher αls decreases the extent to

which BAs lead to global free trade regardless of αls>< αls. However, a higher αms increases

the rents s and l obtain as the hub by making preferential access with m more valuable.

The greater incentive for s and l to become the hub increases βFT−Is,l (θ) and βFT−K (θ).

Given∂βFT−Im,l (θ)

∂αms< 0 then, unlike when αls ≤ αls, a higher αms shifts the αms contour

30

curve upwards and increases the extent to which BAs lead to global free trade. This raises

an interesting dierence. Earlier, global free trade required l's willingness to give up sole

preferential access with m as an insider and become the hub. But, this now requires a

willingness to have sole preferential access with m by becoming the hub.

Propositions 5 and 6 focus on the situation where BAs lead to free trade, and do not

characterize the equilibrium when β > βmin (θ). While a formal characterization of the

FDNE here is rather tedious, the key incentives can be discussed with the aid of Figure 8.

Appendix C gives a formal characterization. In Figure 8, βl (θ) and βs (θ) are threshold

levels of patience for l and s respectively. Specically, l prefers the network path resulting

from (sl) rather than (ml) when β ≥ βl (θ) while (sm,ml) s Ø when β > βs (θ).

The basic issue for β > βmin (θ) is that l may prefer to be an insider with s rather than

m. When β > βFT−Is,l (θ), l may forgo the insider rents withm, and potentially the hub rents,

to permanently protect insider rents with s. This actually happens for β > βl (θ). However,

when β > βl (θ), l may prefer the empty network over being an insider with s. If so, and if s

cannot credibly threaten to form a BA withm, i.e. β > βs (θ), then the empty network is the

unique FDNE. Otherwise, the unique FDNE is (sl). Once β ≤ βl (θ), m and l are insiders

in an FDNE and the set of FDNE depends on βFT−K (θ). For β > βFT−K (θ), the hub

rents do not suciently compensate l for being the hub and l is happy remaining a spoke so

(ml, sm) is the unique FDNE. Conversely, for β ≤ βFT−K (θ), l becomes the hub meaning

(ml, sl, sm) is an FDNE and, in general, the logic from the case of β ∈(βs (θ) , βmin (θ)

]applies for β ∈

(βmin (θ) ,min

βl (θ) , βFT−K (θ)

].

Figure 8: FDNE m no longer fears preference erosion

6.2 Role of BAs as strong building blocs and strong stumbling blocs

Once m no longer fears preference erosion, the extent to which BAs are strong building

(stumbling) blocs jumps (drops) dramatically. Corollary 3 follows directly from Propositions

2, 3 and 6.

Corollary 3. At the threshold level of asymmetry αls = 3 − 5τ , there is a once o jump

(or drop) in the extent to which BAs are strong building (stumbling) blocs.

Figure 9 extends Figure 5 to illustrate Corollary 3. At the threshold level of asymmetry

αls associated with the smallest permissible αms, point C, BAs become strong building

31

Figure 9: Non monotonic eect of asymmetry on role of BAs as SSBs and SSBs

blocs for β ≤ .57 rather than only β ≤ .47. Notice the more dramatic eect for higher

αms. At point C ′ where βFT−Im,l (θ) = .4, BAs are now strong building blocs for β ≤ .75

rather than β ≤ .4. This can be explained as follows. When all countries fear preference

erosion,∂βFT−Im,l (θ)

∂αms< 0: a higher αms increasesm and l's fear of preference erosion as insiders

reducing the scope for global free trade. However, once m no longer fears preference erosion,∂βmin(θ)∂αms

> 0: a higher αms increases l's incentive to temporarily maintain sole preferential

access with m by becoming the hub.

Figure 10 extends Figure 6, emphasizing the increased constructive role of BAs as strong

building blocs. Note, ∂βmin(θ)∂αms

> 0 implies that, for αls > αls = 1.75, global free trade is

attainable in the bilateralism game above the β contour curve. That is, starting from

β = .75 = βmin (θ), a higher αms increases βmin (θ) so that β = .75 < βmin (θ). Thus,

despite the higher discount factor of β = .75 (relative to β = .47 at C) which reduces the

weight placed on hub rents and thus on l's incentive to become the hub, the strong building

bloc role of BAs increases dramatically. Intuitively, once m no longer fears preference

erosion, it exercises no restraint in becoming the hub and l exercises far less restraint in

turn.

7 Conclusion

Saggi and Yildiz (2010, 2011) develop static equilibrium models of trade agreement forma-

tion. They compare the equilibrium where only MFN agreements exist with the equilibrium

where PTAs are also available, thus capturing the equilibrium eect of PTAs on the at-

32

Figure 10: Non monotonic eect of asymmetry on bilateralism and multilateralism FDNE

tainment of global free trade. This paper performs the same comparison, but using a novel

dynamic network theoretic model where countries are farsighted and asymmetric in terms

of market size. The novelty lies in the presence of a new equilibrium concept, a farsighted

dynamic network equilibrium (FDNE), that uses a coalitional simultaneous move game to

endogenously determine which pair of countries form an agreement in any given period.

This is important for two reasons. First, the model shows that market size asymmetry

endogenously determines the order of negotiations. Second, it is well known that the equi-

librium of sequential move games are often sensitive to ad hoc assumptions about the order

of negotiations. Within the dynamic framework constructed, a number of new insights

emerge.

First, the role of preference erosion is central to the equilibrium eect of BAs as strong

building blocs or strong stumbling blocs and its role is intimately linked with market size

asymmetry. Anticipating a spokespoke BA, sequential BA formation yields global free

trade only when insiders fear of preference erosion is suciently small. This occurs when

the insiders' joint market size is small enough. In contrast, when only MFN agreements

exist, the largest country blocks a direct move to global free trade when it is suciently

larger than the other countries. Thus, loosely speaking, BAs are strong building blocs and

necessary for global free trade when there are two smaller countries and one larger country

but they are strong stumbling blocs and prevent global free trade when there are two larger

countries and one smaller country. However, under large enough asymmetry, the largest

country refuses to form a spokespoke BA with the smallest country. Thus, the medium

country no longer fears preference erosion and exercises no restraint in becoming the hub. In

turn, the large country exercises far less restraint and there is a dramatic increase (decrease)

33

in the extent that BAs are necessary for (prevent) global free trade.

Second, unlike Saggi and Yildiz (2010), BAs can be strong stumbling blocs. This pos-

sibility arises because countries are farsighted in a dynamic framework. Despite sole pref-

erential access in each spoke market as the hub, an insider may opt against becoming the

hub recognizing a subsequent spokespoke BA erodes preferential access in each spoke mar-

ket. However, an insider does not consider this subsequent spokespoke BA when becoming

the hub in Saggi and Yildiz (2010) because of the absence of farsightedness in their static

framework.

Third, the model yields predictions consistent with real world events regarding both

BA formation and BA non formation. The model provides an interpretation of recent BA

negotiations between the US, Canada and Colombia and the US, Canada, Australia and

Korea. This interpretation relates the order that negotiations commence to the order that

BAs conclude. Because the commencement of negotiations between the outsider and the

smaller insider induce the larger insider insider to become the hub, the endogenous order

of negotiations drives the interpretation. Hence, this novelty is not merely of theoretical

importance. Moreover, consistent with reality, the model predicts that although NAFTA

style three country PTAs can emerge from the existence of a single BA, sequential formation

of BAs is far more likely enroute to an eective three country PTA. In terms of BA non

formation, the model explanation is preference erosion. An observable implication is that

the conditional probability of spokespoke BAs should exceed that of insideroutsider BAs

which receives empirical support from Chen and Joshi (2010).

Finally, the ambiguities inherent in GATT article XXIV may actually promote global

free trade because they mitigate the fear of preference erosion. By allowing insiders to omit

certain industries from the agreement and phase in tari removal over time, the ambiguities

may increase the immediate benet of the BA to the extent that the hub benets outweigh

the fear of preference erosion.

Appendix

A One period network dependent prots

Let α2 ≡(αl)2

+(αm)2+(αs)

2and let πn,ji denote i's prots given occupation of network po-

sition n with j (see Figure 1 for network notation). Then πI,ji = 116

[(αi + τ

)2+(αj + τ

)2+(αk − 2τ

)2]which reduces to 1

16

[α2 + 2τ

(αi + αj

)− 4ταk + 6τ2

]. Similarly, πHi = 1

16

[α2 + 2τ

(αj + αk

)+ 2τ2

],

πFTi = 116 α

2, πNi = 116

[α2 + 4ταi − 4τ

(αj + αk

)+ 12τ2

], πK,ji = 1

16

[α2+ 2ταi − 6ταj + 10τ2

],

πOi = 116

[α2 + 4ταi − 6τ

(αj + αk

)+ 22τ2

]. The common tari and non prohibitive tari

assumptions are analytically convenient because the dierence between any pair of one pe-

riod prots is then independent of α2. The dierence also has a common factor of τ so, for

34

example, πI,ji − πFTi ∝ αi + αj − 2αk + 3τ . This simple proportionality representation is

extremely useful because dierences in continuation payos across network paths reduce to

linear combinations of dierences in one period prots.

B Proofs

The following Lemmas will help establish lemmas and propositions given stated in the main

text.

Lemma 6. Let ˜ denote that FT is not in the action space and absence of ˜ denote FT

is in the action space. Then, for g 6= FT , i) g /∈ G (N,Ø) implies g /∈ G (N,Ø) and

ii) g ∈ G (N,Ø) implies g ∈ G (N,Ø) unless there is a self enforcing deviation to FT .

Moreover, for g 6= FT , iii) g ∈ γ (P ∗,Ø) i g ∈ γ (P ∗,Ø), and iv) g ∈ G (PS ,Ø) i

g ∈ G (PS ,Ø) for any S ⊂ N , S 6= i.

Proof. To begin, take g /∈ G (N,Ø) where g 6= FT . Then, any self enforcing deviation by

some S ⊂ N from g to some g′ ∈ G (P,Ø), P 6= N , remains self enforcing when FT is in

the action space because, even if FT ∈ G (P,Ø), the deviation is not consistent with FT

since FT requires ai = FT for all i ∈ N . Thus, g /∈ G (N,Ø). Now take g ∈ G (N,Ø). By

construction, there is no self enforcing deviation except, potentially, to FT . This establishes

part ii). Part iii) is trivial because FT requires ai = FT for all i ∈ N .

Finally consider part iv). Because FT requires ai = FT for all i ∈ N , S cannot achieve

FT themselves and thus, for g 6= FT , g ∈ γ (PS ,Ø) i g ∈ γ (PS ,Ø). Hence, consider

unilateral deviations. Take g /∈ G (PS ,Ø). To avoid triviality, suppose g ∈ γ (P ∗,Ø). By

construction, there is no g′ ∈ γ (P ∗,Ø) that deters i ∈ S from deviating to some ai 6= FT .

This implies g /∈ G (PS ,Ø) because i) FT ∈ γ (P ∗,Ø) requires ai = FT and ii) γ (P ∗,Ø) =

γ (P ∗,Ø) or γ (P ∗,Ø) = γ (P ∗,Ø) \ FT . Now take g ∈ G (PS ,Ø). To avoid triviality,

suppose g′ i g for some g′ ∈ γ (P ∗,Ø) and i ∈ S. Then, the deviation by i to a′i and g′ is

deterred by some g ∈ γ (P ∗,Ø). This still deters i because g ∈ γ (P ∗,Ø) ⊆ γ (P ∗,Ø). Thus,

g ∈ G (PS ,Ø).

Lemma 7. Assume FT is not in the action space. Assume, i) (ij) ij (ik) ik (jk) jk(ij), and ii) (ij) i (ik) i Ø for any i ∈ N . Then G (N,Ø) is empty. However, for any

i, j ∈ N , (ij) ∈ G (Pij ,Ø) but Ø /∈ G (Pij ,Ø).

Proof. To begin, note that γ (P ∗,Ø) = Ø, (jk) , (ij) , (ik). Moreover, (jk) ∈ G (Pjk,Ø)

because i) (jk) ∈ γ (Pjk,Ø), ii) (jk) is Pareto dominant for j, and iii) the deviation by k to

ak = i is not self enforcing because it is consistent with (ij) ∈ γ (P ∗,Ø) and (jk) k (ij).

Similar logic establishes (ik) ∈ G (Pik,Ø) and (ij) ∈ G (Pij ,Ø). Thus, the deviations by

S = jk from Ø and (ij) to (jk) ∈ G (Pjk,Ø) are self enforcing. Also, the deviations by

35

S = ik from (jk) to (ik) ∈ G (Pik,Ø) and by S = ij from (ik) to (ij) ∈ G (Pij ,Ø) are self

enforcing. Hence, G (N,Ø) is empty. Finally, Ø /∈ G (PS ,Ø) for any S = i, j ⊂ N because

(ij) S Ø implies Ø /∈ γ (PS ,Ø).

Lemma 8. Assume FT is not in the action space. Suppose the conditions of Lemma 7

are satised except that Ø i (ik). Then G (N,Ø) = (ik). This result does not depend on

(ij) i Ø.

Proof. Note that Ø i (ik) implies (ik) /∈ γ (P ∗,Ø). Moreover, γ (P ∗,Ø) = Ø, (jk) , (ij).Given the proof of Lemma 7, (jk) ∈ G (Pjk,Ø) and (ik) ∈ G (Pik,Ø) which implies Ø, (ij)

and (jk) are not in G (N,Ø).

However, Ø i (ik) implies (ik) ∈ G (N,Ø) and thus G (N,Ø) = (ik). In the proof of

Lemma 7, (ik) /∈ G (N,Ø) relied upon (ij) ∈ G (Pij ,Ø). But, noting Ø ∈ γ (P ∗,Ø) requires

aj 6= k, (ik) /∈ γ (P ∗,Ø) implies (ij) /∈ G (Pij ,Ø) because the deviation by j from aj = i to

aj = k, resulting in (jk) ∈ γ (P ∗,Ø), is now self enforcing. Apart from S = ij to (ij), the

only other protable deviations from (ik) are i) i or j to (ij), ii) j to (jk) and iii) i and/or

j to Ø. However, (jk) ∈ G (Pjk,Ø) and (ik) ∈ G (Pik,Ø) rule out i), ii) and the individual

deviations in iii). Additionally, Ø /∈ γ (Pij ,Ø) rules out the joint deviation in iii).

Finally, suppose Ø i (ij) in addition to Ø i (ik). While, in the proof of Lemma 7,

(jk) ∈ G (Pjk,Ø) relied upon (ij) ∈ γ (P ∗,Ø) making the deviation by k to ak = i not self

enforcing, Ø ∈ γ (P ∗,Ø) now plays the same role.

Lemma 9. Assume FT is not in the action space. Assume the conditions of Lemmas

7 and 8 are satised except that (ij) k (jk). Then, respectively, G (N,Ø) = (ij) and

G (N,Ø) = (ij) , (ik). These results do not depend on (ij) i Ø.

Proof. For Lemma 7, γ (P ∗,Ø) = Ø, (jk) , (ij) , (ik). For Lemma 8, γ (P ∗,Ø) = Ø, (jk) , (ij).Also, Ø i (ij) implies γ (P ∗,Ø) = Ø, (jk) since Ø i (ij) implies Ø i (ik). Finally,

note that Ø ∈ γ (P ∗,Ø) requires, among other things, aj 6= k and ak 6= j.

Three observations establish the proof. First, (ij) ∈ G (Pik,Ø). This follows because i)

(ij) ∈ γ (Pik,Ø) noting that (ij) j Ø, ii) the deviation by i to ai = φ is not self enforcing

because it is consistent with (jk) ∈ γ (P ∗,Ø) and (ij) i (jk), and iii) k's only protable

deviation is to ak = i and (ik) which is not self enforcing because, if (ik) ∈ γ (P ∗,Ø), it is

consistent with (ij) ∈ γ (P ∗,Ø). Second, (jk) ∈ G (Pjk,Ø) when Ø i (ik) or Ø i (ij).

This follows because i) (jk) ∈ γ (Pjk,Ø), ii) (jk) is Pareto dominant for j, and iii) the

deviation by k to ak 6= j is consistent with Ø ∈ γ (P ∗,Ø) but (jk) k Ø. Third, (ij) ∈G (Pij ,Ø) i (ik) k Ø. This follows because (ij) ∈ γ (Pij ,Ø) and the only potentially

protable deviations by i or j are i) i to ai = φ which, as established, is not self enforcing,

and ii) j to aj = k and (jk) which is self enforcing i Ø i (ik) since aj = k is consistent

with (ik) ∈ γ (P ∗,Ø) if (ik) i Ø but only consistent with (jk) ∈ γ (P ∗,Ø) if Ø i (ik).

36

The rst observation implies (jk) /∈ G (N,Ø) and, when (ij) i Ø, Ø /∈ G (N,Ø)

because the deviation by S = ik to ai = j and ak = φ results in (ij) ∈ G (Pik,Ø) which is

self enforcing. The second observation implies Ø /∈ G (N,Ø) when Ø i (ij) because the

deviation by S = jk to (jk) ∈ G (Pjk,Ø) is self enforcing.

The third observation implies (ik) /∈ G (N,Ø) if (ik) i Ø because the deviation by

S = ij to (ij) ∈ G (Pij ,Ø) is self enforcing. However, (ik) ∈ G (N,Ø) if Ø i (ik).

When Ø i (ik), the potentially protable deviations from (ik) are i) i to Ø which, as

established, is not self enforcing, ii) S = ij to (ij) which is not self enforcing because

(ij) /∈ G (Pij ,Ø), iii) i to (ij) which is not self enforcing because the self enforcing deviation

by j to (jk) ∈ γ (P ∗,Ø) implies (ij) /∈ G (Pjk,Ø), iv) j to (ij) or Ø which are not self

enforcing because, given (jk) ∈ γ (P ∗,Ø), they are consistent with (ik) ∈ G (Pik,Ø), and v)

j to (jk) which is not self enforcing because (ik) ik (jk) implies (jk) /∈ γ (Pik,Ø).

Finally, observe that (ij) ∈ G (N,Ø). The protable deviations are i) i to Ø, if Ø i (ij),

and j to (jk) which, as established, are not self enforcing, and ii) k to ak = i and (ik) which is

not self enforcing because, if G (Pij ,Ø) nonempty, (ij) ij (ik) implies (ik) /∈ γ (Pij ,Ø) and

if G (Pij ,Ø) empty then Ø i (ik) meaning (ik) /∈ γ (P ∗,Ø). To complete the proof, note

that part ii) of this paragraph was the rst time that Ø i (ij) aected the argument.

Lemma 10. Assume i) (ij) is Pareto dominant for j and (jk) j g for g ∈ (ik) ,Ø, ii)Ø i (ij) i g for g ∈ (ik) , (jk) , FT. and iii) (ik) k (jk) k Ø. Then (ij) = G (N,Ø).

Proof. Note that γ (P ∗,Ø) = Ø, (jk). Three observations establish the proof. First,

(jk) ∈ G (Pjk,Ø) because i) (jk) ∈ γ (Pjk,Ø) when ai 6= j and aj 6= i, and ii) (jk) jk gfor any g ∈ γ (P ∗,Ø), g 6= (jk). Thus, Ø /∈ G (N,Ø) because the deviation by j and k to

(jk) ∈ G (Pjk,Ø) is self enforcing. Second, (ij) ∈ G (Pij ,Ø) because i) (ij) ∈ γ (Pij ,Ø),

ii) (ij) is Pareto dominant for j and iii) i only prefers Ø but the deviation by i to ai = φ

is not self enforcing because it is consistent with (jk) ∈ γ (P ∗,Ø). Thus, (ik) /∈ G (N,Ø),

(FT ) /∈ G (N,Ø) and (jk) /∈ G (N,Ø) because the deviation by S = ij to (ij) is self

enforcing. Third, (ij) ∈ G (N,Ø). To see this note (ij) ∈ γ (Pij ,Ø) and (ij) is Pareto

dominant for j. Moreover, i only prefers Ø but i) the deviation to ai = φ is not self

enforcing, ii) k's deviation to ak = φ is consistent with (ij) ∈ G (Pij ,Ø) and iii) the joint

deviation by S = ik to Ø is not self enforcing because the subsequent deviation by k to

ak = j is only consistent with (jk) ∈ γ (P ∗,Ø). Hence, G (N,Ø) = (ij).

Attention now turns to proofs of lemmas and propositions stated in the main text.

Proof of Lemma 4

To begin, note that under symmetry43

πH > πI > πFT > πN > πK > πO. (2)

43Country subscripts and superscripts are omitted during the proof because of symmetry

37

Let β > βFT−I (θ). (2) implies (ij) is strictly Pareto dominant for i and j. Thus, by Lemma

1, (ij) = G (N, (ij)) .

Now let β ≤ βFT−I (θ). Note that γ (P ∗, (ij)) = (ij) , (ij, ik) , (ij, jk). The proof

follows from three observations. First, (ij, ik) ∈ G (Pik, (ij)) because (ij, ik) ∈ γ (Pik, (ij))

and, absent (ij, FT ), (ij, ik) ik g for any g ∈ γ (P ∗, (ij)). Thus, the self enforcing deviation

by S = ik to (ij, ik) ∈ G (Pik, (ij)) implies (ij) /∈ G (N, (ij)). Second, (ij) ∈ G (Pij , (ij)).

This follows because i) (ij) ∈ γ (Pij , (ij)), ii) the deviation by i to ai = k is not self

enforcing because it is consistent with (ij, jk) ∈ γ (P ∗, (ij)) and (ij) i (ij, jk), and iii)

similarly, the deviation by j to aj = k is not self enforcing. Thus, the self enforcing

deviation by S = ij from (ij, FT ) to (ij) ∈ G (Pij , (ij)) implies (ij, FT ) /∈ G (N, (ij)).

Third, (ij, FT ) /∈ G (PS , (ij)) for any S ⊂ N . This follows because (ij) ij (ij, FT ) implies

(ij, FT ) /∈ γ (Pij , (ij)) and, due to protable unilateral deviations by i and j respectively,

(ij, FT ) /∈ γ (Pjk, (ij)) and (ij, FT ) /∈ γ (Pik, (ij)). Thus, there is no protable unilateral

or joint deviation from (ij, ik) or (ij, jk) to FT . Moreover, j has no self enforcing deviation

from (ij, ik) to (ij) because aj = φ is consistent with (ij, ik) ∈ G (Pik, (ij)) (similarly for i

and (ij, jk)). Therefore, G (N, (ij)) = (ij, ik) , (ij, jk).Proof of Proposition 1

The proof proceeds by backward induction. First, consider g = (ij, ik). Using (2),

Lemma 1 implies (ij, ik, jk) = G (N, (ij, ik)). Second, consider g = (ij). Lemma 4 implies

G (N, (ij)) = (ij, ik) , (ij, jk) if β ≤ βFT−I (θ) and G (N, (ij)) = (ij) if β > βFT−I (θ).

Finally, consider g = Ø. First, suppose β > βFT−I (θ). (2) implies (ij) is Pareto

dominant for any i, j ∈ N . Thus, letting ΩI−O denote the set of insideroutsider networks,

Lemma 1 implies G (N,Ø) = ΩI−O. Additionally, the Pareto dominance implies (ij) ∈G (Pij ,Ø). Thus, the self enforcing deviation by S = ij from FT or Ø to (ij) ∈ G (Pij ,Ø)

implies FT /∈ G (N,Ø) and Ø /∈ G (N,Ø). Therefore, the set of FDNE is ΩI−O.

Second, suppose β ≤ βFT−I (θ). Thus, for any g ∈ ΩI−O, free trade emerges via a hub

spoke network. Suppose each country is the hub on one such path. Given (2), (ij, ik, jk) i(ij, jk, ik) i (jk, ij, ik) and (ij, jk, ik) i (Ø,Ø,Ø). Thus, Lemma 7 applies. Moreover,

using (2), (ij, ik, jk) i (FT, FT, FT ) but (FT, FT, FT ) i (jk, ij, ik). Hence, there is a

self enforcing deviation by S = ij from FT to (ij) = G (Pij ,Ø), and thus the network path

(ij, ik, jk), i (ij, ik, jk) j (FT, FT, FT ). This reduces to(πI − πFT

)+β

(πK − πFT

)≤ 0

and β ≤ β (θ) ≡ πI−πFTπFT−πK . Therefore, using Lemma 6, FT = G (N,Ø) and is the unique

FDNE if β > β (θ). However, β ≤ β (θ) implies FT /∈ γ (Pij ,Ø). In turn, i) FT /∈ G (N,Ø)

because of the self enforcing deviation by S = ij from FT to (ij) ∈ G (Pij ,Ø) and ii) there is

no self enforcing deviation from any g ∈ ΩI−O to FT . Thus, by Lemma 6, G (N,Ø) = ΩI−O

and the set of FDNE is any path of BAs that leads to free trade.

Proof of Proposition 2

The outcomes of the multilateralism game are Ø and FT . Let πFTi < πNi which reduces

38

to αi > αj + αk − 3τ and, given τ ≤ αs

3 , can only hold if i = l. This implies γ (P ∗,Ø) = Ø.

Then, for any i, j ∈ N , i) Ø ∈ G (Pij ,Ø) and ii) FT /∈ G (PS ,Ø) because FT /∈ γ (Psm,Ø)

while l has a self enforcing deviation from FT ∈ γ (Pml,Ø) and FT ∈ γ (Psl,Ø). Hence,

Ø = G (N,Ø) and Ø is the unique FDNE because there is no self enforcing deviation from

Ø but l has a self enforcing deviation from FT to Ø ∈ G (Psm,Ø). Now let πFTl ≥ πNl .

Then, FT is Pareto dominant for N which implies G (N,Ø) = FT and FT is the unique

FDNE.

Proof of Lemma 5

Let αi > αj . Then, for any k ∈ N , Condition 1 implies

πHk > πFTk > πK,jk > πK,ik > πOk and πHk > πI,ik > maxπI,jk , πK,jk

> πK,ik . (3)

Suppose β > βFT−Ij,i (θ). Then (3) implies (ij) is strictly Pareto dominant for i and j. Thus,

by Lemma 1, (ij) = G (N, (ij)).

Now suppose β ∈(βFT−Ii,j (θ) , βFT−Ij,i (θ)

]noting that γ (P ∗, (ij)) = (ij) , (ij, ik) .

Using Lemma 6 by ignoring (ij, FT ) where useful, six observations establish the proof.

First, (ij, jk) ∈ G (Pjk, (ij)) because i) (ij, jk) ∈ γ (Pjk, (ij)) and ii) the deviation by k

to ak = i is not self enforcing because it is consistent with (ij) ∈ γ (P ∗, (ij)). Second,

(ij, jk) /∈ G (Pik, (ij)) because (ij, ik) ik (ij, jk). Third, (ij, ik) ∈ G (Pik, (ij)). This

follows because i) (ij, ik) ∈ γ (Pik, (ij)) and ii) (ij, ik) k (ij) ∈ γ (P ∗, (ij)) and iii) (ij, jk) ∈γ (P ∗, (ij)) deters i from deviating to ai = φ. Fourth, (ij) /∈ G (PS , (ij)) for any S ⊂ N :

(ij) /∈ γ (Pjk, (ij)) because (ij, jk) jk (ij); (ij) /∈ G (Pij , (ij)) and (ij) /∈ G (Pjk, (ij))

because the deviation by j to aj = k is self enforcing since it is only consistent with (ij, jk) ∈γ (P ∗, (ij)) given aj = k implies (ij) /∈ γ (P ∗, (ij)). Fifth, i) (ij, FT ) /∈ G (Pij , (ij)) because

(ij) ij (ij, FT ), and ii) (ij, FT ) /∈ γ (Pjk, (ij)) because i can protably unilaterally deviate

to (ij). Similarly, sixth, (ij, ik) /∈ γ (Pjk, (ij)) because i can protably unilaterally deviate

to (ij).

The rst observation implies (ij) /∈ G (N, (ij)) because of the self enforcing deviation

by S = jk to (ij, jk) ∈ G (Pjk, (ij)). The third observation implies (ij, jk) /∈ G (N, (ij))

because of the self enforcing deviation by S = ik to (ij, ik) ∈ G (Pik, (ij)). To estab-

lish G (N, (ij)) = (ij, ik) , (ij, FT ), note that the protable deviations from (ij, ik) and

(ij, FT ) are j to (ij, jk) and i and/or j to (ij). From (ij, ik), there is also j and/or k

to (ij, FT ). And from (ij, FT ) there is also i to (ij, ik). However, given G (Pjk, (ij)) and

G (Pik, (ij)) are nonempty, then, respectively, the second, fourth, fth (and third) and sixth

observations imply the deviations by j, i and/or j, j and/or k and, lastly, i are not self

enforcing.

Now consider the nal case, β ≤ βFT−Ii,j (θ). Given (3) and βFT−Ii,j (θ) ≤ 1 i πI,ji −πFTi =

πI,ij − πFTj ≥ 0, then γ (P ∗, (ij)) = (ij) , (ij, ik) , (ij, jk) ≡ γ when βFT−Ii,j (θ) ≤ 1 and

γ (P ∗, (ij)) = γ ∪ (ij, FT ) otherwise. Using Lemma (6) by ignoring (ij, FT ) where useful,

39

six observations establish the proof. First, (ij, ik) ∈ G (Pik, (ij)) because i) (ij, ik) is strictly

Pareto dominant for i and, absent (ij, FT ), for k. Second, given this Pareto dominance,

(ij, ik) ∈ G (Pjk, (ij)) because i) (ij, ik) ∈ γ (Pjk, (ij)) and ii) j prefers (ij) and/or (ij, jk)

but aj = φ or aj = k is consistent with (ij, ik) ∈ γ (P ∗, (ij)). Third, (ij, FT ) /∈ G (Pik, (ij))

and (ij, FT ) /∈ G (Pij , (ij)). This follows because the deviation by i from ai = FT to

ai = k is self enforcing since the deviation is only consistent with (ij, ik) ∈ γ (P ∗, (ij))

given (ij) ∈ γ (P ∗, (ij)) and (ij, jk) ∈ γ (P ∗, (ij)) require ai 6= k and ak 6= i. Fourth,

(ij, FT ) ∈ G (Pjk, (ij)) i πFTi > πI,ji which happens i βFT−Ii,j (θ) > 1. This follows because

(ij, FT ) is Pareto dominant for j and k but (ij, FT ) ∈ γ (Pjk, (ij)) requires πFTi > πI,ji .

Fifth, (ij, jk) /∈ G (PS , (ij)) for any S ⊂ N because of the, already established, self enforcing

unilateral deviation by i (or k) to ai = k (ak = i) and (ij, ik) ∈ γ (P ∗, (ij)). Sixth, (ij) /∈G (PS , (ij)) for any S ⊂ N because i) for ι = i, j, (ij, ιk) ιk (ij) implies (ij) /∈ γ (Pιk, (ij))

and ii) the self enforcing deviation by i to ai = k implies (ij) /∈ G (Pij , (ij)).

The rst observation implies (ij, jk) /∈ G (N, (ij)) and (ij) /∈ G (N, (ij)) because of

the self enforcing deviation by S = ik to (ij, ik) ∈ G (Pik, (ij)). The second observation

implies (ij, FT ) /∈ G (N, (ij)) because of the self enforcing deviation by i to ai = k and

(ij, ik) ∈ G (Pjk, (ij)). The rst, third and fourth observations imply (ij, ik) ∈ G (N, (ij))

i βFT−Ii,j (θ) ≤ 1. To see this note the protable deviations are i) j to (ij, jk) which

is ruled out by the rst observation, and ii) j and/or k to (ij, FT ) which, noting that

(ij) ∈ γ (P ∗, (ij)), is ruled out by the third and fourth observations unless βFT−Ii,j (θ) > 1.44

Thus, (ij, ik) = G (N, (ij)) i βFT−Ii,j (θ) ≤ 1 but G (N, (ij)) = Ø if βFT−Ii,j (θ) > 1. When

βFT−Ii,j (θ) > 1, the rst, fourth, fth and sixth observations for G (PS , (ij)) imply set of

EBA networks in period 2 is (ij, ik) , (ij, FT ).Proof of Proposition 3

The proof proceeds by backward induction where, unless otherwise noted, αi > αj .

First, consider any g = (ij, ik) (i.e. even if αi < αj). Since πFTk > πK,jk , Lemma 1 implies

(ij, ik, jk) = G (N, (ij, ik)). Second, consider g = (ij). For β > βFT−Ij,i (θ), Lemma 5 implies

(ij) = G (N, (ij)). For β ≤ βFT−Ij,i (θ), Lemma 5 implies G (N, (ij)) ⊆ (ij, ik) , (ij, FT )with (ij, ik) ∈ G (N, (ij)) but (ij, FT ) ∈ G (N, (ij)) only if β ∈

(βFT−Ii,j (θ) , βFT−Ij,i (θ)

]or

βFT−Ii,j (θ) > 1.

Finally, consider g = Ø. Let β > βFT−Im,l (θ). Condition 1 implies πI,ml > πNl and

πI,lm > πNm , while βFT−Im,l (θ) < 1 implies πI,ml −πFTl = πI,lm −πFTm > 0. Thus, using (3), (ml)

is Pareto dominant for m and l regardless of G (N, (sm)) and G (N, (sl)). Hence, Lemma 1

implies (ml) = G (N,Ø) and thus (ml) is the unique FDNE.

Now let β ≤ βFT−Im,l (θ). First, consider multilateral beliefs. Here, (ij, FT ) ∈ G (N, g)

for any g = (ij). In this case, Lemma 1 or Lemma 10 implies (ml) = G (N,Ø) and, thus,

(ml, FT ) is the unique FDNE. This follows because using (3) and Assumption 1, i) (ml) is

44The importance of (ij) ∈ γ (P ∗, (ij)) is that it deters the deviation by k to ak = FT when G (Pij , (ij))is empty.

40

Pareto dominant for m and (sm) m g for g ∈ Ø, (sl), (ml) or Ø is Pareto dominant for

l and (sl) s (sm) s Ø, and ii) if Ø is Pareto dominant for l then (3) ensures condition ii)

of Lemma 10.

Now consider bilateral beliefs. Note, conditional on any g ∈ ΩI−O, (ij, ik, jk) is the

FDNE. For β ≤ βm (θ), the denition of βm (θ) together with (3) and Assumption 1 imply

(ml) is Pareto dominant for m and l. So Lemma 1 implies (ml) = G (N,Ø) and (ml, sl, sm)

is the unique FDNE. However, for β > βm (θ) the conditions of Lemma 7 are satised using

(3), Condition 1, Assumption 1 and noting that (sm) s Ø when β ≤ βFT−Im,l (θ). Using

Lemma 7, m and l have a self enforcing deviation from FT to (ml) ∈ G (Pml,Ø). Hence,

Lemma 6 implies ΩI−O are EBA networks and thus ΩFT are FDNE.

FT is also an FDNE if FT ∈ G (PS ,Ø) for some S ⊂ N . Given (ml) ml FT implies

FT /∈ γ (Pml,Ø), Condition 2 is necessary and sucient. Given (3), Condition 2 holds i

FT /∈ γ (Psl,Ø) or FT /∈ γ (Psm,Ø). Moreover, given FT ∈ γ (Psl,Ø) and FT ∈ γ (Psm,Ø),

any attempted deviation by i ∈ S from FT ∈ γ (PS ,Ø) to some g ∈ ΩI−O ⊆ γ (P ∗,Ø) is

deterred by (jk) ∈ γ (P ∗,Ø).

Proof of Proposition 5

The proof proceeds by backward induction where, unless otherwise noted, αi > αj .

First, consider any g = (ij, ik) (i.e. even if αi < αj). Using Condition 3, Lemma 1

implies (ij, ik, jk) = G (N, (ij, ik)) except for g ∈ (sm,ml) , (ml, sm). In this case,

G (N, (ij, ik)) = (ij, ik). Second, consider g = (ij). Given (sm,ml) = G (N, (sm,ml)),

then (3) and Lemma 1 imply (sm,ml) = G (N, (sm)). Given β ≤ βFT−K (θ), and follow-

ing the logic of Lemma 5 for β ≤ βFT−Il,m (θ), (ml, sl) = G (N, (ml)). Given β ≤ βFT−Is,l (θ),

Lemma 5 implies G (N, (sl)) ⊆ (sl,ml) , (sl, FT ) with (sl,ml) ∈ G (N, (sl)) but (sl, FT ) ∈G (N, (sl)) only if β ∈

(βFT−Il,s (θ) , βFT−Is,l (θ)

]or βFT−Il,s (θ) > 1.

Finally, consider g = Ø. Before proceeding, note the following: i) using Condition 3 and

(3), (ml) or (sm) is Pareto dominant for m and given g ∈ (sm) , (ml) and g′ ∈ (sl) ,Øthen g m g′; ii) using (3) and β ≤ βmin (θ), either (ml) or Ø is Pareto dominant for l while

(ml) l (sl) l (sm) and (ml) l FT ; iii) using (3) and β ≤ βmin (θ), (sl) s (sm) s Ø.There are now three cases to consider.

First, let β ≤ βm (θ). By construction, (ml) is Pareto dominant form. Thus, G (N,Ø) =

(ml) follows from either Lemma 1 or Lemma 10.

Second, let β ∈(βm (θ) , βs (θ)

]. Note that (sm) sm (ml) and, given β > βm (θ),

(sl) l FT . Thus, Lemma 7 or Lemma 8 apply depending on whether (sl) l Ø. Sup-

pose (sl) l Ø. Using Lemma 7 and the self enforcing deviation by S = ml from FT

to (ml) ∈ G (Pml,Ø), Lemma 6 implies the set of EBA networks include ΩI−O and thus

the set of FDNE include (ml, sl, sm) , (sl,ml, sm) , (sm,ml). As established in the proof

of Proposition 3, Condition 2 is necessary and sucient for FT to be an FDNE. Now

suppose Ø l (sl) so that Lemma 8 applies. By Lemma 6, G (N,Ø) ⊆ FT, (sl) where

41

(sl) ∈ G (N,Ø) if there is no self enforcing deviation from (sl) to FT . When FT s (sl), the

deviation by i) S = sm to as = am = FT is not self enforcing because, given (sl) /∈ γ (P ∗,Ø),

FT /∈ G (Psm,Ø) since the deviation by m to am = s and (sm) ∈ γ (P ∗,Ø) is self enforcing,

ii) s to as = FT is not self enforcing because, if G (Pml,Ø) nonempty, (ml) ml FT implies

FT /∈ γ (Pml,Ø) and, if G (Pml,Ø) empty, Ø ∈ γ (P ∗,Ø), and iii) m to am = FT is not

self enforcing because it is consistent with (sl) ∈ G (Psl,Ø). Moreover, m's deviation is the

only protable deviation when (sl) s FT . Hence, there is no self enforcing deviation from

(sl) to FT and, thus, (sl) ∈ G (N,Ø). Finally, given G (N,Ø) is nonempty, FT is also an

FDNE unless there is a self enforcing deviation by some S ⊂ N .

Third, let β ∈(βs (θ) , βmin (θ)

]. This implies (ml) s (sm). Thus, Lemma 9 applies.

Suppose (sl) l Ø. Given (ml) ∈ G (Pml,Ø), s has no self enforcing deviation from (ml)

to FT but, since (ml) ml FT , S = ml has a self enforcing deviation from FT to (ml) ∈G (Pml,Ø). Therefore, Lemma 6 implies (ml) = G (N,Ø) and, thus, (ml, sl, sm) is the

unique FDNE. Now suppose Ø l (sl). Lemma 9 implies G (N,Ø) ⊆ FT, (sl) , (ml).(sl) , (ml) ⊆ G (N,Ø) because, as established above, m and/or s has no self enforcing

deviation from (sl), and thus s has no self enforcing deviations from (ml), to FT . Hence,

the set of FDNE is (sl,ml, sm), (ml, sm, sl) and, unless there is a self enforcing deviation

by some S ⊂ N , FT .

Proof of Proposition 6

Condition 3 implies αls ∈ (3− 5τ, 3− 2τ ] and αms ∈[1 + 6−c

3 τ, 3− 5τ]given the

parametrization αls = 3 − cτ for c ∈ (2, 5]. Since Proposition 4 implies∂βFT−Im,l (θ)

∂αms< 0,

let αms = 1 + 13 τ . Then, β

FT−Im,l

(θ)

= 2−(7/3)τ4−4τ < 1

2 . First, suppose βmin (θ) = βFT−K (θ).

Given βFT−K (θ) = −αls+4+αms−4ταms+1+τ , and βFT−K (θ) < 1 by Condition 3, then ∂βFT−K(θ)

∂αls<

0 and ∂βFT−K(θ)∂αms

> 0. Thus, βFT−K (θ) is minimized for θ =(1 + 1

3τ, 3− 2τ, 13

)implying

βFT−K(θ)

= 1322 > 1

2 > βFT−Im,l

(θ)as required. Second, suppose βmin (θ) = βFT−Is,l (θ).

Given βFT−Is,l (θ) = −1+3αms−2ταms+αls+τ

, then∂βFT−Is,l (θ)

∂αls< 0 and, for βFT−Is,l (θ) < 3,

∂βFT−Is,l (θ)

∂αms> 0.

Thus, βFT−Is,l (θ) is minimized for θ =(1 + 1

3τ, 3− 5τ, 13

)implying βFT−Is,l

(θ)

= 35 >

12 >

βFT−Im,l

(θ)as required.

C FDNE for β > βmin (θ)

To streamline the exposition, assume βs (θ) < βmin (θ) when βmin (θ) = βFT−Is,l (θ) (this

is true except for a very small section of the parameter space). The following proposition

characterizes the FDNE for β > βmin (θ).

Proposition 7. Let β > βmin (θ). When Ø is Pareto dominant for l and β > βs (θ), the

unique FDNE is Ø. Otherwise:

42

i) For β > βl (θ) the unique FDNE is (sl).

ii) For β ∈[βFT−K (θ) , βl (θ)

)the unique FDNE is (ml, sm).

iii) For β ∈[βmin (θ) ,min

βl (θ) , βFT−K (θ)

), a) (ml, sl, sm) and, if πNl > πI,sl , (sl) are

FDNE, and b) unless there is a self enforcing deviation, FT is an FDNE.

Proof. This proof is sketched, proceeding by backward induction where i) G (N, (ij, ik)),

G (N, (sm)) and, when β ≤ βFT−K (θ), G (N, (ml)) are as given in the proof of Proposition

5, and ii) G (N, (sl)) follows from application of Lemma 5. When β > βFT−K (θ), it is

simple to show that G (N, (ml)) = (ml, sm).

Now consider g = Ø. If Ø is Pareto dominant for l and β > βs (θ), it is simple to

show that G (N,Ø) = Ø. Thus, suppose these conditions do not hold simultaneously. First,

consider β > βl (θ). By construction, βl (θ) ≥ βFT−Is,l (θ) because otherwise (sl,ml, sm) l gfor some g ∈ (ml, sl, sm) , (ml, sm) which, by (3), is not true. Then, G (N,Ø) = (sl) and

(sl) is the unique FDNE by Lemma 1 when (sl) l Ø and by Lemmas 6 and 10 when

Ø l (sl). Second, consider β ∈(βFT−K (θ) , βl (θ)

]. Then (ml) is Pareto dominant for

m. Since (ml) l (sm), Lemma 1 applies if (ml) l Ø and Lemmas 6 and 10 apply if

Ø l (ml). In either case G (N,Ø) = (ml) and thus (ml, sm) is the unique FDNE. Third,

suppose β ≤ minβl (θ) , βFT−K (θ)

noting, in this range, (sl) l (sm). Initially, let

Ø s (sm). Then, given (ml) l Ø, (ml, sl, sm) is the unique FDNE. Now let (sm) s Ø.Then, given β > βs (θ), Lemma 9 applies. Thus, similar to the proof of Proposition 5,

G (N,Ø) ⊆ (ml) , (sl) , FT with i) (ml) ∈ G (N,Ø), ii) (sl) ∈ G (N,Ø) if Ø l (sl), and

iii) unless there is a self enforcing deviation, FT ∈ G (N,Ø). The associated FDNE are,

respectively, (ml, sl, sm), (sl) and FT .

D National welfare and optimal taris

Let pi (g) be the number of countries j such that ij ∈ g where, by custom, ii ∈ g. Given opti-mal quantities, consumer surplus is CSi (g, θ) = 1

2116

[3αi − (3− pi (g)) τ i (g, θ)

]2. Tari rev-

enue is TR (g, θ) = 14 (3− pi (g)) τ i (g, θ)

[αi − (1 + pi (g)) τ i (g, θ)

]. Domestic rm prots

are πi (g, θ) =∑j|ij∈g

116

[αj + (3− pj (g)) τ i (g, θ)

]2+∑j|ij /∈g

116

[αj − (1 + pj (g)) τ i (g, θ)

]2.

Welfare of country i is then Wi (g, θ) = CSi (g, θ) + TRi (g, θ) + πi (g, θ). Let the tilde

components of Wi (g, θ) be dened as their nontilde counterpart absent the fractions; e.g.˜CSi (g, θ) =

[3αi − (3− pi (g)) τ i (g)

]2. ThenWi (g, θ) ∝ ˜CSi (g, θ)+8 ˜TRi (g, θ)+2πi (g, θ).

The optimal tari for country i is τ i (g, θ) = 3αi

11pi(g)−1 .

The model's main results depend on three categories of conditions: i) those underlying

the fear of preference erosion, ii) those underlying the equilibrium of the multilateralism

game, and iii) those capturing that m may no longer fear preference erosion.

Underlying the fear of preference erosion under Condition 1 is i) the formation of spoke

spoke BAs and ii) the FTI condition βFT−Ii,j (θ) =πHi −π

I,ji

πHi −πFTi. Replacing prots with wel-

43

fare, WFTi −WK,k

i > 0 ensures formation of spokespoke BAs. Additionally, the following

conditions are required for βFT−Ii,j (θ) ∈ (0, 1): WHi − W I,j

i > 0, WHi − WFT

i > 0 and

W I,ji −WFT

i > 0. WHi −WFT

i > 0 follows trivially because, absent consumer and tari

revenue eects, the spokespoke BA merely reduces i's prots in foreign markets. However,

the sign of WHi −W

I,ji and W I,j

i −WFTi depend on θ. Since WH

l −WI,ml < WH

m −W I,lm

and W I,ml −WFT

l < W I,lm −WFT

m , the rst two important conditions are WHl −W

I,ml > 0

and W I,ml −WFT

l > 0. In addition, when (ml) is the FDNE for β > βFT−Im,l (θ) this relies

on πI,ml − πNl > 0 and πI,lm − πNm > 0. Thus, since W I,ml −WN

l < W I,lm −WN

m , the third

important condition is W I,ml −WN

l > 0.

The important condition underlying the equilibrium of the multilateralism game is that

l blocks the three country MFN agreement if πFTl − πNl > 0. Since WFTl −WN

l < WFTm −

WNm < WFT

s −WNs , the fourth important condition is WFT

l −WNl > 0.

Finally, the condition dening when m no longer fears preference erosion is πK,sl −πFTl > 0. Since WK,s

l − WFTl < WK,s

m − WFTm , the fth important condition is that

WK,sl −WFT

l > 0 is possible. WK,sl −WFT

l><0 allows for Condition 1 or Condition 3 to

hold. This preserves the non monotonicity between market size asymmetry and the role of

BAs as strong building/stumbling blocs.

Now, is it possible for all these conditions to hold when the government cares about

national welfare and sets optimal taris? Under symmetry, the answer is no becauseW I,ml <

WFTl . Intuitively, this implies βFT−Ii,j (θ) > 1 and so the fear of preference erosion is never

large enough that insiders forgo the benet of being the hub. However, moderately large

degrees of asymmetry allow all the conditions to be satised. Henceforth, αm ≡ 1 while

αl ≥ 1 and αs ≤ 1. It is useful to note that W I,ml −WN

l reduces to αl . 1.3 ≡ αl. So, thisis an upper bound on the level of asymmetry.

To begin, suppose WFTl − WK,s

l > 0. For W I,ml − WFT

l > 0 to hold, s must be

suciently small. Specically, W I,ml −WFT

l = 0 for αl ≈ αl and αs ≈ .9. In addition,∂(W I,m

l −WFTl )

∂αl> 0 but

∂(W I,ml −WFT

l )∂αs < 0 so W I,m

l − WFTl > 0 for αs . .9 ≡ αs and

αl ≈ αl. Indeed, W I,ml −WFT

l > 0 holds for any αl ∈[1, αl

]when αs . .78. In addition,

WHl −W

I,ml > 0 for any αl ∈

[1, αl

]when αs & .57. Thus, a lower bound on αs is αs = .57.

Given WFTl −WK,s

l > 0 holds for any αl ∈[1, αl

]when αs & .73 and for some interval

X ⊆[1, αl

]when αs & αs, there is a well dened range where the fear of preference erosion

means m and l prefer to remain insiders rather than become the hub when αl ∈[1, αl

]and

αs ∈ [αs, αs]. When the FTI condition is satised for both m and l, Lemma 1 implies the

unique FDNE is that they remain insiders. When the FTI is violated for at least one of

the insiders, Lemma 5 suggests the unique EBA network is that l becomes the hub with m

and s forming the subsequent BA since αs . αs implies WFTs > WK,m

s > WK,ls > WO

s in

which case the unique FDNE is (ml, sl, sm).45 In addition, like the political economy model

45A dierence with the political economy model in the main text is that it is not necessarily true that

44

in the text,∂βFT−Ii,j (θ)

∂αis< 0 for (i, j) = (m, l) , (l,m) so greater asymmetry reduces the extent

to which BAs lead to global free trade.

Now consider the equilibrium of the multilateralism game. For αs & αs, WFTl −WN

l >

0 for any αl ∈[1, αl

]. However, WFT

l − WNl < 0 for αl = αl and αs = αs. Thus,

given∂(WFT

l −WNl )

∂αl< 0 and

∂(WFTl −WN

l )∂αs > 0, the sign of WFT

l − WNl > 0 depends on

θ for αl ∈[1, αl

]and αs ∈ [αs, αs]. Hence, the equilibrium of the multilateralism game

depends on θ. This means that BAs can be strong building blocs or strong stumbling

blocs because for any given θ, regardless of the equilibrium in the multilateralism game,

β <(>)max

βFT−Im,l (θ) , βFT−Il,m (θ)

implies BA formation leads (does not lead) to global free

trade.

So far, it was assumed that WFTl −WK,s

l > 0. However, as noted, WFTl −WK,s

l < 0

for some interval X ⊂[1, αl

]when αs . .73. Thus, the FTK condition determines

the EBA network conditional on g = (ml). Conditional on (ml) and β > βFT−K (θ) ≡WHl −W

K,sl

WHl −W

FTl

, Lemma 1 implies (ml, sm) is the unique EBA network and FDNE. Otherwise,

Lemma 5 and Proposition 7 suggest (ml, sl) is the unique EBA network and (ml, sl, sm)

is the unique FDNE since WFTs > WK,m

s > WOs for αs . αs. Moreover, for αs .

.83, minβFT−K (θ) , βFT−Is,l (θ) , βFT−Is,l (θ)

> max

βFT−Im,l (θ) , βFT−Il,m (θ)

for any αl ∈[

1, αl]. Thus, at the threshold level of asymmetry θ for which WFT

l = WK,sl then, con-

ditional on g ∈ (ml) , (sl), global free trade is attained along the equilibrium path only

for β < maxβFT−Im,l

(θ), βFT−Il,m

(θ)

. In contrast, at the level of asymmetry θε such that

WFTl = WK,s

l + ε, global free trade is attained along the equilibrium path for the larger

interval β < βFT−K(θε)which mirrors Proposition 6.

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