Journal of International Economics 82 (2010) 49–62

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Journal of International Economics

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Backward stealing and forward manipulation in the WTO

Kyle Bagwell, Robert W. Staiger ⁎Department of Economics, Stanford University, Stanford CA, 94305 United States; and NBER

⁎ Corresponding author. Department of Economics, St94305 United States.

E-mail addresses: kbagwell@stanford.edu (K. Bagwe(R.W. Staiger).

1 An early empirical paper of Rose (2004) seems tgrowing list of papers (e.g., Evenett et al., 2004, Tomz et aWei, 2007) now provide empirical confirmation that GAsubstantial impacts on trade flows.

2 TheWTO does grant certain exceptions to MFN, for eof free trade agreements and customs unions. We abstraWe also take as given the MFN clause, and do not offusefulness. For formal analyses of the role of the MFN cfor example Bagwell and Staiger (1999, 2005), Caplin anEthier (2004), Ludema (1991), McCalman (2002) and Ssive survey, see Horn and Mavroidis (2001).

3 This feature is noted, for example, by Horn and MavIn the WTO, negotiations mainly take place betweenSometimes this is ‘officially sanctioned,’ as in the case of PHowever, also in seemingly multilateral negotiationbetween a very limited number of countries...” (Horn an

0022-1996/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.jinteco.2010.04.005

a b s t r a c t

a r t i c l e i n f o

Article history:Received 27 March 2007Received in revised form 12 April 2010Accepted 14 April 2010

JEL classificaton:F13

Keywords:GATTWTOTrade negotiations

Motivated by the structure of WTO negotiations, we analyze a bargaining environment in which negotiationsproceed bilaterally and sequentially under the most-favored-nation (MFN) principle. We identify backward-stealing and forward-manipulation problems that arise when governments bargain under the MFN principlein a sequential fashion. We show that these problems impede governments from achieving the multilateralefficiency frontier unless further rules of negotiation are imposed. We identify the WTO nullification-or-impairment and renegotiation provisions and its reciprocity norm as rules that are capable of providingsolutions to these problems. In this way, we suggest that WTO rules can facilitate the negotiation of efficientmultilateral trade agreements in a world in which the addition of new and economically significant countriesto the world trading system is an ongoing process.

anford University, Stanford CA,

ll), rstaiger@stanford.edu

o contradict this view, but al., 2007, and Subramanian andTT/WTO negotiations have had

xample to allow the formationct from these exceptions here.er here an explanation for itslause in trade agreements, seed Krishna (1988), Choi (1995),aggi (2004). For a comprehen-

roidis (2001), who observe: “...subsets of member-countries.rincipal Supplier negotiations.s, ‘actual’ negotiations occurd Mavroidis, 2001, p. 271).

l rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Under the auspices of the World Trade Organization (WTO) – andGATT, its predecessor organization created in 1947 – governmentshave met with broad success in liberalizing world trade.1 This successis especially remarkable in light of three prominent features of theGATT/WTO negotiating environment. First, WTO negotiations abideby the most-favored-nation (MFN) principle, under which a WTO-member country must provide all member-countries with the sameconditions of access to its markets.2 Second, WTO negotiations takeplace overwhelmingly among small numbers of countries.3 And third,GATT/WTO negotiations have extended overmore than half a century,during which time the addition of new countries to the world trading

system – via either the process of economic development or the act ofaccession to the GATT/WTO – has occurred on a continuing basis. As aconsequence of these three features, it is routine for a country toengage in market access negotiations on a product with one country,having previously negotiated tariff commitments on that productwith another country, all subject to MFN.

In this sequential MFN negotiating environment, a pair of potentialimpediments to multilateral efficiency may be identified. First, underMFN, any market access concession that a country makes to an earlynegotiating partner is automatically available to future negotiatingpartners as well. To reduce the associated potential for free-riding, acountry might then engage in inefficient “foot-dragging,” offering littleto early negotiating partners in order tomaintain its bargaining positionfor later negotiations. A second impediment to efficiency might arise iflater negotiatingpartners themselves engage in “bilateral opportunism”

and seek toalter themarket access implicationsof earlier negotiations totheir own advantage. More broadly, we may associate the firstimpediment with forward manipulation, in which early agreementsare manipulated to alter the outcome of later negotiations, and thesecond impediment with backward stealing, in which later agreementsare structured to take surplus from earlier negotiating partners.

Does the GATT/WTO owe its success to the fact that these potentialimpediments are simply unimportant? Or can its rules instead becreditedwithprovidinggovernmentswith someassurance that forward-manipulation and backward-stealing problems will not become severe?In this paper, we suggest that the potential impediments to efficiencycreated by these problems are important. And we identify GATT/WTOrules that can help governments overcome these impediments.

Our analysis is carried outwithin a three-country two-goodworld, inwhich a home-country government negotiates bilaterally and sequen-tially with each of two trading partners, subject to the MFN principle.

5 Aswill become clear below, it is important that the exporting government's negotiatedtrade policy commitments can stimulate its exports. In a general equilibrium setting thisfeature follows from Lerner symmetry even when negotiations only cover import tariffs

50 K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

We also permit governments to make direct international transfers aspart of their bilateral negotiations.Wedo this for three reasons. The firstreason is to ensure analytical tractability: the feasibility of directinternational transfers simplifies our analysis considerably. The secondreason is pedagogical: in the presence of international transfers, it isclear that static bargaining (among all three countries) would yieldefficient outcomes, and this permits us to highlight the issue of dynamicbargaining inefficiencies that is the focus of our analysis. And the thirdreason is to endow governments with a reasonably flexible portfolio ofpolicy instruments. While it is not standard for GATT/WTO tradenegotiations to involve explicit transfers as part of the agreement, thesenegotiations do often involve more than just tariff reductions.4 Ourassumption that direct international transfers are feasible may be seenas an attempt to capture these additional policy dimensions in a simplemodel,with “reality”positioned somewhere inbetween theextremes ofnegotiations over tariffs only and negotiations over tariffs and directinternational transfers.

Within this framework, we characterize the multilateral efficiencyfrontier, and we then explore whether this frontier can be reached insubgame perfect equilibria of specific bargaining games that entailsequential and bilateral negotiations under MFN. We explore this issuein two broad steps. We first show that, in our basic sequential MFNbargaining game, the backward-stealing problem makes it impossiblefor governments to reach the multilateral efficiency frontier: beginningfrom any efficient combination of tariffs and transfers, the homegovernment and its later negotiating partner can always alter the tariffsand transfers under their control in a way that benefits them at theexpense of the (unrepresented) early negotiating partner. When weimpose anexogenous “security requirement” that later agreementsmaynot involve backward stealing, we find that the forward-manipulationproblem makes it generally impossible for governments to reach theefficiency frontier: as a general matter, the home government canengage in inefficient foot-draggingwith its early negotiating partner bykeeping its tariff high, and both the home government and its earlynegotiating partner can thereby benefit at the expense of the(unrepresented) later negotiating partner, who is stuck with a less-favorable disagreement point.

With the backward-stealing and forward-manipulation problemsidentified in our basic sequentialMFN bargaining game,we then turn tothe second broad step of our analysis. We demonstrate that renegoti-ation opportunities such as those provided in the GATT/WTO can curtailthe significance of early negotiation outcomes for the disagreementpayoffs of subsequent negotiating partners, and thereby alleviate theinefficiency associated with forward manipulation. And we show thatthe GATT/WTO reciprocity norm and nullification-or-impairmentprovisions can mimic a security requirement, and thereby can be seenas helping to alleviate the backward-stealing problem. When joinedtogether, we establish that these rules permit governments to achievethe multilateral efficiency frontier in a wide range of circumstances.

Our main finding is then that the GATT/WTO rules analyzed in thissecond step permit governments engaged in sequentialMFNbargainingto achieve efficient outcomes that are otherwise precluded by thebackward-stealing and forward-manipulation problems identified instep one. But this finding raises a further question: Is there any evidencethat theseGATT/WTO ruleswere adopted at least in part for the purposeof addressing the problems that our analysis suggests they are well-designed to solve?

In this regard, it is widely acknowledged (e.g., Rhodes, 1993) thatmuchof theGATT architecturewas inspired byUnited States experienceunder the 1934 Reciprocal Trade Agreements Act (RTAA). What is lesswell-appreciated is the way in which the RTAA was itself influenced by

4 For example, the Agreement on Trade-Related Aspects of Intellectual PropertyRights negotiated in the Uruguay Round is often interpreted as a transfer from thedeveloping world to industrialized countries that was granted in exchange for certainmarket access concessions (such as the phase-out of the Multifiber Arrangement).

the successes and failures of themany international attempts that camebefore it to address the problem of high trade barriers. In fact, as wedescribe inmore detail elsewhere (see Bagwell and Staiger, 2010a), at abroad level by 1934 the United States was (a) frustrated with itsexperience in multilateral tariff bargaining, and (b) based on Europeanexperience, well-aware that the effectiveness of bilateral tariff bargain-ing could be undone by the twin problems of “concession erosion”(backward stealing) and “bargaining tariffs” (forward manipulation).And so, under the RTAA, the United States sought to devise a method ofbilateral tariff bargaining that would not be susceptible to thesefundamental problems. The central elements of this method includedunconditional MFN as well as tactics for preserving reciprocity inbilateral negotiations; andaswehaveobserved, theGATT/WTOadoptedthe essential approach embodied in the RTAA.

While our paper is broadly related to a literature in IndustrialOrganization on contracting with externalities (see, for example, Aghionand Bolton, 1987, McAfee and Schwartz, 1994, and Marx and Shaffer,2004, 2008), in the International Trade literature thereare twopapers thatare most closely related to the present analysis. The first paper is Bagwelland Staiger (2005). In that paper, we are also concerned with thepossibility of inefficient negotiating outcomeswhen pairs of countries cannegotiate bilaterally. But there are two important differences betweenthat paper and the present analysis. First, in our earlier paper we identifyrules of negotiation that serve to protect the welfare of governments thatare not participating in a bilateral negotiation, andwe relate these rules toWTO principles, but we do not ask the central question of the presentanalysis: starting from an inefficient (non-cooperative) set of policies, cana simple set of rules be identified which (i) allow governments whoengage in sequential bilateral MFN negotiations to arrive at an efficientarrangement, and (ii) have a counterpart in GATT articles? Providing ananswer to this question requires a model of the sequential bargainingprocess, something that our earlier paper does not provide. A secondimportantdifference is thatwedonotpermitdirect international transfersinourearlierpaper.We indicatebelowhowthepossibilityof internationaltransfers affects our earlier results. The second related paper is Limao(2007), who explores an idea related to our foot-dragging result. Heshows that a government may engage in foot-dragging under MFN toenhance its bargaining position with regard to a subsequent negotiatingpartner.However, in Limao'smodel, foot-dragging arises in anticipationofa subsequent preferential agreement with non-trade objectives, while inourmodel foot-dragging arises in anticipation of subsequentMFNmarketaccess negotiations.

The next section introduces the three-country two-good model andcharacterizes the efficiency frontier. Section 3 introduces the basicsequential MFN bargaining game, and identifies the backward-stealingproblem, while Section 4 identifies the forward-manipulation problem.Sections 5 and 6 introduce renegotiation opportunities and nullifica-tion-or-impairment/reciprocity provisions as a means by which toalleviate the forward-manipulation and backward-stealing problems,respectively. Section 7 concludes.

2. The model

2.1. The basic setup

We consider a perfectly competitive general equilibrium environ-ment.5 We assume that country A exports good y to countries B and C

(for recent empirical confirmation that import tariffs act as significant export taxes, see forexample Irwin, 2007, andTokarick, 2007). Inapartial equilibriumsetting this featurewouldrequire that the exporting government negotiate directly over export policies, which runscounter toGATT/WTOpractice. Hence,whileworking in a partial equilibriummodelwouldsimplify our analysis, we prefer to adopt a general equilibrium setting so that we maymaintain our focus on negotiations over import tariffs.

51K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

in exchange for imports of good x from B and C. Country Amay levy anMFN import tariff τA, while countries B and Cmay each levy their ownimport tariff, τB and τC, respectively.6 We adopt the convention that τj

represents one plus the ad valorem import tariff of country j, and welet τ denote the vector of tariffs {τA, τB, τC}. Country A may also makedirect (consumption) transfers to country B and/or country C. Wedenote the (positive or negative) transfer from A to B by tB and from Ato C by tC, measured in units of good y. The total net transfers madefrom A to its trading partners is then tA≡ tB+ tC, and we let t denotethe vector of transfers {tA, tB, tC}.

Provided that country A's (MFN) tariff does not prohibit trade witheither of its trading partners B and C, there will be a common exporterprice for good x in countries B and C, andwe denote this price by Px⁎. Theexport price for good y in country A is denoted by PyA.Wemay define theratio of “world” prices (relative exporter prices) as Pw≡Px⁎/PyA. We referto Pw as the world price or the terms of trade between country A and itstrading partners B and C. Similarly, we let Pj≡Px

j/Pyj denote the priceof good x relative to the price of good y prevailing locally in country ja{A, B, C}.We refer to P j as the ratio of local prices in country j. With non-prohibitive tariffs, international arbitrage links world and local prices:

PA = τAPw≡PA τA; Pw� �

; P j = Pw= τ j≡P j τ j

; Pw� �

for j∈ B;Cf g

We assume that the international transfers have no secondaryburden or blessing (i.e., that they do not affect the equilibrium termsof trade).7 In each country, the sum of net transfers and tariff revenueis distributed to consumers in a lump-sum fashion.

For any world price, each country's trade must balance in light ofits net transfers:

PwMA = EA−tA; and Mj−t j = PwE j; j∈ B;Cf g ð1Þ

where Mj and Ej for ja{A, B, C} denote, respectively, imports andexports for country j. We assume that transfers are never so large as tocause a country to export or import both goods (i.e., we do not allow acountry's transfer to be larger than its trade in good y). Marketclearing determines the equilibrium world price as a function of thevector of tariffs τ. With Pw(τ) denoting the equilibrium terms of trade,the x-market-clearing condition is given by:

MA PA τA; Pw� �

; Pw; tA

� �= EB PB τB; Pw

� �; P

w; tB

� �

+ EC PC τC; Pw� �

; Pw; tC

� �ð2Þ

wherewe nowexpress imports and exports as explicit functions of localand world prices and transfer levels. The y-market is assured to clear atPw(τ) by Eqs. (1)–(2). We assume that the Marshall–Lerner stabilityconditions are met globally (ensuring a unique Pw given τ), so that aninward shift of a country's import demand curve improves its terms oftrade, and that the Lerner and Metzler paradoxes are ruled out, so that∂Pw/∂τAb0, dPA/dτAN0, ∂Pw/∂τ jN0 and dPj/dτ jb0 for ja{B, C}.

With PA held fixed, a change in Pw or tA can affectMA only throughthe effect on A's national income. But the income effect of a smallchange in Pw, measured in units of good y, is given by the importvolume MA. With analogous observations for B and C, we thus record

6 In this 2-good MFN environment, countries B and C have no basis for tradebetween them. However, the key features of reciprocity and MFN that underpin ouranalysis extend naturally to other trading patterns. For example, these features aremaintained if a third good z is added which, like good y, is exported by country A tocountries B and C (see Bagwell and Staiger, 2002, Appendix B.3). Moreover, it isstraightforward to show (using arguments analogous to those in Appendix B.3 ofBagwell and Staiger) that the features of reciprocity and MFN that we emphasize alsohold in a more symmetric 3-good 3-country setting in which each country imports onegood from its two trading partners and exports a different good to each of them.

7 This is a strong assumption, and so we emphasize that while it simplifies ouranalysis, it is not critical for our results.

the following structure on each country's trade function (subscriptsdenote partial derivatives):

MAPw≡M

AtA × MA; EBPw≡E

BtB × EB; and ECPw≡E

CtC × EC ð2aÞ

Finally, we represent the objectives of each government as ageneral function of its local prices, its terms of trade, and the nettransfers it grants or receives. In particular, we represent the welfareof the government of country j by Ŵ j(Pj(τj, Pw), Pw, tj) for ja{A, B, C}.We place the following basic restrictions on these objective functions.First, under analogous reasoning to that which leads to (2a), weimpose the following structure on each country's objective function:

WAPw≡W

AtA × MA; W

BPw≡W

BtB × EB; and W

CPw≡WC

tC × EC ð3Þ

Asbefore, this structure reflects the linkbetweendirect internationaltransfers and the income effects of changes in Pw. And second, weassume that, holding its local prices and its terms of trade fixed, eachgovernmentwould prefer an increase in net transfers toward it:ŴtA

Ab0;ŴtB

B N ;ŴtCCN0. Under (3), this implies aswell that, holding its local prices

and its net transfer fixed, each country would prefer a terms-of-tradeimprovement: WPw

Ab0; WPw

BN0; WPw

CN0. As we have argued extensively

elsewhere (see Bagwell and Staiger, 1999), by leaving governmentpreferences over local prices unspecified, our representation ofgovernment objectives is very general and is consistent with national-income-maximizing governments as well as governments that aremotivated by various political/distributional concerns.

Our three tariffs and two transfers provide one degree of freedom inachieving any level of welfare for the three governments. This meansthat any welfare triple can be achieved with an arbitrary market-clearingworld price orwith any one instrument set at an arbitrary level.As this feature is important later, we record it in the following lemma(proved in the Appendix):

Lemma 1. Any welfare triple can be achieved with an arbitrary market-clearing world price or with any one instrument set at an arbitrary level.

2.2. The efficiency frontier

DefiningWj(τ, t j)≡Ŵ j(P j(τj,Pw(τ)), Pw(τ),t j), we may now charac-terize the efficiency frontier. We define the efficiency frontier withrespect to the governments' own preferences, and it is characterized bythe set of solutions to:

Max τ;tB ;tCð Þ WA τ; tA≡tB + tC� �

s:t: WB τ; tB� �

≥ —W

BE; WC τ; tC

� �≥ —

WCE

where W—BE and W

—CE denote the welfares of the governments ofcountries B and C, respectively, evaluated at the efficient policies. Thefive first-order conditions that characterize the efficient selection of{τ, tB, tC}, given W

—BE and W—CE, can be written as:8

WAτA

WAtA

� WBτA

WBtB

� WCτA

WCtC

= 0;WA

τB

WAtA

� WBτB

WBtB

� WCτB

WCtC

= 0;

WAτC

WAtA

� WBτC

WBtB

� WCτC

WCtC

= 0;

WB τ; tB� �

= W— BE

; and WC τ; tC� �

= W— CE

:

ð4Þ

8 We assume throughout that Wj for ja{A, B, C} is everywhere (twice) differentiableand globally concave.

Fig. 1. The sequential bargaining structure.

52 K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

In words, efficiency condition (4) states that, for j = A, B, Crespectively, a small change in τ j which is accompanied by thechange in tB that keeps B indifferent and the change in tC that keeps Cindifferent must keep A indifferent as well.

Throughout the paper we restrict our focus to efficient policycombinations that call for tariffs positioned below the reaction curvesof each country, and we ask whether such policy combinations can beimplemented as equilibria of specific bargaining games. This below-the-reaction-curves restriction comes with little loss of generality. Ineach of the games we consider – as in GATT/WTO negotiations –

governments agree to bind their tariffs at specified levels, and thesebindings then place upper limits on permissible tariff choices. As aconsequence, any efficient combination of policies that required atleast one country to set its tariff above its reaction curve would beunattainable in the bargaining games we consider, provided only thatsubsequent to the conclusion of negotiations each government ispermitted (as we assume) to set its tariff unilaterally subject to theconstraint that it does not exceed its negotiated tariff binding.Efficiency might be achieved with a subset of countries on their tariffreaction curves, but the unilateral nature of the tariff commitmentsthat efficiency would require of the remaining countries is at oddswith the “reciprocal” nature of GATT/WTO tariff negotiations.9 Ratherthan make these arguments repeatedly throughout the paper, wefocus from the beginning on efficient policy combinations that call fortariffs positioned below the reaction curves of each country. Werecord this restriction as:

dWj= dτ j

N 0; j∈ A;B;Cf g ðA1Þ

In addition to (A1), we restrict our focus as well to efficient pointsthat satisfy:

sign dWB=dτA

� �= sign dWC

=dτA� �

ðA2Þ

At an efficient point satisfying (A2), B and C agree on the direction (ifany) that each would like τA to move. Exploring cases where theincentives of B and C are opposed might also be of interest, but thealigned case is a natural starting point for analyzing MFN tariffbargaining between A and each of its trading partners.

We treat (A1)–(A2) as maintained assumptions throughout thepaper that define the relevant region of the efficiency frontier. Theseassumptions imply the direction in which each government wouldprefer each policy to move beginning from an efficient point. In theAppendix we prove:

Lemma 2. At any efficient point, the following restrictions apply:

ið Þ dWj=dτj N 0; j∈ A;B;Cf g;

iið Þ dWj=dτAb0; dWA

=dτjb0; j∈ B;Cf g;iiið Þ dWj

=dτn j N 0; j; n j∈ B;Cf g:ðR1Þ

2.3. The bargaining structure

In the following sections we explore whether the efficiencyfrontier can be reached in a variety of specific bargaining environ-

9 One reason for the reciprocal nature of GATT/WTO tariff commitments is toincrease compliance with the negotiated commitments. In particular, enforcement inthe GATT/WTO is achieved primarily through the threat of withdrawal of negotiatedtariff commitments (see Bagwell and Staiger, 2002, and Bown, 2004), a threat thatwould be unavailable to a country that was already on its reaction curve. While weabstract from such enforcement issues in our formal analysis here, they provide anadditional reason for our below-the-reaction-curve focus.

ments. Common across these environments is the feature thatnegotiations proceed bilaterally and sequentially under MFN. As wenoted in the Introduction, bilateral tariff bargaining under MFN is astaple of the GATT/WTO whose antecedents date back to the bilateraltariff bargaining procedures under the RTAA. Fig. 1 illustrates the basicstructure of the sequence of bargains for the governments of countriesA, B and C. According to our economic model, exporters fromcountries B and C sell into A's market, while exporters from countryA sell into the markets of B and C, but B and C do not trade with eachother. As a consequence, Fig. 1 depicts a sequence of bilateral MFNmarket access negotiations, first between A and B over the tariffs eachcontrols and the transfer between them, and second between A and Cover the tariffs each controls and the transfer between them.

3. Backward stealing and bargaining inefficiencies

According to Lemma 2, any point on the efficiency frontier mustsatisfy (R1), and under (R1) efficiency condition (4) implies:

�Wn jtj

Wn jτj

= 0 N −WAtA

WAτj

N � Wjtj

Wjτj

for j; n j∈ B;Cf g ð5Þ

where we use dtA/dt j=1 for ja{B, C}. With τj on the vertical axis andt j on the horizontal axis, Fig. 2 depicts the “lens” implied by Eq. (5). AsFig. 2 illustrates, beginning from any efficient policy combination,the governments of country A and either of its trading partners canenjoy mutual gains – at the expense of the government of the thirdcountry – if A's transfer to this trading partner is increased slightlyabove the efficient level (denoted t jE) and the trading partner's tariff isreduced slightly below the efficient level (denoted τ jE). We summa-rize this observation with:

Lemma 3. At any point on the efficiency frontier, and for j; n j ∈ {B, C}, itis possible to reduce τ j and increase t j so as to increase WA and Wj at theexpense of W\j.

The lens described in Lemma 3 is significant, because it signals thebroad potential for a “backward-stealing” problem when govern-ments negotiate bilaterally and sequentially, even when thosenegotiations are constrained to abide by MFN. In effect, with no changeto its own tariff whatsoever, the government of country A can use itstransfer policy to “pay” one of its trading partners to liberalize and

Fig. 2. The backward-stealing lens for j,\j∈{B, C}.

53K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

generate a beneficial improvement in A's terms of trade, all at theexpense of the third country.10

WenowdefinetheBasicSequentialMFNGameor, forshort, theBasicGame. In stage 1, country A makes a take-it-or-leave-it proposal to Bconcerning tariff bindings (i.e., permissible upper bounds on appliedtariffs) τA and τ–B, as well as a transfer from A to B, t–B. Then, in stage 2,countryAmakesa take-it-or-leave-itproposal toCconcerningbindingsτ–A (with the stage-2 binding τ–A set no higher than its stage-1 level τA)and τ–C, as well as a transfer from A to C, t–C. The Basic Game has thefollowing features:

Stage 1: A proposes {τA, τ–B, t–B}, which B accepts or rejects.Stage 2: If B accepts, A proposes {τ–A≤ τA, τ–C, t–C}, which C accepts or

10 Lemma 3indicate in thbilateral intediscriminatorthat can be etariffs that ththat the MFNthe particularefficiency frois that eveninternationaltariffs with biwhat is achiesome indepethe often-statGATT/WTO sstatement of11 In subseqthat are recesection, we nindependent12 We assumin its “natura(1987) obserreject A's offreceiving we

rejects. If B rejects, A proposes {τ–A, τ–C,t–C}, which C accepts orrejects.

The Basic Game is illustrated in Fig. 3.11 Here and throughout thepaper,we assume that, subsequent to the conclusionof negotiations (e.g.,after stage 2 of the Basic Game), each government sets its applied tariffunilaterally and simultaneously with the other governments subject tothe constraint that it does not exceed its negotiated tariff binding(s).

We impose a global “stability” condition on tariff reaction curves torule out the existence of “unstable” Nash equilibria.12 Denoting j's

is related to Propositions 5 and 8 of Bagwell and Staiger (2005). As wee Introduction, in that paper we did not allow governments to makernational transfers. Proposition 5 of that paper established in ay tariff environment that any efficient tariff vector produces a “lens”ntered into by A and j through mutual reductions in the (discriminatory)ey apply to one another's imports. Proposition 8 of that paper showedrestriction can reduce, but cannot eliminate, the possibility of a lens, insense that the existence of a lens is confined to a subset of points on the

ntier when the MFN restriction is imposed. What Lemma 3 above impliesthis limited effect of MFN on the existence of a lens is undone whentransfers are possible. This is because the possibility of joining MFNlateral international transfers effectively allows governments to replicatevable with discriminatory tariffs alone. This implication may itself be ofndent interest, because it suggests a possible note of caution regardinged proposals to make direct international transfers an explicit part of theystem (see Kowalczyk and Sjostrom, 1994, for a particularly forcefulthis proposal, and also Bronckers and van den Broek, 2005).uent sections, we introduce notation for and discuss in detail the payoffsived when some or all of A's proposals are rejected. For the presenteed only note that the payoff for C when B accepts and C rejects isof the specific proposal that C chose to reject.e that an interior Nash equilibrium exists in which each country trades

l” direction, i.e., in the direction that would prevail absent tariffs. As Dixitves, autarky Nash equilibria may exist as well. In the event that B and Cer, we assume that the interior Nash equilibrium is played, with j thenlfare WjN for ja {A, B, C}.

best-response tariff function by τjR(•) for ja{A, B, C} (and recallingthat subscripts denote partial derivatives), this stability condition isrecorded in:

Each country's best-response tariff function everywhere satisfies“reaction-curve stability,” i.e., for i≠j≠k∈ A;B;Cf g

1 NτiRτj τjR

τi+ τjR

τkτkRτi

h i+ τiRτk τkRτi + τkRτj τ

jRτi

h in o1� τkRτj τ

jRτk

h i ðA3Þ

In words (A3) ensures, for example, that binding A's tariff below itsreaction curve could not induce changes in the best-response tariffs ofB and C which, together, would induce an even greater reduction inA's best-response tariff. As with (A1) and (A2), we treat (A3) as amaintained assumption in what follows.

Analysis of the Basic Game is made complicated by the fact thatgovernments negotiate tariff bindings, which only place upper limitson their applied tariffs. We therefore describe at this point only thesubgame which is featured in our next result, namely, the subgame inwhich both B and C accept A's proposals.When both B and C agree, wedenote the tariffs applied under the (full) agreement by τA≡τA(τ–, t–),τB≡τB(τ–, t–), and τC≡τC(τ–, t–), where τ– denotes the vector of final tariffbindings {τ–A, τ–B, τ–C} and t– denotes the vector of transfers { t–A, t–B, t–C}.The tariffs τA, τB and τC are defined by the first-order conditions

WAτA + λA = 0; WB

τB + λB = 0; and WCτC + λC = 0 ð6Þ

evaluated with tB= t–B and tC= t–C, and where λA, λB and λC are theLagrange multipliers on the constraints τA≤τ–A, τB≤τ–B and τC≤τ–C,respectively. By Eq. (6), τA=min{τ–A, τAR (τB, τC, t–A)} is the appliedtariff for A, B's applied tariff is τB=min{τ–B, τBR(τA, τC, t–B)}, and C'sapplied tariff is τC=min{τ–C, τCR(τA, τB, t–C)}. In this subgame, the payoffsfor A, B and C, are respectivelywA(τ–, t–)≡WA(τA, τB, τC, t–A),wB(τ–, t–)≡WB(τA, τB, τC, t–B), and wC(τ–, t–)≡WC(τA, τB, τC, t–C).

Fig. 3. The basic game.

13 When it is clear from context, we let τjR denote j's best-response tariff to theapplied tariffs of A and \ j when tj≡0 for j,\ ja{B, C}.

54 K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

We focus on subgame perfect equilibria (SGPE) of the Basic Game.We will say that the outcome is efficient (inefficient) when thepayoffs correspond to a point on (off) the efficiency frontier. Under(A1), we are interested in points on the efficiency frontier where eachcountry's (applied) tariff is constrained to lie below its reaction curve.Clearly, achieving such a point as the outcome of the Basic Gamerequires that A reach agreement with both B and C, and at such a pointeach country's applied tariff is then set equal to the level of its binding,or τj=τ–j for ja{A, B, C}. From our description of the subgame justabove, we must then have wA(τ–, t–)=WA(τ–, t–A), wB(τ–, t–)=WB(τ–, t–B),and wC(τ–, t–)=WC(τ–, t–C). Hence, we ask whether there exists a SGPEof the Basic Game in which the associated choices of (τ, t–) imply atriple {WA(τ–, t–A),WB(τ–, t–B),WC(τ–, t–C)} that is efficient. We now state:

Proposition 1. There does not exist a SGPE of the Basic Game in whichthe outcome is efficient.

This result may be seen as follows. Starting from stage-2 choicesthat would achieve the efficiency frontier, A and C can do better forthemselves if C liberalizes further (i.e., reduces τ–C). C's importliberalization benefits A by increasing the price of A's export good onworld markets (i.e., by improving A's terms of trade), and A cancompensate C for C's implied welfare loss with an increased transferto C (i.e., increased t–C) while enjoying the gains from higher exportprices against B. Hence, efficient outcomes are precluded by thebackward-stealing problem identified in Lemma 3.

Finally, we observe that, while we have derived Proposition 1 in atake-it-or-leave-it bargaining context, it is clear fromFig. 2 (with j=C)that the proposition holds inmore general bargaining environments aswell, provided only that the stage-2 bargain between A and C isefficient (i.e., exhausts all feasible gains fromcooperation in that stage)and therefore leads to a tangency between the indifference curves of Aand C in Fig. 2.

4. Forward manipulation and bargaining inefficiencies

Backward stealing prevents efficient outcomes in the Basic Gameanalyzed in the previous section. Suppose, then, that a “securityconstraint” were introduced into the Basic Game, wherein thegovernments of countries A and C were prevented from reducing thewelfare of B with their negotiations. (We postpone the question ofhow such a constraint might be maintained until Section 6.) Couldgovernments achieve efficient outcomes in this augmented bargaininggame? In this section, we show that the answer to this question isgenerally “No.”More specifically, we identify an incentive for “forwardmanipulation” that can keep governments from the efficiency frontier.

To accomplish this, we impose on the Basic Game the followingsecurity constraint: any agreement reached in stage-2 between A and Cmust leave B at least aswell off as it would be if instead the negotiationsbetweenAandCended indisagreementandonly the stage-1 agreementwere implemented. Under this security constraint, there certainly canbe no backward stealing. Hence, we say that a stage-1 agreementbetween A and B is secure against backward stealing if and only if,following an agreement between A and B in stage 1, any agreementbetween A and C satisfies this security constraint.

In order to formalize this constraint, wemust define B's payoff in thesubgame of the Basic Game where B accepts and C rejects. In thissubgame, there is no transfer between A and C, and C does not agree tobind its tariff,whileA andB agree to bind their tariffs and agree aswell toa transfer between them. Hence, in this subgame, C selects its best-response tariff, τCR, to the tariffs applied by A and B under theiragreement. We denote the tariffs applied by A and B under theiragreement by τA\C≡τA\C(τA, τ–B, t–B) and τB\C≡τB\C(τA, τ–B, t–B), respec-tively. The tariffs τCR, τA\C and τB\C satisfy the threefirst-order conditions

WCτC = 0; WA

τA + λAnC = 0; and WBτB + λBnC = 0 ð7Þ

evaluatedwith tB=t–B and tC≡0, andwhereλA\C andλB\C are the Lagrangemultipliers on the constraints τA\C≤ τA and τB\C≤τ–B, respectively.13 ByEq. (7), τA\C=min{τA, τAR(τB\C, τCR, t–B)} is A's applied tariff, and B'sapplied tariff is τB\C=min{τ–B, τBR(τA\C, τCR, t–B)}. In this subgame, then, Breceives wB\C(τA, τ–B, t–B)≡WB(τA\C, τB\C, τCR, t–B). We may now state thesecurity constraint formally:

wB τ–; t–� �

≥wBnC τA;τ–

B;t–

B� �ð8Þ

We next define the Secure-Contract Game. In stage 1 of this game,country A makes a take-it-or-leave-it proposal to B concerningbindings τA and τB, as well as a transfer from A to B, t–B. Then, instage 2, country Amakes a take-it-or-leave-it proposal to C concerningbindings τ–A (with the stage-2 binding τ–A set no higher than its stage-1level τA) and τ–C, aswell as a transfer fromA to C, t–C, subject to ensuringthat any agreement reached in stage 1 is secure against backwardstealing. The Secure-Contract Game has the following features:

Stage 1: A proposes {τA, τ–B, t–B}, which B accepts or rejects.

Stage 2: If B accepts, A proposes {τ–A≤τA, τ–C, tC}, where wB(τ–, t)≥wB\C(τA, τ–B, t–B), which C accepts or rejects. If B rejects, A

proposes {τ–A, τ–C, t–C}, which C accepts or rejects.

We introduce a second “stability” condition for the best-responsetariff functions:

Each country's best-response tariff function everywhere satisfies“terms-of-trade stability,” i.e., for i≠j≠k∈ A;B;Cf g;

∂ pw

∂τi

( )×

∂ pw

∂τi+

∂ pw

∂τjτjRτi+ τjR

τkτkRτi

h i1� τkRτj τ

jRτk

h i +∂ pw

∂τkτkRτi + τkRτj τ

jRτi

h i1� τkRτj τ

jRτk

h i8<:

9=; N 0

ðA4Þ

In words (A4) ensures, for example, that the drop in the market-clearing terms of trade implied by a reduction in B's tariff below itsreaction curve would not be completely reversed by the best-response tariff adjustments of A and C that B's tariff reductionwould induce.

To characterize the SGPE of the Secure-Contract Game, it is usefulto begin by considering the disagreement welfare levels in this gamefor the governments of countries B and C, in the event that A reachesagreement with the other trading partner.

For B, this disagreement welfare is determined by the equilibriumof the stage-2 subgame between A and C that follows stage-1disagreement between A and B. In this subgame there is no transferbetween A and B, and B does not agree to bind its tariff, while A and Cagree to bind their tariffs and agree aswell to a transfer between them.Hence, in this subgame, B selects its best-response tariff, τBR, to thetariffs applied by A and C under their agreement.We denote the tariffsapplied by A and C under their agreement by τA\B≡τA\B(τ–A, τ–C, t–C) andτC\B≡τC\B(τ–A, τ–C, t–C), respectively. The three tariffs τBR, τA\B and τC\B aredefined by the three first-order conditions

WBτB = 0; WA

τA + λAnB = 0; and WCτC + λCnB = 0 ð9Þ

evaluated with tB≡0 and tC= t–C, and where λA\B and λC\B are theLagrange multipliers on the constraints τA\B≤τ–A and τC\B≤τ–C,

15 To see this, suppose that Eq. (11) is violated so that τA≥τAR(τB\C, τCR, t–B) and τ–B≥τBR(τA\C, τCR, t–B). In this case, if C were to disagree in stage 2, A's stage-1 proposal wouldimplement the Nash tariff equilibrium under the transfer t–B. Moreover, to satisfyEq. (10a), the implied world price under the stage-1 proposal must be the same as theworld price implied by the full agreement: if the world price were to move against B inthe full agreement, B would be hurt as long as it remained on its reaction curve, andhurt further once it was held below its reaction curve by τ–B, and so Eq. (10a) could nothold for world price movements in this direction; if the world price were to move in B'sfavor, B would benefit as long as it remained on its reaction curve, and could be hurt byfurther world price movements in this direction once it was forced below its reactioncurve by τ–B, but satisfying Eq. (10a) in this fashion would be inconsistent withefficiency and (A1) and (A2). So the (Nash) world price implied under the stage-1proposal is also the world price implied under the full agreement. Finally, according to(A1), we must have B's applied tariff rise from its (Nash) level under the stage-1agreement to the efficient level τ–B. This implies, then, that the transition from the

55K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

respectively. By Eq. (9), τA\B=min{τ–A, τAR(τBR, τC\B, t–C)} is A's appliedtariff, and τC\B=min{τ–C, τCR(τA\B, τBR, t–C)} is C's applied tariff. In thissubgame, then, B's payoff is wBD(τ–A, τ–C, t–C)≡WB(τA\B, τBR, τC\B, tB≡0).Letting A's equilibrium stage-2 proposal to C in this subgame bedenoted by {τ–A\B, τ–C\B, t–C\B}, and observing that C will accept theequilibrium proposal, B's disagreement welfare in its stage-1negotiation with A is then given by wBD(τ–A\B, τ–C\B, t–C\B).14 For futurereference, we denote B's disagreement welfare by W

—BD. Importantly,as viewed from stage 1, W

—BD is tied down by the requirement ofsubgame perfection, and A therefore has no means by which to(credibly) manipulate B's disagreement welfare to its own advantage.

Circumstances are different, however, for the government of countryC. Its disagreement welfare iswCD(τA, τ–B, t–B)≡WC(τA\C, τB\C, τCR, tC≡0).Recalling that τA\C=min{τA, τAR(τB\C, τCR, t–B)} and τB\C=min {τ–B,τBR(τA\C,τCR,t–B)}, the key point is that C's disagreement welfare leveldepends on the stage-1 agreement reached between A and B and hence,in contrast to B, A can (credibly)manipulate C's disagreementwelfare toits own advantagewith its stage-1 policy proposal to B.We now presentthe next Lemma, which is proved in the Appendix and summarizes theimportant properties of wCD:

Lemma 4. wCD(τA,τ–B, t–B)=WC(τA,τ–B, τCR, tC≡0) for τAbτAR (τB\C, τCR, t–B)and τ–BbτBR(τA\C, τCR, t–B), and for any such (τA, τ–B) that, together with τCR,fails to drive C to autarky, wCD(τ A, τ–B, t–B) is strictly decreasing in τA, strictlyincreasing in τ–B, and independent of t–B.

In effect, with disagreement placing C on its reaction curve and for anyτAbτAR(τB\C, τCR, t–B) and τ–BbτBR(τA\C, τCR, t–B) that fail to drive C toautarky, C's disagreement welfare falls with a small adjustment ineither τA or τ–B that lowers the implied world price Pw(τA, τ–B, τCR). Welet PCa

w be the world price when C disagrees if its disagreement welfareis driven to the minimum (autarky) level, which we denote by W

—minCD .

We wish to explore the conditions under which the SGPE of theSecure-Contract Game lead to efficient outcomes. Consider any stage-1proposal {τA, τ–B, t–B} that would induce in the Secure-Contract Game apoint on the efficiency frontier {W

—AE,W—BE,W

—CE} forwhichW—CENW

—minCD .

This proposal must satisfy

wBnC τA;τ–

B; t–B

� �= W

— BE ≥ W— BD ð10aÞ

and

wCD τA; τ–B; t–B

� �= W— CE ð10bÞ

The first part of condition (10a) states that the security constraintmust hold with equality: if it held with strict inequality there wouldbe room for backward stealing according to Proposition 1. The secondpart of condition (10a) states that B must receive at least itsdisagreement welfare level. And the condition in (10b) must hold,since otherwise either C would reject A's stage-2 offer (if “N”) or Acould reduce the transfer to C in its stage-2 offer and do better (if “b”).In addition, this proposal must satisfy

τ AbτAR τBnC;τCR; t–

B� �;and= or τ–

BbτBR τAnC;τCR; t–

B� �ð11Þ

14 To see that C will accept A's equilibrium proposal, observe that this is assuredprovided that there exists an agreement between A and C that beats Nash (for them)when B has not agreed with A, and B is therefore on its tariff reaction curve. Under(A4), the following agreement accomplishes this. (i) Set τ–C slightly below C's Nash(and reaction curve) tariff level, and set τ–A above A's resulting best-response tarifflevel. This creates a second order loss for C, and by (A4), it worsens the terms of tradefor B and improves the terms of trade for A. Since both A and B remain on theirreaction curves, B suffers a first-order loss while A enjoys a first-order gain (this can beestablished as in the Appendix proof of Lemma 4). (ii) Set t–C slightly positive, to offsetthe second order loss of C, and preserve A's first-order gain.

Otherwise, the proposal could not induce a point on the efficiencyfrontier.15 We prove in the Appendix:

Proposition 2. Under (A4), there does not exist (generically) aSGPE of the Secure-Contract Game in which the outcome is efficientand W

— CENW—

minCD .

Intuitively, beginning from proposals that efficiently deliver W—BE

and W—CE, if W

—CENW—

minCD , then Eq. (11) and (A4) together ensure that

there exists (generically) an adjustment in τA or τ–B which reduces C'spayoff and, along with adjustments in t–B, τ–A, τ–C, and t–C, improves A'spayoff.

Evidently, efficiency in the Secure-Contract Game requires thatW—CE=

W—

minCD , and this requirement places rather extreme demands on the

environment within which the Secure-Contract Game can delivergovernments to the efficiency frontier. In particular, with τ–B tied downby the combination of policies to which A must navigate to achieve thisoutcome, it must then be feasible for A to position τA so that C facesautarky if it rejects A's stage-2 proposal.16 If this cannot be accomplishedwith a choice of τA, because for example accomplishing thiswould requireA to set an applied tariff τA\C thatwas above its best-response level, thenAcannot both give C its minimal payoffW

—minCD and achieve efficiency, and in

this case Proposition 2 indicates that A will find it desirable to sacrificeefficiency in order to lower C's payoff toward W

—minCD . More generally,

Proposition 2 suggests that governments will achieve efficient bargainingoutcomes in theSecure-ContractGameunder somespecial circumstances,but under many plausible circumstances the outcome of the Secure-Contract Game is inefficient.

The source of inefficiency identified in Proposition 2 arises from A'sdesire to use its stage-1 negotiations with B to position itself morefavorably for stage-2 negotiations with C by sticking C with a less-favorable disagreement point. Fig. 4 illustrates. With τA on the verticalaxis and t–B on the horizontal axis, we consider a stage-1 proposal underwhich it would be “feasible” to achieve efficiency, i.e., a stage-1 proposal{τAf, τ–Bf, t–Bf} thatwould induce in the Secure-ContractGame the efficientpoint {W

—AE, W—BE, W

—CE} with {W—BE=W

—BD} and W—CENW

—minCD . We have

observed that attention may be restricted to stage-1 proposalsthat satisfy Eq. (11), and for purposes of illustration we assumethat τAfbτAR(τB\C, τCR, t–Bf) and τ–BfbτBR (τA\C, τCR, t–Bf). According toProposition 2, A would not choose τAf and t–Bf if it chooses τ–Bf. Wewish to illustrate in this case that it is always possible for A to raise itswelfare by proposing τA′NτAf. To understand why, let us fix τ–B at τ–Bf

and consider varying the proposed τA and t–B around τAf and t–Bf,respectively, so as to hold wB\C(τA, τ–Bf, t–B) fixed at W

— BD. Under the

stage-1 agreement to the full agreement describes a movement from the Nash tariffequilibrium (under the transfer t–B) to a point on the efficiency frontier, in which (i) theworld price remains unaltered, (ii) B's tariff is raised, and therefore (iii) B's tradevolume is diminished. But it is easy to demonstrate that achieving a point on theefficiency frontier at the Nash world price is inconsistent with a drop in B's tradevolume.16 More specifically, achieving W

— CE=W—

minCD requires that C face its autarky terms-of-

trade PCaw in the event that it rejects A's stage-2 proposal, and therefore, by (A3) and

(A4) and maintaining our focus on interior Nash equilibria, a stage-1 proposal thatachieves efficiency requires that τ–BbτBR(τA\C, τCR, t–B). As a consequence, τ–B and t–B mustbe consistent with efficiency and satisfy W

— B(PB(τ–B, PCaw), PCa

w, t–B)=W— BD by Eq, (10a).

Fig. 4. The forward-manipulation lens.

56 K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

security constraint, Bwill accept any suchproposal. Further, let the stage-2 proposal of {τ–A, τ–C, t–C} that is associatedwith any {τA, τ–Bf, t–B}maximizeWA(τ– , t–A) subject to WB(τ– , t–B)=wB\C(τA, τ–Bf, t–B) and WC(τ– , t–C)=wCD(τA, τ–Bf, t–B) and τ–A≤ τA. Clearly, C will accept the stage-2proposal, and so by construction the welfare level for A associatedwith WA(τ–, t–A) is attainable in the Secure-Contract Game. In effect,then, with τ–B

fixed at τ–Bf, any change in τA and t–B implies by thisconstruction an associated change in {τ–A, τ–C, t–C}, and Fig. 4 depicts thewelfare consequences of these changes.

Consider, then, the indifference curves associated with WA(τ–, t–A),WB(τ–, t–B) and WC(τ–, t–C) under this construction which pass throughthe efficient point (τAf, t–Bf) in Fig. 4. C's indifference curve is horizontalthrough this point, since WC(τ–, t–C)=wCD(τA, τ–Bf, t–B) is strictlydecreasing in τA but independent of t–B by Lemma 4. B's indifferencecurve through this point could have positive or negative slope (it isdepicted in the figure with positive slope) but, importantly, it cannotbe horizontal, since WB(τ–, t–B)=wB\C(τA, τ–Bf, t–B) is strictly increasingin t–B. Therefore, the indifference curves associated withWB(τ–, t–B) andWC(τ–, t–C) are not tangent to each other as they pass through theefficient point (τAf, t–Bf) in Fig. 4, and as a consequence, by efficiencycondition (4) A's indifference curve cannot be tangent to either B's orC's indifference curve at this point. Moreover, A's indifference curvemust be flatter than B's at this point, since otherwise a “downward”lens would exist between the indifference curves of A and B intowhich A and B could move and all three governments would gain,contradicting the efficiency of this point. Therefore, as Fig. 4 depicts,there is an “upward” lens created by the indifference curves of A and Bat this point, implying that A can gain by raising τA above τAf andadjusting t–B to maintain B's welfare. A's gain from this maneuvercomes at the expense of C's welfare (and multilateral efficiency).17

We observe that this logic is related to a concern about the “foot-dragging” maneuver for handling free-riders as this maneuver wasdescribed in the Introduction. According to this concern, country Amight be induced under MFN to offer “too little” in the way of tradeliberalization to its early negotiating partners, in order to maintain itsbargaining position for later negotiations. Proposition 2 provides a

17 As noted, Figure 4 illustrates the case where W— BE=W

— BD and W— CENW

—minCD . If there

exists a (τAf, τ–Bf) underwhich it is feasible to efficiently deliverW— BE=W

— BD andW— CE=

W—

minCD in the Secure-Contract Game, then at this point there is no lens between A and B.

For example, in the casewhere τAfbτAR (τB\C, τCR, t–Bf) and τ–BfbτBR (τA\C, τCR, t–Bf), a smallchange in τA and an accompanying change in t

–B that left B indifferent would leave Cindifferent as well (C would be indifferent to any small change in τA and t

–B by the first-order condition that definesW

—minCD ), and so by efficiency condition (4) A's indifference

curve must be tangent to B's indifference curve as well in this case.

formal justification for this concern, and Fig. 4 illustrates the foot-dragging incentive to maintain τA above its efficient level.

In summary, Proposition 2 indicates that the Secure-Contract Gamecan deliver efficient bargaining outcomes only in a very limited set ofcircumstances. In the circumstances where inefficiency arises, thisinefficiency is associatedwith forwardmanipulation. In thenext section,we consider how this new source of inefficiency might be handled.

5. Preventing forward manipulation through GATT/WTO rules

One way to correct the inefficiency associated with forwardmanipulation is to eliminate the possibility of forward manipulationitself. In principle, this might be achieved by introducing renegotiationopportunities, provided that these renegotiation opportunities aresufficiently “sweeping” so that they separate C's disagreement payofffrom the stage-1 determination of {τA, τ–B, t–B}. In fact, during theUnited States experience with bilateral MFN tariff bargaining underthe RTAA, the threat to withdraw ormodify a concession granted to anearly negotiating partner was seen as providing an important “offequilibrium path” means of maintaining bargaining leverage for laternegotiations with other countries (see Tasca, 1938, p. 146), and it mayhave reduced to some extent the reliance on foot-dragging for thispurpose.

The GATT/WTO explicitly provides for renegotiation. This is trueboth within a multilateral round of negotiation, when agreementsreached between negotiating pairs early in the round are viewed astentative and may be revisited if subsequent negotiations with otherpartners do not go as expected (e.g., Jackson, 1969, p. 220), and it isalso true outside of multilateral rounds, where explicit renegotiationsof previous agreements are permitted (e.g., Jackson, 1969, pp. 229–238). Just how sweeping these renegotiating opportunities are is aquestion of degree, and presumably depends on circumstances.

In this section, we consider whether introducing sweepingrenegotiation possibilities into the Secure-Contract Game can solvethe forward-manipulation problem and lead (in the presence of thesecurity constraint) to efficient outcomes. We first describe the novelfeatures of the Contract Renegotiation Game:

Stage 1: A proposes {τA, τ–B, t–B}, which B accepts or rejects.Stage 2: If B accepts, A proposes {τ–A≤ τA, τ–C, t–C}, where wB(τ–, t–)≥

18 As Figure2, or (ii) B aassume thatcorrespondin

wB\C(τA, τ–B, t–B), which C accepts or rejects. If B rejects, Aproposes {τ–A, τ–C, t–C}, which C accepts or rejects.

Stage 3: If B accepts in stage 1 and C rejects in stage 2, then A proposes

c

{τ–Ar, τ–Br, t–Br}, which B accepts or rejects.

The Contract Renegotiation Game is illustrated in Fig. 5. Notice thatwe have modeled the renegotiation stage 3 as arising only if B acceptsA's original proposal in stage-1 (we have also modeled renegotiationas arising only if C rejects in stage 2, but this is not crucial).18With thismodeling choice, we attempt to capture the relative ease with whichearlier “tentative” agreements can be adjusted within GATT/WTOrounds and/or earlier commitments can be renegotiated under GATTArticle XXVIII between rounds.

In the Secure-Contract Game, the source of inefficiency can betraced to the problem of forward manipulation, whereby A's stage-1proposal to B influences C's disagreement payoff in its stage-2negotiations with A. In the Contract Renegotiation Game, this linkagehas been curtailed, but it has not been eliminated. To see this, notethat if B accepts A's stage-1 proposal, and if C then rejects in stage 2,C's disagreement payoff will be determined by the renegotiationbetween A and B in stage 3. In this case, the details of A's stage-1

5 illustrates, in the event that (i) B rejects in stage 1 and C rejects in stagecepts in stage 1, C rejects in stage 2 and then B rejects in stage 3, wethe players adopt their Nash equilibrium strategies and earn the

g Nash payoffs.

Fig. 5. The contract renegotiation game.

19 It might be wondered why bypass does not arise in the Secure-Contract Game. Thereason is that, after B accepts, A can pin C at a welfare level that is lower than WCN,since no further negotiations follow, and so A has no incentive to bypass B.20 Formally, for j,\ja {B, C}, and with tj≡0≡ t\ j, consider the three tariffs defined byŴPA

A =0, ŴPjj =0 and Wτ\ j

\ j =0. Country j may be said to be a symmetric participantwith A in a multilateral Nash tariff war if the terms of trade implied by these threetariffs is equal to the terms of trade implied by the Nash tariffs defined by Wτi

i =0 foria {A, B, C}. Intuitively, with country \j positioned on its reaction curve, when countriesA and j are symmetric participants in a multilateral Nash tariff war, neither succeeds inmoving the terms of trade in its favor relative to the terms of trade that would obtain ifeach chose its tariff “without terms-of-trade considerations in mind,” i.e, so as to solveŴPA

A =0 for A andŴPjj=0 for j. With this definition in hand, it may now be seen that, if

A and j are symmetric participants in the multilateral Nash tariff war, then a bilateralagreement between them could achieve ŴPA

A =0 for A and ŴPjj=0 for j while

preserving the Nash terms of trade, thereby preserving as well the welfare of \j; butfrom here A could do better yet with an alternative proposal that worsened j's terms oftrade below the Nash terms of trade and compensated j with a higher transfer tj, andthe lower-than-Nash terms of trade under this alternative proposal would leave \jwitha lower-than-Nash welfare (for the proof that a government positioned on its tariffreaction curve experiences welfare changes that are the same sign as changes in itsterms of trade, see the proof of Lemma 4 in the Appendix). Arguing in this fashion, itcan be seen that (A5) holds if B and C are not too asymmetric with A when theyparticipate in a multilateral Nash tariff war.

57K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

proposal to B are immaterial for C's disagreement payoff in its stage-2negotiations with A, provided only that B accepts A's stage-1 proposaland therefore “locks in” a stage-3 renegotiation opportunity with Ashould C disagree in stage 2. However, if B does not accept A's stage-1proposal, then B has no renegotiation rights with A in stage 3, and soin this case C's disagreement payoff in its stage-2 negotiations with Awill be its Nash payoff. As a consequence, in the Contract Renegoti-ation Game the possibility of forward manipulation has been reducedto the question of “bypass”: Might A choose to make an unacceptableproposal to B in stage 1 in order to bypass B and negotiate with Cagainst a Nash disagreement payoff? The question of bypass can alsobe seen to arise with C: Having made a stage-1 proposal that wasaccepted by B, might A choose to make an unacceptable proposal to Cin stage 2 in order to bypass C and renegotiate with B against a Nashdisagreement payoff in stage 3?

To ensure that the bypass problem does not prevent governmentsfrom reaching the efficiency frontier in the Contract RenegotiationGame, an additional condition is needed. To state this condition,consider the particular disagreement welfare levels in this game forthe governments of countries B and C, in the event that A reachesagreement with the other trading partner. For the government ofcountry B, this disagreement welfare is determined by the equilibriumof the stage-2 subgame between A and C that follows stage-1disagreement between A and B. This subgame is identical to that in theSecure-Contract Game, and we previously recorded B's payoff in thissubgame as wBD(τ–A\B, τ–C\B, t–C\B)≡WB(τA\B, τBR, τC\B, tB≡0), which wedenoted byW

— BD. For the government of country C, this disagreementwelfare is determined by the equilibrium of the stage-3 (renegotia-tion) subgame between A and B that follows stage-1 agreementbetween A and B and stage-2 disagreement between A and C.Denoting A's equilibrium proposal in this subgame by {τ–A\C, τ–B\C, t–B\C},C's payoff in this subgame is wCD(τ–A\C, τ–B\C, t–B\C)≡WC(τA\C, τB\C, τCR,tC≡0), which for future reference we denote by W

—CD.Importantly, as viewed from stage 1 (stage 2), W

—BD (W—CD) is tied

down by subgame perfection, and A therefore cannot manipulate thesedisagreement payoff levels to its own advantage. Bypass, however,concerns the possibility that Amight choose to confront a negotiating

partner with the Nash disagreement payoff WjN rather than W— jD for

ja{B, C}. We now state a condition to rule out the bypass problem:

—W

BD≤WBN;—W

CD≤WCN ðA5Þ

Under (A5), the minimal disagreement payoffs for B and C in theContract Renegotiation Game are given by W

—BD and W—CD, respectively,

and each of these disagreement payoffs is achieved onlywhen A reachesan initial agreement with the other trading partner.19 Condition (A5)essentially requires thatB andCnot be too asymmetricwithAwhen theyparticipate in amultilateralNash tariff war.20Weprove in theAppendix:

Proposition 3. Under (A5), forward manipulation does not impede theattainment of the efficiency frontier in the Contract Renegotiation Game.

When viewed in light of Proposition 2, Proposition 3 suggests thatrenegotiation provisions such as those provided in the GATT/WTO can

58 K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

alleviate the efficiency costs associated with forward manipulation, inthe sense that efficient bargaining outcomes may be anticipated in awider set of circumstances, at least so long as these provisions allowfor sufficiently “sweeping” renegotiation opportunities as we havemodeled them here. Still, as (A5) indicates, as a general solution toforwardmanipulation, renegotiation has its limits, as it may introducea bypass problem into negotiations in some circumstances (i.e., in thecircumstances where (A5) is violated).

22 Formally, we may define the market access that one country affords to a second bythe first country's volume of import demand for the exports of the second country at agiven world price. Hence, the market access that countries B and C each afford to A ata given world price p w is defined by their respective import demands at that worldprice: MAj(τj, tj; p w)≡Mj(pj (τj, p w), p w, tj) for ja {B, C}. Similarly, the market accessthat country A affords to country j is A's residual import demand for j's exports – afterthe other country's export supply to A has been netted out – at a given world price:MAAj(τA, τ\j, tB, tC; p w)≡MA(pA(τA, p w), p w, tA) – E\j(p\j(τ\j, p w), p w, t\j) for ja {B, C}.Finally, we define the balance of market access rights and obligations between A and jthat is implied by a vector of negotiated tariffs and transfers at a given world price byBAj (τ, tB, tC; p w)≡ [MAj(τj, tj; p w) – pw×MAAj(τA, τ\j, tB, tC; p w)] for ja {B, C}, where alltariffs are evaluated at their applied levels. With this definition, it is thenstraightforward to show that two vectors of tariffs imply the same balance of marketaccess rights and obligations if and only if they imply the same terms of trade. Forfurther discussion of the relationship between the balance of market access rights andobligations and the terms of trade, see Bagwell and Staiger (2002).23 We have abstracted from a number of the legal/institutional elements associatedwith non-violation complaints in the GATT/WTO (see Bagwell et al., 2002, for a recentdiscussion of non-violation complaints in the GATT/WTO). Among them is the notionof what level of market access B could reasonably anticipate it had attained in its stage-1negotiation with A. Arguably, as the WTO is a forum for bilateral negotiations, itwould be unreasonable for B not to anticipate that countries A and C might engage insubsequent negotiations. But these subsequent negotiations may be structured in avariety of ways, some of which could potentially have large adverse impacts on B'sinterests. If the GATT/WTO norm of reciprocity is seen to define what B can reasonablyanticipate concerning the outcome of A's subsequent negotiations with C, then it maybe concluded that the anticipated stage-2 negotiations will leave B unaffected, andhence the level of market access that country B can reasonably anticipate as a result ofits stage-1 negotiations with country A is simply that which is implied by their stage-1negotiations. Notice that, according to this argument, reciprocity is not being imposedas an additional restriction on the outcome of stage-2 agreements. Instead, reciprocityis introduced as a negotiating norm: if a bilateral negotiation does not satisfy thisnorm, then the parties to the negotiation may be vulnerable to claims of nullification

6. Preventing backward stealing through GATT/WTO rules

We now reconsider and interpret the security constraint imposedin Section 4 and maintained throughout Section 5 (i.e., the require-ment thatwB(τ–, t–)≥wB\C (τA, τ–B, t–B)). As suggested by our “terms-of-trade manipulation” interpretation of the backward-stealing problemoffered in Section 3, there is a link between this security constraint anda requirement that stage-2 negotiations between A and C leaveunaltered the terms-of-trade implied as a result of stage-1 negotia-tions. This link is suggestive of a role forGATT/WTO rules in this regard,because as we have shown elsewhere (Bagwell and Staiger, 1999,2002) the GATT/WTO norm of reciprocity can be interpreted as fixingthe terms of trade, in the sense that “reciprocal” changes in marketaccess, i.e., changes that preserve the balance of market access rightsand obligations, leave the terms of trade unaltered.21 Guided by thissuggestion, we ask: Is there something in GATT/WTO rules that mightwork along the lines of such a security constraint?

To answer this question within our bargaining games, we focuson B's opportunity to respond to subsequent negotiations between Aand C that upset the original balance of B's market access rights andobligations in away that is unfavorable to B (i.e., that worsen B's termsof trade from the level implied by B's agreement with A). In thiscircumstance, we consider the possibility that B has the opportunity torespond with a tariff increase above its bound level that restores thisoriginal balance (i.e., that restores the original terms of trade). Thisopportunity can be seen to exist in the GATT/WTOwithin multilateralrounds of negotiation, in the sense that governments may choose tomodify or withdraw tentatively offered concessions when imbalancesarise at the conclusion of a round of GATT/WTO negotiations. And itcan be seen to exist as well between rounds of multilateralnegotiations, where governments have the opportunity to seekredress under the “non-violation nullification-or-impairment” provi-sions contained in GATT Article XXIII when they experience nullifica-tion or impairment of their market access rights as a result of anegotiating partner's subsequent (and GATT-legal) actions. In thissection, we seek to capture this opportunity formally, and askwhetherit might serve an analogous role to the security constraint analyzedabove. For concreteness, we focus explicitly on the between-roundsinterpretation, and in particular on the possible role for non-violationcomplaints in this context.

We introduce B's opportunity to respond to a non-violationnullification-or-impairment of its market access rights as follows.First, we define τBNV as the level of B's tariff which, in combinationwithτ–A and τ–C, wouldmaintain the terms of trade at the level implied by A'sstage-1 agreementwith B. Thus, for example, in the event that τ–A and τ–C

bind A and C below their respective reaction curves, τBNV is definedimplicitly by Pw(τ–A, τBNV, τ–C)= Pw(τA\C, τB\C, τCR). We then provide Bwith the opportunity to increase its tariff binding from an initiallyagreed-upon level τB to τBNV whenever A and C reach a stage-2agreement that implies a worsening of B's terms of trade (i.e., thatimplies Pw(τ–A, τB, τ–C)b Pw(τA\C, τB\C, τCR)). In this way, we endowBwiththe opportunity to restore the original balance of market access rights

21 Shirono (2004), Limao (2006, 2007) and Karacaovali and Limao (2008) provideempirical evidence of this form of reciprocity in GATT/WTO negotiations.

and obligations between it and country A if this balance is upset by A'ssubsequent negotiations with C.22

We now describe the WTO-Contract Game:

Stage 1: A proposes {τA, τB, t–B}, which B accepts or rejects.Stage 2: If B accepts, A proposes {τ–A≤ τA, τ–C, t–C}, which C accepts or

or impairmenaccess agreemthe designersconcern for mments.

rejects. If B rejects, A proposes {τ–A, τ–C, t–C}, which C accepts orrejects.

Stage 3: If B accepts in stage 1 andC accepts in stage 2, then B selects τ–B≤

max [τB, τBNV].

Stage 4: If B accepts in stage 1 and C rejects in stage 2, then A proposes

{τAr, τBr, tBr}, which B accepts or rejects.

The WTO-Contract Game is illustrated in Fig. 6. As compared to theContract Renegotiation Game, the WTO-Contract Game displays twodifferences. First, in stage 2, the security constraint is no longer imposed.And second, immediately after stage 2 (in the new stage 3), B's non-violation nullification-or-impairment response is inserted, permitting Bto choose to increase its tariff binding if this is required to prevent A'sstage-2 agreement with C from eroding B's terms of trade.23

We seek conditions under which any SGPE of the WTO-ContractGame will achieve a point on the efficiency frontier. We focus on thefeasibility of efficiently delivering W

—BD to B and W—CD to C under (A5),

since if this is feasible in the WTO-Contract Game then A will surelymake proposals that implement it. We say that it is feasible in theWTO-Contract Game to efficiently deliver W

—BD and W—CD if and only if there

exists a triple {τAf, τBf, t–Bf} such that the outcome of the WTO-ContractGame is efficient, satisfies (A1) and (A2), and gives B the payoffW

—BD andC the payoff W

—CD when the stage-1 proposal is {τAf, τBf, t–Bf}.Further progress can be made by considering a particular combina-

tion of efficient policies that we have elsewhere (e.g., Bagwell andStaiger, 1999) referred to aspolitically optimalpolicies.More specifically,for any level of transfers the politically optimal tariffs solve ŴP j

j =0 for

t by a third party, if the third party had previously negotiated a marketent with one of them. In this regard, Hudec (1990, pp. 23–24) notes thatof GATT added nullification-or-impairment provisions precisely out of aaintaining reciprocity established by negotiated market access agree-

Fig. 6. The WTO contract game.

59K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

ja{A, B, C}, and it can be shown that politically optimal tariffs achievetheefficiency frontier definedbyEq. (4).24 Intuitively, politically optimaltariffs are efficient, because the incentive of governments tomanipulatethe terms of trade with their tariff choices is the source of internationalinefficiency in theNash equilibriumand politically optimal tariffs do notreflect this incentive. We denote by τpo the vector of politically optimaltariffs τjpo for ja{A, B, C} that, along with associated transfers t jpo,efficiently deliver W

—BD and W—CD, and let Ppow ≡ Pw(τpo).25

By the first-order conditions that define them, politically optimaltariffs satisfy (A1) and (A2).26 Suppose, then, that there exists a τApo≥τApo

and a τBpo≤τBpo such that the stage-1 proposal {τA= τApo, τB= τBpo, t–B=tBpo} satisfies the condition Pw(τA\C, τB\C, τCR)=Ppo

w . If Awere tomake thisproposal in stage-1 and B accepted, then the level of τBNV which definesB's stage-3 non-violation right in response to a stage-2 agreementreached between A and C is defined implicitly by Pw(τ–A, τBNV, τ–C)=Ppo

w .Turningnowto stage2, if Awere tomakea stage-2proposal of {τ–A=τApo,τ–C=τCpo, t–C=tCpo} and if Cwere to accept this proposal, then τBNV=τBpo

and in stage 3 B would select τ–B=τBpo, and in this way W—BD and W

—CD

would be delivered efficientlywith politically optimal policies. Hence,wemay conclude that, provided there is no alternative stage-2 proposalwhich would be preferred by A, the existence of the stage-1 proposaldescribed above is sufficient to ensure that it is feasible in the WTO-Contract Game to efficiently deliverW

—BD andW—CD, and therefore that the

outcome of the WTO-Contract Game will be efficient.Consider, then, the possibility that A might deviate to an alternative

stage-2 proposal. Observe first that politically optimal tariffs exhibit the

24 This can be shown as follows: (i) express the three efficiency conditions in Eq. (4)in terms of the alternative Ŵj functions, (ii) impose that tariffs are politically optimal,and (iii) then use Eqs. (3) and (2) to confirm that the efficiency conditions aresatisfied.25 There must exist a set of politically optimal policies that delivers W

— BD and W— CD

provided only that the politically optimal tariffs are bounded from above and frombelow as transfers are altered.26 More specifically, (A1) and (A2) may be restated in terms of the Ŵj functions as,respectively, ŴP j

j×[dP j/dτj]+ŴP w

j×[∂Pw/∂τj]N0 for ja {A, B, C}, and sign [(Ŵ PB

B /τB+Ŵ P w

B )×∂Pw/∂τA]=sign [(Ŵ PCC /τC+Ŵ P w

C )×∂Pw/∂τA]. With politically optimal tariffsdefined by ŴP j

j=0 for ja{A, B, C,}, it is now direct to confirm that politically optimal

tariffs satisfy (A1) and (A2).

special feature that no government would desire a different tradevolume if this possibility were offered to it at fixed terms of trade (this iswhat ŴPj

j=0 for ja{A, B, C} means). As a consequence, A could not do

better under a deviant stage-2 proposal that satisfied Pw(τ–A, τ–B, τ–C)=Ppow

in light of B's stage-3 response, i.e., under a deviant stage-2 proposal thatimplies τBNVa [τB,τBR(τA\B,τC\B,tBpo)]. There are then two otherpossibilities.

A first possibility is that A could deviate to a stage-2 proposalimplying τBNVb τB, in which case τ–BNτBNV and Pw (τ–A, τ–B, τ–C)NPpow .27 Buteven if this proposal provided A and C with their ideal trade volumes(implyingŴPj

j=0 for ja{A, C}) at the new terms of trade, the decline in

A's terms of trade implied by Pw (τ–A, τ–B, τ–C)NPpow ensures that A cannotgain under such a deviation.28 The remaining possibility is that A coulddeviate to a stage-2 proposal implying τBNVNτBR (τA\B, τC\B, tBpo), inwhich case τ–B=τBR(τA\B,τC\B,tBpo) and Pw(τ–A,τ–B,τ–C)bPpow . The potentialfor A to gain from this kind of deviation arises because, with t–B=tBpo

alreadydetermined in stage 1,Amight achieve higherwelfarewith tarifflevels for itself andCwhichplaced B on its tariff reaction curve thanwithpolitically optimal tariffs. Letting (τpoA\B, τpoC\B, tpoC\B) denote the tariff choicesthat maximize WA(τA, τBR, τC, tA=tBpo+ tC) while delivering W

– CD to C,this potential is ruled out by:

WA τpo;tApo¼tBpoþtCpo� �

≥ WA τAnBpo ;τBR;τCnBpo ;tA¼tBpoþtCnBpo

� �ðA6Þ

If (A6) is violated, then by negotiating with C, A could “win thetariff war”with B (i.e, with the transfer to B, tBpo, paid in either case, Acould do better under non-cooperative tariff interaction with B than

27 To see that a stage-2 proposal by A implying τBNVbτB implies in turn that τBNτBNV,observe that: (i) stage-3 permits τBNτBNV in this case; and (ii) τBNVbτBpo in this case, sothat B's best-response tariff is strictly above τBNV (see note 26), and therefore B desiresτBNτBNV in this case as well.28 That A's payoffmust fall with a deviant stage-2 proposalwhich leads to a deteriorationin its terms of trade (i.e., a rise in Pw) can be seen as follows. Beginning from the politicaloptimum,A candonobetterunder a rising Pw than if the tariffs ofA andCare adjusted soastomaintainŴPj

j=0 for ja {A, C} and tC is adjusted so as tomaintainŴC=WCD. In this case,

wehave that dtC/dPw=−ŴPwC/ŴtC

C=−EC,where the second equality follows fromEq. (3),and therefore dŴA/dPw=ŴPw

A+ŴtA

A ×dtC/dPw=EB×ŴtAA b0, where the second equality

follows from Eqs. (2) and (3).

60 K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

under the politically optimal tariffs).29 Assumption (A6) effectivelyrules out this extreme degree of asymmetry, by requiring that B is notso small that A could win the tariff war. As there is no alternativestage-2 proposal which would be preferred by A, we may now state:

Lemma 5. Under (A5) and (A6) , in any SGPE of the WTO-ContractGame, the outcome is efficient if there exists a τApo≥τApo and a τBpo≤τBpo

such that the stage-1 proposal {τA=τApo, τB=τBpo, tB=tBpo} satisfiesPw (τA\C, τB\C, τCR)=Ppo

w .

Lemma 5 provides a sufficient condition for efficient outcomes inthe WTO-Contract Game. To interpret the circumstances under whichthis condition is met, we note that under (A3) and (A4), the highestvalue of P w(τA\C, τB\C, τCR) consistent with τApo≥τApo and τBpo≤τBpo isachieved at τApo=τApo and τBpo=τBpo. With τApo=τApo andτBpo=τBpo, (A3) and (A4) then imply Pw(τA\C, τB\C, τCR)NPpow .30 Onthe other hand, the lowest value of Pw(τA\C, τB\C, τCR) is achieved atτApo=τAR(τBpo, τCR, tBpo) and τBpo→0, and unless C is sufficiently largerelative to B we must then have P w(τA\C, τB\C, τCR)=Pw(τAR, τB→0,τCR)bPpow . Hence, if C is not too large relative to B, there will exist aτApo≥τApo and a τBpo≤τBpo such that the stage-1 proposal {τA=τApo,τB=τBpo, tB= tBpo} satisfies Pw(τA\C, τB\C, τCR)=Ppo

w . As a consequence,we may state:

Proposition 4. Under (A4), (A5) and (A6), in any SGPE of the WTO-Contract Game, the outcome is efficient provided that C is not too largerelative to B.

Observe that, if Pw(τA\C, τB\C, τCR)≤Ppow when τA=τAR and τB=τBpo,

which is guaranteed if C is sufficiently small, then achieving efficientpolitically optimal tariffs in the WTO-Contract Game can beaccomplished without the utilization of B's non-violation right (i.e.,we may then have τB=τBpo), but in this case negotiations between Aand C must conform to reciprocity (i.e., the movement from τApo toτApo and from τCR to τCpo must leave the terms of trade unaltered). Inthis way, Proposition 4 suggests that non-violation nullification-or-impairment rights can help to guard against backward stealing in anMFN environment by inducing later negotiations to abide by thereciprocity norm, and in doing so to preserve the value of earlierconcessions.31We note also that the requirement in Proposition 4 that

29 The fact that a large country might potentially “win the tariff war” with a smallercountry was pointed out originally by Johnson (1953–54) in the context of national-income-maximizing governments and explored further by Kennan and Riezman(1988). In those papers, a country's welfare under Nash tariffs is compared to itswelfare under free trade, and a country is said to win the tariff war if the former isbigger than the latter. The comparison we make above is related, but with twodifferences. First, the definition of τAnB

po ; τCnBpo ; tCnBpo

� �gives A a Stackelberg-leader

position while B is the Stackelberg follower, so that A's welfare when it interacts non-cooperatively with B is its Stackelberg-leader welfare, rather than its Nash welfare.Hence, the first difference is that the “tariff war” we refer to here is the Stackelbergtariff war rather than the Nash tariff war. And second, rather than comparing thewelfare under the tariff war to that under free trade, we compare it to welfare underpolitically optimal tariffs. We invoke the “win the tariff war” terminology in the textabove, because in the special case of national-income-maximizing governmentspolitically optimal tariffs correspond to free trade, and so in this case our comparison isbetween the (Stackelberg) tariff war and free trade.30 If both τApo and τ

Bpoimpose a binding constraint on A and B, respectively, when C

disagrees, then Pw τAnC; τBnC; τCR� �

= Pw τApo; τBpo; τCR� �

N Pwpo . If only τApo is non-

binding, then Pw τAnC ; τBnC ; τCR� �

N Pw τApo; τBpo; τCR� �

N Pwpo by (A3) and (A4). Finally,

if τBpo

is non-binding, then Pw τAnC; τBnC; τCR� �

N Pwpo by (A3) and (A4).

31 The idea that MFN tariff reductions conforming to reciprocity can neutralize 3rd-party effects is identified and explored in Bagwell and Staiger (2005). While it mightseem puzzling that a grant of market access through an MFN tariff cut could be offeredto one bargaining partner in exchange for a reciprocal tariff cut from that bargainingpartner without generating any greater trade flows from competing exporters locatedin third countries, the puzzle is resolved once it is observed that the bargainingpartner's own tariff cut will make its exporters more competitive relative to those inthird countries (which is why, as observed in note 5, it is important for our results thatthe exporting government's negotiated trade policy commitments can stimulate itsexports).

C is not large relative to B is suggestive of an efficiency-enhancing rolefor the “chief” – or “principal” – supplier rule utilized by the UnitedStates under the RTAA (see Tasca, 1938, pp. 146–147) and adopted aswell in the GATT/WTO, whereby the largest suppliers to a market aretypically granted the position of the early negotiating partners.

More broadly, in light of this discussion it is evident that thebackward-stealing and forward-manipulation problems which pre-vent governments from achieving efficient bargaining outcomesunder sequential bilateral negotiations in MFN environments (Pro-positions 1 and 2) can in principle be addressed with the inclusion offeatures that have representation in the bargaining environmentshaped by GATT/WTO rules. In particular, opportunities for renego-tiation can in principle prevent the inefficiencies that arise as a resultof the forward-manipulation problem (Proposition 3), while non-violation nullification-or-impairment rights operating in the presenceof a reciprocity norm can in principle prevent the inefficienciesassociated with backward stealing (Proposition 4).

7. Conclusion

Motivated by the structure of WTO negotiations, we analyze abargaining environment inwhich negotiations proceed bilaterally andsequentially under the MFN principle. Our analysis proceeds in twosteps. In a first step, we identify backward-stealing and forward-manipulation problems that arise when governments bargain underthe MFN principle in a sequential fashion. We show that theseproblems impede governments from achieving the multilateralefficiency frontier unless further rules of negotiation are imposed. Inour second step, we identify the WTO reciprocity norm and itsnullification-or-impairment and renegotiation provisions as rules thatare capable of providing solutions to these problems. In this way, wesuggest that WTO rules can facilitate the negotiation of efficientmultilateral trade agreements in a world in which the addition of newand economically significant countries to the world trading system isongoing.

We have shown that the backward-stealing and forward-manip-ulation problems arise under very general circumstances, and thatthese problems can be interpreted as reflecting underlying incentivestomanipulate the terms of trade.We reiterate here, though, that theseproblems can equally well be given an interpretation in terms ofmarket access: each problem reflects the incentives of negotiatingpartners to position the balance of market access rights andobligations in a way that is disadvantageous for unrepresentedgovernments. When interpreted from this perspective, the backward-stealing and forward-manipulation problems take on heightenedpractical relevance, because the balance of market access rights andobligations is a dominant theme in GATT/WTO discussions. And fromthis perspective, the potential importance of the role played by theWTO reciprocity norm and its nullification-or-impairment andrenegotiation provisions in facilitating efficient bargaining outcomesmay be appreciated.

Our findings are also consistent with the historical experiencewhich led to the RTAA on which many of the essential features of theGATT/WTO are founded. As we have described, by 1934 the UnitedStates was frustrated with its experience in multilateral tariffbargaining, but also well-aware that the effectiveness of bilateraltariff bargaining could be undone by the twin problems of backwardstealing and forward manipulation. Our results indicate that the RTAAand later the GATT and WTO succeeded in devising a method ofbilateral tariff bargaining that was not prone to these fundamentalproblems. This is not to say that bilateral tariff bargaining under theGATT/WTO is necessarily free from problems such as foot-draggingand free-riding. In fact, Limao (2007) presents evidence consistentwith the occurrence of foot-dragging in GATT tariff bargainingoutcomes, and Ludema and Mayda (2009) report evidence consistentwith free-riding in GATT market access negotiations (though Bagwell

61K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

and Staiger (2010b) find little evidence of free-riding in the context ofWTO accession negotiations). Rather, our results simply suggest thatthese problems would likely be far more wide-spread in the absenceof the GATT/WTO rules highlighted by our analysis.

Finally, we have focused on the possibility of achieving efficientbargaining outcomes in various negotiating environments, but wehave not characterized equilibrium outcomes in the environmentswhere efficiency cannot be achieved. Hence our results do not indicatethe severity of the inefficiency that arises when backward-stealingand forward-manipulation problems are present. We leave this tofuture research.

Acknowledgments

This paper has benefitted from the detailed comments of tworeferees. We also thank Henrik Horn, Nuno Limao, Alberto Martin,Petros Mavroidis, Jim Rauch, Lex Zhao and seminar participants atColorado, Columbia, Duke, Maryland, Oregon, Princeton, Stanford,Wisconsin, the NBER Summer Institute, the WTO and the Conferenceof the Japan Society of International Economics for very helpfulcomments, the European University Institute for their hospitalityduring which part of this paper was drafted, and the NSF for providingfunding. All errors are ours.

Appendix A

In this Appendix, we provide proofs of all Lemmas and Proposi-tions not established in the text.

Lemma 1. Any welfare triple can be achieved with an arbitrary market-clearing world price or with any one instrument set at an arbitrary level.

Proof. Consider an arbitrary set of policies (τ, t) and associatedwelfare levels Ŵ(Pj(τj, Pw), Pw, tj) for ja{A, B, C} and market-clearingworld price Pw(τ). According to Eqs. (2) and (2a), a small change dPw

in the market-clearing world price can be engineered as follows:(i) define the change in τj for ja{A, B, C} according to dPj(τj(Pw), Pw)/dP w≡0; and (ii) define the change in tj for ja{B, C} according to dEj (Pj

(τj(P w), Pw), Pw,tj(P w))/dPw≡0 implying dtj=−EjdPw by Eq. (2a),which by Eq. (2) then implies dtA=−MAdPw and therefore implies aswell dMA(PA(τA(P w), Pw), Pw,tA(Pw))/dPw=0 by Eq. (2a). Hence, themarket-clearing condition (2) continues to be satisfied when thesepolicy changes are made and the market-clearing world price changesby dPw. But by Eq. (3), these policy changes leave dŴj=0 for ja{A, B,C}. Next observe that the same changes in τj for ja{A, B, C} and tj forja{B, C} described just above for engineering a small change in P w canachieve the desired change in any particular tariff τj for ja{A, B, C},since changing τj for ja{A, B, C} according to dPj(τj(Pw), Pw)/dPw≡0implies dτA/dPw=−τA/Pw and dτj/dPw=1/Pj for ja{B, C}. And theability to engineer a desired change in a particular transfer tj for ja{B, C}is implied directly by the changes described just above, since accordingto those changes dtj=−EjdPw. □

Lemma 2. At any efficient point, the following restrictions apply:

ðiÞ dWj= dτj N 0; j∈ A;B;Cf g;

ðiiÞ dWj= dτAb0; dWA

= dτjb0; j∈ B;Cf g;ðiiiÞ dWj

= dτn j N 0; j; n j∈ B;Cf g:ðR1Þ

Proof. (A1) states (R1)(i). For (R1)(iii), note that (A1), (A2) andEq. (4) imply dWj/dτAb0 for ja{B, C}. But dWj/dτA=[(1/τj)ŴPj

j+ŴPw

j]

(∂Pw/∂τA) and dWj/dτ\ j=[(1/τj)ŴPj

j+ŴPw

j](∂Pw/∂τ \ j

) for j, \ j∈{B,C}, andso ∂P w/∂τAb0b∂P w/∂τ\ j for j, \ j∈{B,C} implies sign[dWj/dτA]=−sign[dWj/dτ

\ j] for j, \ j∈{B,C}. (R1)(iii) follows. Finally, Eq. (4), (A1) and

(R1)(iii) imply dWA/dτjb0 for ja{B, C}, which gives (R1)(ii). □

Lemma 4. wCD(τA,τ–B, t–B)=WC(τA, τ–B,τCR, tC≡0) for τAbτAR (τB\C, τCR, t–B)and τ–BbτBR(τA\C, τCR, t–B), and for any such (τA, τ–B) that, together with τCR,fails to drive C to autarky, wCD(τ A, τ–B, t–B) is strictly decreasing in τA, strictlyincreasing in τ–B, and independent of t–B.

Proof. Utilizing the relationshipWC(τ,tC)≡ŴC(PC(τC,Pw(τ)),Pw(τ),tC),

we observe that ∂WC=∂τA = dWC=dτA = W

CPC = τC + W

CPw

� �∂Pw = ∂τAh i

,

while C's reaction curve is defined implicitly by ŴpCC +θCŴP w

C=0

where θc≡[∂Pw/∂τc]/[dPc/dτc]b0. It follows that, with τAbτAR(τB\C,τCR,t–B)and τ–BbτBR(τA\C,τCR,t–B) and therefore wCD(τA,τ–B,t–B)=WC(τA,τ–B,τCR,tC≡0), and with C positioned on its reaction curve, ∂wCD/∂τA=[1−θC/τCR]ŴPw

C[∂Pw/τA]b0 provided that τA and τ–B are non-prohibitive.

Analogous arguments applied to τ–B imply ∂wCD/∂τ–B=[1−θC/τCR]ŴPwC

[∂Pw/∂τB]N0. □

Proposition 2. Under (A4), there does not exist (generically) a SGPEof the Secure-Contract Game in which the outcome is efficient andW CENWmin

CD .

Proof. Consider any efficient outcome that is feasible in the Secure-Contract Game and for which, by Eq. (11), τAfbτAR(τB\C,τCR,t–Bf) and/orτBfbτBR(τA\C,τCR,t–Bf). Starting from the stage-1 proposal {τAf,τ–Bf,t–Bf},we must establish that A can find an alternative stage-1 proposal thatit strictly prefers as long as WCENWmin

CD . (A) If τAfbτAR(τB\C,τCR,t–Bf),then increase the proposed τA slightly; this leads to a strict reductionin wCD by Lemma 4 if τ–BfbτBR(τA\C,τCR,t–Bf) and by (A4) if instead τ–Bf≥τBR(τA\C,τCR,t–Bf), thereby ensuring that WCENwCD. Now adjust t–B

to fix wB\C at WBE. If τ–BfbτBR(τA\C,τCR,t–Bf), then by Lemma 4 wCD isunaltered by the adjustment in t–B. If instead τ–Bf≥τBR(τA\C,τCR,t–Bf), thenwCDmay be altered by the adjustment in t–B (because in thiscase B's applied tariff is not constrained by the binding τ–Bf and τBR

(τA\C,τCR,t–Bf) may rise or fall with t–B, affecting wCD), and thecombined impact on wCD of the described adjustments in τA and t–B

is then ambiguous: generically (i.e., except in knife-edge cases),however, these adjustments do not leave wCD unaltered; therefore,by choosing the direction of the original change in τA, we may(generically) find an adjustment in τA and t–B that strictly lowerswCD and fixes wB\C at WBE, thereby assuring that B will accept thisalternative proposal. Next, by combining the implied adjustment int–B with adjustments in the stage-2 proposals for τ–A, τ–C and t–C thatfix the levels of WB and WC at WBE and WCE respectively, andmaintain τ–A≤τA, the efficiency condition (4) implies that there canbe no (first-order) effect of these combined adjustments onWA. Butwith WC=WCENwCD under this adjusted proposal, A can thenreduce the level of t–C it proposes in stage-2 and enjoy a strictwelfare benefit from this maneuver. (B) If τ–BfbτBR(τA\C,τCR,t–Bf),then reduce the proposed τ–B slightly; this leads to a strict reductionin wCD by Lemma 4 if τAfbτAR(τB\C,τCR,t–Bf) and by (A4) if insteadτAf≥τAR(τB\C,τCR,t–Bf), thereby ensuring that WCENwCD. Now adjustt–B to fixwB\C at WBE. If τAfbτAR(τB\C,τCR,t–Bf), then by Lemma 4wCD isunaltered by the adjustment in t–B. If instead τAf≥τAR(τB\C,τCR,t–Bf),then wCD may be altered by the adjustment in t–B, and the impact onwCD of the described adjustments in τ–B and t–B is then ambiguous:generically, however, these adjustments do not leave wCD unal-tered; therefore, by choosing the direction of the original change inτ–B, we may (generically) find an adjustment in τ–B and t–B thatstrictly lowers wCD and fixes wB\C at WBE, thereby assuring that Bwill accept this alternative proposal. Next, by combining theimplied adjustments in τ–B and t–B with adjustments in the stage-2proposals for τ–A, τ–C and t–C that fix the levels of WB and WC at WBE

and WCE respectively, and maintain τ–A≤τA, the efficiency condi-tion Eq. (4) implies that there can be no (first-order) effect of thesecombined adjustments on WA. But with WC=WCENwCD under thisadjusted proposal, A can then reduce the level of t–C it proposes instage-2 and enjoy a strict welfare benefit. □

62 K. Bagwell, R.W. Staiger / Journal of International Economics 82 (2010) 49–62

Proposition 3. Under (A5), forward manipulation does not impedethe attainment of the efficiency frontier in the Contract RenegotiationGame.

Proof. We first observe that, under (A5), A can do no better for itselfin the Contract Renegotiation Game than to efficiently deliver WBD toB and WCD to C, and so it will choose to do so when this is feasible. Wefocus, then, on characterizing these feasibility conditions. That is,What conditions in addition to (A5) assure that there exists a stage-1proposal {τA,τ–B,t–B} that would induce in the Contract RenegotiationGame a point on the efficiency frontier {WAE,WBE,WCE} for whichWBE=WBD and WCE=WCD? By Lemma 1, for τ–B fixed arbitrarily,there exists {τ–A(τ–B),τ–C(τ–B),t–B(τ–B),t–C(τ–B)} that achieves {WAE,WBE=WBD,WCE=WCD}. We will say that τ–B is consistent with (A1)and (A2) if (A1) and (A2) are satisfied at {τ–A(τ–B),τ–C(τ–B),t–B(τ–B),t–C(τ–B)}.Then under (A5), the SGPE of the Contract Renegotiation Game mustbe efficient if there exists a τ–B consistent with (A1) and (A2) and aτAf≥τ–A(τ–B) such that wB\C(τAf,τ–B,t–B(τ–B))=WBE=WBD. When theseconditions are met, the stage-1 proposal {τAf,τ–B,t–B(τ–B)} would inducethe stage-2 proposal {τ–A(τ–B),τ–C(τ–B),t–C(τ–B)} and therefore lead to thepayoffs {WAE,WBE=WBD,WCE=WCD}, andA candonobetter than this.But the required conditions (other than (A5)) are simply those neededto satisfy the security constraint at the efficient point. □

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