ALL OR NOTHING?

THE SCOPE OF COOPERATION IN INTERNATIONAL FISHERIES

Abstract

Many internationally shared fish stocks require international cooperation to overcome the

threat of over-exploitation or even depletion. Ideally, the cooperative management of such

stocks should apply to the resource as a whole, covering its entire geographic range of

occurrence. Nevertheless, many international fishery agreements exclude areas under national

jurisdiction and limit cooperation to the high seas. Although most fishery conventions call for

compatibility of intra-EEZ and high seas management measures it must be expected that

under this narrow scope of cooperation countries pursue primarily national interests when

they determine their domestic fishery policy. In this paper, we make use of a two-stage

coalition formation model to analyze the outcome of several scenarios of cooperation both in

terms of coalition stability and social welfare. The underlying bioeconomic model captures

the interdependency of fish stocks by explicitly incorporating a migration process between the

various fishing zones. Our results indicate that any deliberate restriction of cooperation

reduces the stability of fishery coalitions and leads to welfare losses. Furthermore, we

demonstrate the detrimental consequences both for coalition stability and social welfare if the

interdependency of populations is neglected in international fisheries management, be it

wilfully or due to a lack of information.

JEL References: Q22, C72, F53, K33

Keywords: coalition formation model, restricted cooperation, compatibility of management

measures, marine scientific research, free-riding, biological model, economic model, shared

fish stock, regional fishery management organizations.

1

1 Introduction

Managing global and international commons requires voluntary international cooperation due

to the absence of any supranational institution that could enforce a potentially optimal

management strategy. While in general a tragedy of the commons does not inevitably result,

depending on the specific circumstances, internationally shared fish resources seem to be

particularly vulnerable and subject to overexploitation1. They feature the particularity that

they have been partially privatized under the legal regime of the United Nations Convention

on the Law of the Sea (UNCLOS, see UN 1982). According to Articles 56 and 57 of the

Convention, every coastal state has the right to establish an Exclusive Economic Zone (EEZ),

adjacent to its territorial waters and 200 nautical miles in breadth, in which it exercises

sovereign rights regarding the conservation and management of all living (and non-living)

marine resources. Beyond the EEZ limits, in the high seas, the open access regime persists,

i.e. the resources are subject to exploitation by all interested nations (Art. 87). Consequently,

the remaining public part of the resource is threatened by excessive exploitation whereas the

fish stocks within the EEZs are under national jurisdiction allowing for their optimal

management, at least in principle. Therefore, the need for international cooperation seems to

be limited to high seas fisheries and indeed, Art. 118 of the UNCLOS calls for the formation

of regional fisheries management organizations (RFMOs) with the aim of an optimal

cooperative management of high seas fish resources.

So far so good, but although environmental economists usually treat trees and fish equally as

renewable resources, there is a difference between them that makes it difficult to privatize fish

resources: fish move! In other words, the populations in the various fishing grounds are

interdependent and the exploitation of the stock in a certain area generates an externality on

neighboring fishing grounds2. The significance of migratory behavior is reflected in the

common classification of internationally shared fish stocks which distinguishes, inter alia,

1 For a documentation of the state of internationally shared fish resources, see Maguire et al. (2006).

2 From a more general point of view, conservation efforts in the high seas can be seen as an impure public good

because they create additional private benefits in the EEZs.

2

between highly migratory stocks which are to be found both within the EEZs and the adjacent

high seas and are highly migratory in nature and straddling stocks which also cover both

EEZs and the high seas but are more stationary (cf. Munro et al. 2004, p.3).

Obviously, from a social planner‟s view, an optimal utilization and conservation of shared

fish stocks would require a consistent and integrated cooperative management of the resource

in its entire geographic range. However, this has been a controversial issue during the

negotiations preceding many fishery agreements as most coastal states refuse to subject their

national fishery policies to international conventions. Regarding the legal framework, the

UNCLOS calls for cooperation “both within and beyond the exclusive economic zone” (Art.

64 (1)) in the case of highly migratory species, whereas for straddling stocks Art. 63(2) only

requires a cooperative management in the high seas. In both cases it is proposed that

cooperation should take place either directly or through the development of RFMOs. The

1995 UN Fish Stocks Agreement (UN 1995), dealing explicitly with the conservation and

management of straddling and highly migratory fish stocks, restates this distinction (Art. 7(1))

but at the same time emphasizes the sovereignty of coastal states regarding intra-EEZ fishery

management as well as the importance of compatibility of conservation measures (Art. 7(2)).

In view of this ambiguity and vagueness it is not surprising that actual RFMO convention

texts greatly differ with regard to the scope of cooperation. For example, the Convention of

the International Commission for the Conservation of Atlantic Tunas applies to “[…] the

Convention area except the territorial sea and other waters, if any, in which a state is entitled

under international law to exercise jurisdiction over fisheries” (ICCAT, 2007, Art. IX(3)).

Hence, the convention restricts cooperation to the high seas despite the highly migratory

nature of most tuna populations. Most convention texts include an article calling for the

compatibility of measures3 but they never cede fishery management within waters under

national jurisdiction to an international committee.

3 See, for example, NAFO (2004), Art. XI (3) and NEAFC (2007), Art. 5 (2). For the latter, a performance

review criticized that there was no mechanism established to ensure the consistency of measures (Arbuckle et al.

2006, p. 36).

3

In this work we investigate how the stability of fishery coalitions and their performance in

terms of aggregated payoffs are affected by the decision to restrict cooperation to the high

seas. In detail, we consider two scenarios according to whether countries take into account the

interdependency of fish stocks or not. In the first scenario, we assume that countries are well

informed about migration patterns and the corresponding need for an integrated management

of intra-EEZ and high seas resources but nevertheless they are reluctant to ensure the

compatibility of domestic fishery policies with international obligations. In fact, several

countries have explicitly expressed their unwillingness to give up national sovereignty

regarding the management of intra-EEZ fisheries4, whether they involve straddling and highly

migratory stocks or not. The second scenario, by contrast, assumes that the migratory nature

of the fish stocks is completely neglected, either because of a lack of scientific information or

because its significance is underestimated. Consequently, countries consider it unnecessary to

pursue an integrated management approach and choose their fishing strategies independently

for the high seas and the EEZs. Accordingly, any potential cooperation will only address the

management of resources in the high seas, neglecting any externality on fish stocks in

adjacent EEZs.

So far, the literature on cooperative arrangements in international fisheries has not yet

developed a suitable framework to describe the issue of restricted cooperation appropriately

and to examine its consequences. The strategic interaction of sovereign fishing nations is most

suitably described with concepts from game theory or, more specific, coalition theory

whenever more than two countries are involved. By now, there exists an extensive literature

on international fishery coalitions5 which has focused mainly on how cooperative gains are

shared (cooperative coalition theory) or under which conditions coalitions will be stable (non-

cooperative coalition theory). Kaitala and Munro (1993) provided the first preliminary

analysis of high seas fishery management, considering a cooperative game involving a coastal

state and a distant water fishing nation (DWFN). Several authors examined the outcome of

different solution concepts, such as Shapley value and nucleolus, by modeling bargaining

4 For a thorough discussion thereof, see Munro et al. (2004) and Burke (1994).

5 For an overview of the literature on coalitions in fisheries, see Lindroos et al. (2007).

4

within an RFMO as a cooperative game (see e.g. Li 1998, Kaitala and Lindroos 1998,

Lindroos 2004). Pintassilgo (2003) introduced the partition function approach from non-

cooperative game theory to the analysis of high seas fishery management, which explicitly

considers the impact of externalities on the stability of coalitions and permits to examine the

stability of partial cooperation (e.g. coalitions in which not all countries participate). Since

these authors have clearly focused on the high seas because of its open access regime, they

neglected the existence of adjacent EEZs and any potential strategic incentive associated with

it. Considering the impact of migration on fishing behavior makes it necessary to introduce a

spatial dimension into the bioeconomic model. Recently, migratory patterns have received

increasing attention because they are influenced by climate change such that management

policies and fishery agreements have to adapt to the new situation (Miller and Munro 2004,

Sissener and Bjørndal 2005, Hannesson 2006). However, very few articles have dealt with

the impact of migration on fishing behavior in a game theoretic setting (McKelvey et al. 2002,

Hannesson 1997, Naito and Polasky 1997). While these articles do not consider the formation

of coalitions, Arnason et al. (2000) use cooperative game theory in their semi-empirical

analysis of the Norwegian spring-spawning herring fishery. They assume stochastic migratory

behavior of the fish stock and compare the competitive outcome, represented by Markov

perfect equilibria, with the fully cooperative outcome.

Finus et al. (2010) have introduced a bioeconomic setting that both captures the spatial

dimension of international fisheries and makes use of non-cooperative coalition theory to

model the formation of fisheries agreements. They have shown that, in certain circumstances,

previously unstable coalitions can be stabilized if the existence of EEZs is no longer neglected

and the impact of fishing activities in the high seas on intra-EEZ fish stocks is taken into

account. In this paper we extend their model, allowing for restricted cooperation. Section 2

describes the biological part of our setting, which is basically a Gordon-Schaefer model with

an additional term accounting for migration. Section 3 deals with the economic behavior of

countries, i.e. it introduces the coalition formation model, and specifies the various scenarios

of cooperation. Subsequently, section 4 presents and discusses the results of the simulations

and section 5 concludes.

5

2 The Biological Model

2.1 The Classical Gordon-Schaefer Model

The analysis of cooperation and coalition structures in international fisheries requires

concepts from fishery biology to describe the underlying biological processes, has to take into

account the legal framework given by international marine law, and should properly model

the economic behavior of the respective protagonists. Our biological model6 is based on the

classical Gordon-Schaefer model (Gordon 1954, Schaefer 1954) which has been frequently

used to analyze the steady-state of an exploited (fish) resource (for an introduction, cf. Clark

2005).

We assume that a given number of coastal states N exploit a shared fishery resource which is

characterized by its carrying capacity k and its intrinsic reproduction rate r . In an open

access regime, the steady state of the fish stock in the classical Gordon-Schaefer-model would

be described by the following equations:

dX

G X H X 0dt

(1)

X

G X rX 1k

(2)

N

i

i 1

XH X q E

k

. (3)

Eq. (1) states that in the steady-state, growth G and harvest H are balanced such that the

stock size X remains constant in time, denoted by t . Eq. (2) specifies the growth process,

making use of a commonly used logistic growth function. Finally, eq. (3) represents the

assumption that (total) harvest depends linearly on the (sum of) individual fishing efforts iE

of state i , where q denotes the catchability coefficient.

6 The classical Gordon-Schaefer model is commonly referred to as a bioeconomic model since it already

incorporates economic activities, namely fishing. However, we call it a biological model, because it only

describes the response of the ecosystem to exploitation, and separate it from the economic model discussed in

section 3 which captures the economic incentives.

6

However, the traditional open access and laissez-faire regime has been replaced by the legal

framework defined by the 1982 UNCLOS. As mentioned in the introduction, parts of the

system have been privatized through the establishment of exclusive economic zones. Hence,

there are two types of geographical zones, the high seas, i.e. the common property where all

nations can fish, abbreviated HS , and the exclusive economic zones, the private properties

where only the respective coastal state i is allowed to fish, abbreviated iEEZ . Thus, if we

denote the entire size of the system by totk for clarity, we assume that only a share of the

resource is subject to open access and define:

HS totk k (4)

EEZ tot

1k k

N

. (5)

Hence, in our international context, players are sovereign countries engaged in fishing, i.e.

coastal states, each owning an EEZ with exclusive fishing rights, though they can also fish in

the high seas.

2.2 Capturing the Spatial Dimension

Apparently, the issue now features a spatial dimension which has to be reflected in the model.

Therefore we introduce a vector of fish stocks, 1 N HSX ,...,X ,XX , describing the

population in each fishing zone. The steady-state condition then reads as follows:

d

D 0dt

X

G H X . (6)

Because fishing zones are not isolated but interconnected via migration, we have introduced

the term DX which links the various fish stocks (see discussion below). The components of

the growth vector 1 N HS(G ,...,G ,G )G and the harvest vector EEZ ,1 EEZ ,N HS( H ,...,H ,H )H

are defined as before (eqs. (2) and (3)), where we just have to insert the respective carrying

capacity and take into account that all countries are allowed to fish in the high seas whereas

only a single coastal state fishes in each EEZ:

7

HSHS HS HS

HS

XG X rX 1

k

(2a)

ii i i

EEZ

XG X rX 1 , i 1,...,N

k

(2b)

N

HSHS HS HS ,i

i 1 HS

XH X q E

k

(3a)

iEEZ ,i i EEZ ,i

EEZ

XH X qE ,i 1,...,N

k . (3b)

In order to model the interdependence of fish stocks, we have to specify a certain spatial

setting and a certain migration process. To be able to analyze the dispersal pattern in a most

symmetrical and tractable way, we choose an intuitive and symmetric arrangement of the

N 1 zones: the EEZs are arranged in a circle with the high seas at its center, as depicted in

Figure 1. This avoids boundary effects that would emerge with a linear arrangement and

approximates well the geographical settings of many examples (like the various Donut Holes,

see Meltzer 1994). Migration itself is modeled as a density-dependent diffusion process7, i.e.

the strength of migration between neighboring fishing grounds is given by the difference in

stock densities, scaled by the product of the zone sizes (Kvamsdal and Groves 2008):

2 2i 1 i i 1 i HS iEEZ EEZ EEZ HSi

EEZ EEZ EEZ EEZ HS EEZ

X X X X X XD d k k k k

k k k k k k

X (7)

N

i HSEEZ HSHS

i 1 EEZ HS

X XD dk k

k k

X . (8)

In eq. (7), we have introduced the diffusion parameter d which represents a universal

measure for the intensity of the diffusion process.

7 For a more detailed justification of this specification of migration and possible alternatives, see Sanchirico and

Wilen (2005) and Finus et al. (2010).

8

For a given combination of fishing efforts EEZ ,1 EEZ ,N HS ,1 HS ,NE ,...,E ,E ,...,EE , we are now

able to calculate the resulting steady-state stocks by inserting the efforts into the harvest

functions, inserting harvest, growth and diffusion functions into the steady-state condition and

solving for the steady-state stocks. Given the fishing efforts and the resulting stocks, we can

easily determine the harvest each country obtains, both from fishing in the high seas and in its

respective EEZ. In the following section we define the payoffs that are associated with a

certain harvest and, what is more important, we deal with the economic behaviour of

countries, i.e. we specify the rules which they follow when choosing their decision variables,

namely fishing efforts.

Figure 1: Migration Pattern and Spatial Arrangement of Fishing Zones*

* Arrows indicate potential dispersal.

3 The Economic Model

3.1 Coalition Formation Model

Cooperation among a group of players corresponds to the establishment of an RFMO with the

purpose of managing and conserving the fish stocks jointly. Participation in an RFMO is open

to all nations as reflected by Article 8(3) of the UN Fish Stocks Agreement (UN 1995).

9

Moreover, states which decide against membership in an RFMO cannot be prevented from

harvesting.

In order to capture these institutional features, we chose from the set of coalition formation

games the single coalition open membership game due to d‟Aspremont et al. (1983) which

has been frequently applied in the literature on international environmental agreements (e.g.

Carraro 2000 and Finus 2003, 2008 for overviews). This coalition game is a two-stage game.

In the first stage, players decide upon their membership. Those players that join the RFMO

form the coalition and are called members, those that do not join are called non-members

(outsiders) and act as singletons. The decisions in the first stage lead to a coalition structure

(N-n)K C, 1 where C is the set of n coalition members, n {0,1,...,N } , and (N-n)1 is the

vector of N n singletons. Given the simple structure of the first stage, a coalition structure

is fully characterized by coalition C . In the second stage, players choose their economic

strategies which are fishing efforts in our bioeconomic model. The game is solved backward.

3.2 Second Stage of the Game and Scenarios of Cooperation

In the second stage, given some coalition C has formed in the first stage, players base their

choice of fishing efforts on the resulting payoffs. Each player generates economic payoffs

i ,EEZ and i ,HS from fishing in his own EEZ and the high seas, respectively:

EEZ ,i EEZ ,i i EEZ ,ipqE X cE E E (9)

HS ,i HS ,i HS HS ,ipqE X cE E E (10)

where p is the (exogenously) given fish price and c is the (constant) marginal cost of fishing

effort, which is assumed to be identical for all players for simplicity.8 Each player i has two

strategic variables, namely the fishing effort in the own EEZ, EEZ ,iE , and the fishing effort in

8 The assumption of symmetric players is widespread in the literature on coalition formation, not only on

international environmental treaties but also in the context of other economic problems (see e.g. Bloch 2003, and

Yi 2003 for an overview).

10

the high seas, HS ,iE . It is a common assumption in the literature on fishery management

(Gordon 1954, Sanchirico and Wilen 1999, Pezzey et al. 2000) that costs depend linearly on

extraction efforts, though they are strictly convex if expressed in terms of harvests EEZ ,iH and

HS ,iH . Note that all stocks (and therefore payoffs) depend on the whole vector of fishing

efforts, EEZ ,1 EEZ ,N HS ,1 HS ,NE ,...,E ,E ,...,EE , due to the process of migration that links the

various fishing grounds.

As mentioned above, it is our intention to investigate the outcome of restricted cooperation

and the significance of awareness of the interdependence of stocks. Therefore we define

several scenarios which differ in the scope of cooperation and the information on which

fishing effort decisions are based. For notational clarity, we define the scenarios by giving the

formal expressions that describe the respective maximizing behaviour.

Scenario A: Perfect cooperation with complete information

This scenario serves as the base case and has been studied extensively in Finus et al. (2010).

Members as well as outsiders are informed about the interdependence of fish stocks and

members maximize total coalitional payoffs both when choosing efforts in the high seas and

in their own EEZ9.

Members: ,

, ,maxEEZ i

EEZ i HS iE

i C i C

,

, ,maxHS i

EEZ i HS iE

i C i C

Non-Members: ,

, ,maxEEZ j

EEZ j HS jE

,

, ,maxHS j

EEZ j HS jE

9 Since all players have the same constant marginal cost of fishing, the distribution of effort among coalition

members is irrelevant. Thus, in our calculations we maximize payoffs with respect to the total coalitional effort

HS ,C HS ,i

i C

E E

. However, we do not use this simplification here because it would complicate the notation.

In other words, there will always be several equilibria (with the same aggregate coalitional effort HS ,CE ) and by

selecting the symmetric equilibrium, we avoid the need for transfers. Alternatively, we could use an equal

sharing rule.

11

Scenario B: Imperfect cooperation with complete information

This scenario relates the restrictions of cooperative arrangements to the unwillingness to give

up national sovereignty. Consequently, when choosing fishing efforts in its own EEZ, every

coalition member maximizes its own payoff and does not account for coalitional interests.

Nevertheless, it is aware of the interaction between populations and of any potential adverse

impact of domestic fishing on revenues from the high seas fishery and vice versa. This is

reflected by the assumption that every member maximizes its total individual payoff, which

includes its share of the coalitional payoff from the high seas, when choosing intra-EEZ

fishing efforts:

Members: ,

, ,

1max

EEZ i

EEZ i HS iE

i Cn

,

, ,maxHS i

EEZ i HS iE

i C i C

Non-Members: ,

, ,maxEEZ j

EEZ j HS jE

,

, ,maxHS j

EEZ j HS jE

At first sight, deliberately limiting the scope of cooperation to the high seas appears to be

irrational since it implies the separate choice of two potentially contradictory strategies by one

player, namely the fishery management strategy in the EEZ and in the high seas. However,

one might expect that the less ambitious an agreement, the more countries will join it. In fact,

Barrett (2002) and Finus and Maus (2008) have shown for international environmental

agreements in general and climate coalitions in particular that in some cases “modesty may

pay”, provided that the higher participation compensates for the restricted scope of

cooperation.

Scenario C: Imperfect cooperation with no information

In contrast to scenario B, this scenario assumes that member countries might indeed be

willing to cooperate without any restrictions, but nevertheless they only choose their fishing

efforts in the high seas cooperatively because they are not aware of the interdependence of

fish stocks. The same holds for outsiders, i.e. every country merely considers its payoff from

fishing in the own EEZ when choosing intra-EEZ fishing efforts and totally neglects the

effects of domestic fishing activities on the high seas fishery (and vice versa):

12

Members: ,

,maxEEZ i

EEZ iE

,

,maxHS i

HS iE

i C

Non-Members: ,

,maxEEZ j

EEZ jE

,

,maxHS j

HS jE

From a more general point of view, this topic touches upon the much broader issue of the

significance of information in strategic interactions. It is commonly known that information

always has a positive value in decision theory, since a single decision maker could always

replicate his previously chosen strategies. However, in a game situation where decision

makers interact strategically, and in particular in the context of climate coalitions, several

authors have shown that it depends on the specific setting whether additional information

from scientific research is beneficial (in the sense that it increases social welfare) or actually

disadvantageous (Ulph and Maddison 1997, Na and Shin 1998, Kolstad 2007, Finus and

Pintassilgo 2009). Despite this unclear impact of information on coalition formation, joint

scientific marine research and the exchange of scientific data are usually regarded as

necessary first steps towards more ambitious management agreements in international

fisheries (Munro 2004, p.5, Gulland 1980, ch. 3).

3.3 First Stage of the Game

In subsection 2.2 we have introduced the steady-state condition (eq. 6) as a biological

equilibrium concept, i.e. we have assumed that growth, harvest and migration are balanced

such that stocks in each zone do not vary in time. Similarly, we choose an equilibrium

concept for the coalition game in which the effort and membership decisions of players are

balanced such that no player has an incentive to revise his decision.

It follows from the above that equilibrium fishing efforts in the second stage

depend both on the coalition structure C and the scenario of cooperation

scenario , scenario , scenario S A B C , i.e. C,S* *E E . Equilibrium efforts *(C,S )E

have to be inserted into the payoff functions (9) and (10) to determine individual payoffs

* * *

i EEZ ,i HS ,i(C,S ) (C,S ) (C,S ) . Having determined equilibrium individual payoffs for

13

every possible coalition structure in the second stage, we can now proceed to the first stage

and check for stability of a given coalition structure.

For the first stage, we use the equilibrium concept of internal and external stability, i.e. a

coalition C is considered to be stable if it fulfills the following two conditions:

Internal Stability

No member i C finds it profitable to deviate, i.e. the gain iG from leaving the coalition is

non-positive: * *

i i iG : (C\{ i },S ) (C,S ) 0, i C .

External Stability

No non-member j C finds it profitable to join the coalition, i.e. the gain jQ from joining

the coalition is non-positive: 0* *

j j jQ : (C { j },S ) (C,S ) , j C .

Note that the grand coalition is externally stable by definition as there is no outsider left that

could join the coalition. Even more important, the coalition structure of only singletons is

stable by definition, which ensures existence of a stable coalition structure. This follows from

the fact that, if all players announce not to be a member of the coalition, i.e. C , a single

deviation by one player will make no difference. This would be different for C {i } , which

also implies the singleton coalition structure and which would also be internally stable, but

not necessarily externally stable if a second player wants to join.

4 Results and Discussion

4.1 Preliminaries

From sections 2 and 3 it follows that we have to determine the biological and economic

equilibrium simultaneously meaning that we search for a situation in which both fish stocks

are constant in time and players do not have an incentive to deviate from their strategies. A

closer look at the steady-state equation (6) and the payoff maximization conditions in

14

subsection 3.2 reveals that this requires solving a system of 3N 1 non-linear equations10

for

which no analytical result exists. Therefore, we have to rely on numerical simulations to solve

the steady state equations and the FOCs, which are derived from the maximization conditions,

simultaneously for equilibrium stocks and efforts for every possible coalition structure.

It is evident that computing time and memory requirements increase exponentially with the

number of players. For this reason, we have to confine ourselves to the case of N 3 players.

This is certainly the minimum number of players that makes the analysis of coalition

formation interesting, but as it turns out, it is sufficient to derive interesting qualitative results.

For N 3 , we have to consider three possible coalition structures, namely the grand

coalition, the two-player coalition and the all-singletons coalition structure. Furthermore, we

restrict the analysis to symmetric parameter values for all players. Consequently, all possible

two-player coalitions are equivalent with symmetric payoffs for coalition members, though

they differ from the payoff of a non-member.

Of course, simulations require the assumption of numerical values for the parameters of the

model. As it turns out that results only depend on what is commonly referred to as the

„inverse efficiency parameter‟ tot

c

pqk, we normalize p and q to 1. The parameter totk is

normalized to 4 as there are four zones.11

Hence, with reference to the inverse efficiency

parameter, a variation of the cost parameter c is, ceteris paribus, de facto a variation of the

relation cpq

. The cost and growth parameters are set to values c 0.25,0.5,0.75 and

r 0.25,0.5,0.75 , respectively. The spatial allocation of property rights is then captured by

the parameter according to equations (4) and (5). We vary in the interval [0,1] ,

10

There are N 1 stocks, N fishing efforts in the high seas and N fishing efforts in the EEZs.

11 This is in line with the common normalization k 1 applied in articles dealing with a single zone

(e.g. Pezzey et al. 2000). In our model, assuming no diffusion between zones ( 0d ), setting

totk 4 and 0.25 results in four isolated zones with carrying capacities k 1 . See equations

(4) and (5).

15

starting from a totally privatized resource ( 0 ), gradually increasing the degree of

publicness in steps of 0.05 , and ending in a completely public resource ( 1 ). Note

that this also covers the case in which all zones have equal size ( 0.25 ). The diffusion

parameter d is varied in the interval d 0,1.28 , covering a wide range from isolated

( d 0 ) to highly interactive fishing grounds.

In Finus et al. (2010), the base scenario A is discussed, representing unrestricted cooperation

under complete information. They find that the grand coalition is never stable, but partial

cooperation by two players can be stable if the public share of the resource, , is sufficiently

small and migration is sufficiently weak.

4.2 Perfect/Imperfect Cooperation under Complete Information

Here, we compare scenario A (perfect cooperation under complete information) and B

(imperfect cooperation under complete information), i.e. we assume that all countries are well

aware of the interdependence of fish stocks and imperfect cooperation is a consequence of the

unwillingness to give up sovereignty in fishery management. The main question is whether

this unwillingness has a negative impact on social welfare or whether it might even be

beneficial because less ambitious cooperation might be more feasible.

Result 1a: Under restricted cooperation, the grand coalition is never stable.

In detail, the incentive to leave the grand coalition,

* *

i i iG : (C 1,2,3 \{ i },S ) (C 1,2,3 ,S ) 0, i C B B , is always positive12

.

Hence, restricting cooperation does not have a stabilizing effect for the grand coalition. But

the following result is even worse:

Result 1b: Under restricted cooperation, the two-player coalition is never stable.

12

This and all following results hold for all parameter values, except for border cases like 0, d 0 for

which cooperation is irrelevant and the outcome is identical for all coalition structures.

16

To be exact, internal stability fails, i.e. there is always a positive incentive to leave

a two-player coalition13

: * *

i i iG : (C 1,2 \{ i },S ) (C 1,2 ,S ) 0, i C B B .

Remember that in the base scenario A, the two-player coalition proved to be stable for some

parameter values. Hence, the limitation of cooperation to the high seas does not only achieve

little with respect to the grand coalition, it even destabilizes previously stable two-player-

coalitions. In fact, the all singletons coalition structure turns out to be the only stable one

under restricted cooperation. Then, however, the unwillingness to cooperate both in EEZs and

high seas is irrelevant because no stable coalition emerges and countries act non-

cooperatively anyway. Furthermore, our results indicate that the all singletons coalition

structure always generates the lowest total payoffs. Hence, we can merge Result 1a and Result

1b:

Result 1: Restricting cooperation does not stabilize fishery coalitions and has a weakly

decreasing impact on social welfare.

Result 1 clearly disproves the idea that restricting cooperation has any positive impact on the

stability or performance of fisheries coalitions. The destabilizing effect results from the fact

that in scenario B coalition members undermine their own conservation efforts in the high

seas when choosing fishing efforts in their own EEZ. Although they are aware of the negative

impact of intra-EEZ fishing on resources in neighbouring EEZs and the high seas, they only

take into account their own payoff from the high seas and therefore neglect the externality

they impose on other players. The gains from restricted cooperation are obviously not

sufficient to stabilize fishery coalitions. Hence, we have to abandon the hope that an

agreement which leaves intra-EEZ resources under national jurisdiction will achieve a higher

participation or better management results. Countries should, on the contrary, seek to agree on

a comprehensive management scheme that covers the entire range of the fish stock.

13

Without loss of generality, we have considered the coalition formed by player 1 and 2.

17

4.3 The Impact of Ignorance

Here, we compare scenarios A and B, which assume that countries take into account the

migratory behaviour of fish stocks, with scenario C, where this is totally neglected.

Result 2a: Under ignorance (no information), the grand coalition is never stable.

The incentive to leave the grand coalition is always positive, just as before in scenarios A and

B: * *

i i iG : (C 1,2,3 \{ i },S ) (C 1,2,3 ,S ) 0, i C C C . Similarly, we

obtain:

Result 2b: Under ignorance (no information), the two-player coalition is never stable.

The incentive to leave a two-player coalition is always positive:

* *

i i iG : (C 1,2 \{ i },S ) (C 1,2 ,S ) 0, i C C C . Compared to scenario A,

neglecting the interdependence of fish stocks destabilizes even previously stable coalitions.

The all singletons coalition structure remains as the only stable one and, on top of that, it

generates lower aggregate payoffs than the all singletons coalition structure in scenarios A

and B. Taken together, we can conclude:

Result 2: Neglecting migration always has a negative impact on social welfare.

The detrimental impact of total ignorance is due to the fact that ignorant players do not only

compete against each other but they even neglect negative consequences of their fishing

activities in one zone on their own payoffs obtained from a neighbouring zone. Unlike in

other game situations, the players in international fisheries cannot derive any benefit from a

veil of ignorance. In case of the all singletons coalition structure, which turns out to be the

only stable one, scenario C corresponds to a situation where six independent players are

engaged in the fishery, three in the high seas and one in each EEZ, and it is commonly known

that the inefficiency of the uncooperative Nash equilibrium increases in the number of

players. Result 2 emphasizes the significance of marine scientific research (which could

reveal interactions between populations) by showing that it does not only facilitate optimal

fishery management but may even foster cooperation among fishing nations. This requires,

18

however, that the migratory behaviour of fish stocks is not neglected but incorporated both

into theoretical bioeconomic modelling and international fishery management strategies. The

significance of migration obviously depends on its strength, represented by the diffusion

parameter d :

Result 3: The welfare-loss due to the neglect of biological interdependencies increases in

the strength of migration.

This result partially justifies the distinction that is made between the management of highly

migratory stocks and straddling stocks (cf. Art. 63 and 64 UNCLOS). The welfare losses that

result from a management approach that neglects migration are indeed smaller for straddling

stocks than for highly migratory stocks.

5 Conclusion

This paper presented an integrated model for internationally shared fish resources. Due to its

spatial dimension it allows to analyze the outcome of cooperation which is restricted to the

high seas, as observed in many RFMOs. In a two-stage coalitional game we have investigated

the outcome of several scenarios, both in terms of coalition stability and social welfare. In

detail, we have focused on two issues: Firstly, we have found that any deliberate restriction of

cooperation to the high seas, due to the unwillingness to give up national sovereignty over

areas under national jurisdiction, decreases coalition stability and leads to welfare losses.

Instead of seeking an unambitious fishery agreement that does not interfere at all with

national sovereignty, countries should go for all or nothing and try to agree on full and

binding compatibility of management measures within EEZs and beyond. Modesty does not

pay in this case. Furthermore, we have analyzed the impact of a complete lack of information

(i.e. ignorance about the interdependence of fish stocks) on the stability of coalitions and the

corresponding payoffs obtained from the fishery. Here, we have found that information about

the interaction of populations (possibly obtained from marine scientific research) is beneficial

in the sense that it stabilizes cooperative agreements and facilitates optimal management

policies. International management strategies and bioeconomic models should therefore take

into account the migratory behavior of fish stocks.

19

References

Arbuckle, M., Atkinson, B., & Germani, V. (2006), Performance Review Panel Report of the

North East Atlantic Fisheries Commission.

Arnason, R., Magnusson, G., & Agnarsson, S. (2000). The Norwegian spring-spawning

herring fishery: a stylized game model. Marine Resource Economics, 15, 293-319.

Barrett, S. (2002). Consensus Treaties. Journal of Institutional and Theoretical Economics,

158, 529-547

Bloch, F. (2003). Non-cooperative Models of Coalition Formation in Games with Spillovers.

In: Carraro, C. (ed.). The Endogenous Formation of Economic Coalitions. Cheltenham:

Edward Elgar, ch. 2, 35-79.

Burke, W. T. (1994). The new international law of fisheries : UNCLOS, 1982 and beyond

Oxford monographs in international law, Clarendon Press.

Carraro, C. (2000), Roads towards International Environmental Agreements. In: Siebert, H.

(ed.), The Economics of International Environmental Problems. Mohr Siebeck, Tübingen,

169-202.

Clark, C. (2005). Mathematical Bioeconomics - Optimal Management of Renewable

Resources (2nd ed.). Wiley, New Jersey.

d'Aspremont, C., Jacquemin, A., Gabszewicz, J. J., & Weymark, J. A. (1983). On the Stability

of Collusive Price Leadership. Canadian Journal of Economics , 16, 17-25.

Finus, M. (2003). Stability and Design of International Environmental Agreements: The Case

of Transboundary Pollution. In H. Folmer and T. Tietenberg (Eds.): International Yearbook of

Environmental and Resource Economics (p. 82-158). Cheltenham, UK: Edward Elgar.

Finus, M. (2008). Game Theoretic Research on the Design of International Environmental

Agreements: Insights, Critical Remarks, and Future Challenges. International Review of

Environmental and Resource Economics: 2, 29-67.

20

Finus, M., & Maus, S. (2008). Modesty May Pay! Journal of Public Economic Theory, 10,

801-826.

Finus, M., & Pintassilgo, P. (2009). The Role of Uncertainty and Learning for the Success of

International Climate Agreements, Stirling Economics Discussion Paper 2009-16.

Finus, M., Schneider, R., & Pintassilgo P. (2010). Spatial Allocation of Property Rights – The

Case of International Fishery. Forthcoming.

Gordon, H. (1954). The Economic Theory of a Common Property Resource: the Fishery.

Journal of Political Economy , 62, 124-142.

Gulland, J.A. (1980). Some problems of the management of shared stocks. FAO Fisheries

Technical Paper, No. 206. Rome, FAO. 22 p.

Hannesson, R. (1997). Fishing as a Supergame. Journal of Environmental Economics and

Management, 32, 309-322.

Hannesson, R. (2006). Sharing the herring: fish migrations, strategic advantage and climate

change. In: Hannesson, R., Barange, M., & Herrick Jr, S.F., (eds.), Climate Change and the

Economics of the World's Fisheries. Edward Elgar. 66-99.

ICCAT (2007), International Convention for the Conservation of Atlantic Tunas, ICCAT

Basic Texts, 5th

Revision, Annex I.

Kaitala, V., & Lindroos, M. (1998). Sharing the benefits of cooperation in high sea fisheries:

a characteristic function game approach. Natural Resource Modeling , 11, 275-299.

Kaitala, V., & Munro, G. (1993) The Management of High Seas Fisheries. Marine Resource

Economics, 8, 313-329.

Kolstad, C. D. (2007). Systematic uncertainty in self-enforcing international environmental

agreements. Journal of Environmental Economics and Management, 53, 68-79.

21

Kvamsdal, S. F., & Groves, T. (2008). Spatial management of a fishery under parameter

uncertainty. Discussion paper, Norwegian School of Economics and Business Administration.

Department of Economics , 2008:13.

Li, E. (1998). Cooperative High-Seas Straddling Stock Agreement As A Characteristic

Function Game. Marine Resource Economics, 13, 247-258.

Lindroos, M. (2004). Sharing the benefits of cooperation in the Norwegian spring-spawning

herring fishery. International Game Theory Review , 6, 35-54.

Lindroos, M., Kaitala, V., & Kronbak, L. G. (2007). Coalition Games in Fisheries Economics.

In: Bjørndal, T., Gordon, D.V., Arnason, R., & Sumaila, U. R. (eds.), Advances in Fisheries

Economics. 184-195.

Maguire, J.-J.; Sissenwine, M.; Csirke, J.; Grainger, R.; Garcia, S. (2006). The state of world

highly migratory, straddling and other high seas fishery resources and associated species.

FAO Fisheries Technical Paper. No. 495. Rome: FAO. 84p.

McKelvey, R., Sandal, L., & Steinshamn, S. (2002). Fish Wars on the High Seas: a Straddling

Stock Competition Model. International Game Theory Review, 4, 53-69

Meltzer, E. (1994). Global overview of straddling and highly migratory fish stocks: The

nonsustainable nature of high seas fisheries. Ocean Development & International Law, 25,

255-344.

Miller, K. A., & Munro, G. R. (2004). Climate And Cooperation: A New Perspective On The

Management Of Shared Fish Stocks. Marine Resource Economics, 19, 367-393.

Munro, G., Van Houtte, A., & Willmann, R. (2004). The Conservation and Management of

shared fish stocks: legal and economic aspects. FAO Fisheries Technical Paper. No. 465

Rome, FAO. 67p.

Na, S.-l., & Shin, H. S. (1998). International environmental agreements under uncertainty,

Oxford Economic Papers, 50, 173-185.

22

NAFO (2004), Convention on Future Multilateral Cooperation in the Northwest Atlantic

Fisheries. Dartmouth: North Atlantic Fisheries Organization.

Naito, T., & Polasky, S. (1997). Analysis Of A Highly Migratory Fish Stocks Fishery: A

Game Theoretic Approach. Marine Resource Economics, 12, 179-201.

NEAFC (2007), “New” Convention, London: North East Atlantic Fisheries Commission.

Pezzey, J. C. V., Roberts, C. M., & Urdal, B. T. (2000). A simple bioeconomic model of a

marine reserve. Ecological Economics, 33, 77-91.

Pintassilgo, P. (2003). A coalition approach to the management of high seas fisheries in the

presence of externalities. Natural Resource Modeling , 16, 175-197.

Sanchirico, J. N., & Wilen, J. E. (1999). Bioeconomics of Spatial Exploitation in a Patchy

Environment. Journal of Environmental Economics and Management , 37, 129-150.

Sanchirico, J. N., & Wilen, J. E. (2005). Optimal spatial management of renewable resources:

matching policy scope to ecosystem scale. Journal of Environmental Economics and

Management , 50, 23-46.

Schaefer, M. B. (1954). Some Aspects of the Dynamics of Populations Important to the

Management of the Commercial Marine Fisheries. Bulletin of the Inter-American Tropical

Tuna Commission , 1, 25-56.

Sissener, E. H. & Bjørndal, T. (2005). Climate change and the migratory pattern for

Norwegian spring-spawning herring - implications for management. Marine Policy, 29, 299-

309.

Ulph, A. & Maddison, D. (1997). Uncertainty, Learning and International Environmental

Policy Coordination. Environmental and Resource Economics, 9, 451-466.

UN (1982). United Nations Convention on the Law of the Sea, UN Doc. A/CONF.62/122.

23

UN (1995). Agreement for the Implementation of the Provisions of the United Nations

Convention on the Law of the Sea of 10 December 1982 Relating to the Conservation and

Management of Straddling Fish Stocks and Highly Migratory Fish Stocks, UN Doc.

A/CONF.164/37

Yi, S.-S. (2003). Endogenous Formation of Economic Coalitions: a Survey of the Partition

Function Approach. In Carraro, Carlo (eds.), The Endogenous Formation of Economic

Coalitions. The Fondazione Eni Enrico Mattei (FEEM) Series on Economics and the

Environment. Cheltenham: Edward Elgar, ch. 3, 80-127.