Coalitions in Fisheries

Why game theory?

• Whenever there is more than one interest group (country, fishermen etc.) strategic behaviour / competition may prevent optimal harvest control

• International fisheries have very limited possibilities to prevent strategic behaviour / free-riding

Alternative game models

• Non-cooperative games– only individual benefits matter

• Cooperative games– sharing of benefits

• Coalitional games– how coalitions form

Cooperative games

• Assume Sweden, Norway and Finland can form coalitions when harvesting fish stocks

• Possible coalitions {SWE}, {FIN}, {NOR}, {SWE, NOR}, {SWE, FIN}, {NOR, FIN}, {SWE, NOR, FIN}

Cooperative Solutions

• How should they share cooperative benefits?

• The solutions search an allocation of cooperative benefits given e.g. individual & group rationality

Coalitional games: Searching for equilibrium cooperation structures

NOR SWE FIN

{NOR, SWE, FIN}

{NOR, FIN} SWE

Non-Cooperation

Partial Cooperation

Full Cooperation

How to make cooperation more attractive?

1. Threat (trigger) strategies

2. Side payments

3. Safe Minimum Bioeconomic Levels of fish stocks (Reference points)

4. Give fishermen more responsibility in harvest control

Motivation

• Recent papers Ruseski (JEEM 1998) and Quinn & Ruseski (NRM 2001) using the Schaefer-Gordon game model do not allow for coalition formation

• The problem of new entrants in Regional Fisheries Management Organisations (RFMOs)

” States having a real interest in the fisheries concerned may become members of such organization or participants in such arrangement.”

--> new entrants make cooperation more difficult

The model

• Gordon-Schaefer production with logistic growth, stock in steady state

• Countries choose their coalition in the first stage and fishing effort in the second stage

• Symmetric versus asymmetric countries with respect to unit costs of effort

• Stability of full cooperation when every country prefers cooperation to free riding

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Steady state

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Partial Cooperation

Symmetric countries

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Cooperation stable if n < 3

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Cooperation may be stable for any n

Effect of fishing costs on stabilityof full cooperation: three asymmetriccountries

Stability conditionF

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Costs of countries k and j affect stability via free rider profits

0 10 20 30 40 50 60 70 80 90-35

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Figure 1: Effect of ck on total free-rider profits

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10

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30

40

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revenue

cost

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Figure 2: Effect of cj on total free-rider

profits

F

Example: New entrants and stability

• Introduce one new entrant into a fishery with three original members that are symmetric

• Initially no cooperation, but new entrant may create incentives for cooperation

• Every country may be economically and biologically better off

Figure 4: Effect of the new entrant on stability of full cooperation

0 5 10 15 20 25 30 35 40 45-4

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stability condition

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Conclusions

• Cost structure of the fishery important in determining the stability of cooperation

• Limited number of new entrants to RFMOs may improve stability of cooperation if the new entrants have low enough costs (but not too low)

12

32

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ij

jicrit bb

bbnThe sustainable number of new entrants :

MANAGEMENT OF REGIONAL FISHERIES ORGANISATIONS: AN APPLICATION OF THE

SHAPLEY VALUE

The Shapley value

• Lloyd Shapley 1953• Possible orders of coalition formation are equally

likely• Countries have already agreed to cooperate• Interpretations:

– Average outcome of the negotiations– Marginal contributions of countries to each

coalition– Sum of dividends that each coalition pays to its

members

Objective function of the players

max ( , ) ( ) ( )J x E e px t c E t dtirt

i i00

c c c cC C D D1 2 1 2

x x x xC D D C2 1 2 1

st dx/dt = F(x) - i=1...4 Ei x,

i = C1,C2,D1,D2

hi=Eix, Ci(x)=ci/xwhen x(t)=ci/p, i=0

Assumptions of the model

• The countries outside coalitions play non-cooperatively against the ones inside the coalition

• C-game perspective: The coalitions that the countries can form with one another define their contributions in the cooperative agreement and consequently their bargaining strengths

• C-function normalised so that the values of the coalitions are between 0 and 1

Characteristic function

v*(i) = 0

v i j J x J x E E E Ei j i ji j

CN

CN

DN

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, 0 0

1 2 1 2

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CN

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, , , 0 0 0

1 2 1 21 21 2

Extending the c-game: Restricted Coalitions and n players

• Simple restriction leads to changes in bargaining strengths of fishing nations

• Setting restricted coalition’s value equal to zero

• Ability to calculate Shapley imputations to a large number of players

Restricted coalition formation

• Only same type of countries want to join together, feasible subcoalitions are {C1,C2} and {D1,D2}, ie we have 4 players

• In the case where the DWFNs have high unit costs of fishing they can improve their negotiation position by refusing to form a coalition with the coastal states

• - > 0zDSi

R zDSi

C1 C2

D1 D2

Cooperation structure

Case I: DWFNs gain individually from coalition restrictions

• Costs of the DWFNs are higher than for the coastal states

• However, when the value of the coastal state coalition is larger than 3/5 then the core is empty for the restricted case

• When the cost difference between DWFNs is large (when the more efficient DWFN has a stronger incentive to join the coastal state coalition) then the result does not apply

Case II: DWFNs gain together from coalition restrictions

• We compare the sum of restricted and unrestricted Shapley values of the DWFNs

• cC1 < cD1 cC2 < cD2

• If cC2 = cD2 then DWFNs are indifferent between coalition restriction and unrestriction

Case III: DWFNs are worse off with coalition restrictions

• cC1 < cD1 cD2 < cC2

• Note that in principle roles can be changed to have same results for coastal state

• In cases 2 and 3, for country D2 coalition restrictions may be individually beneficial

• Coalition restriction means here that all countries will negotiate with one another but if a coalition is restricted then the negotiations are not successful

Increasing number of players

• Provide Shapley values for n player game

• Two most efficient players act as veto players, their presence is necessary for a coalition to have a positive bargaining strength

• limitation: it may not be possible to have a large number of countries in the Regional Fisheries Management Organisation

Parallel fisheries agreements

Parallel fisheries agreements

• Typically modelling n countries exploiting one common fish stock x

• How many countries cooperate, compare to non-cooperative and full cooperative outcomes

• However, there are almost always more species

• There can therefore be two parallel fisheries agreeements, one for x and one for y

Class I: One stock, many agreements

• Think of 4 countries exploiting x

• Two agreements: Countries 1,2 sign a bilateral agreement and also countries 3,4 sign an agreement

• Stability

• Allocation

Example I

• Stage 1: Coalition formation• Stage 2: max ph – cE

• Two parallel agreements exist if it is not optimal to break the bilateral agreements (1,2) and (3,4)

• For example country 3 compares the payoff v(1,2) v(3,4) to v(1,2,3) v(4) and v(1,2) v(3) v(4)

• Payoff to individual country also depends on allocation (sharing of cooperative benefits)

Class II: Multiple stocks

• issue linkage, interconnected games

• Multi-species fisheries

• The set of countries exploiting each stock may be same or different

• Consider three countries exploiting two stocks: Countries 1,2 sign a bilateral agreement on x but for y all countries sign an agreement

• x and y fisheries may be biologically and economically dependent

Example II

• Consider a three-player case where full cooperation is stable in x fishery. This means that the gains of full cooperation exceeds the sum of gains from free-riding:

• C =17 & F = 14 total benefits 17

• Assume further that full cooperation is not stable for y fishery:

• C = 17 F = 18 total benefits 13

• In this case joint management of the stocks would be beneficial since it would make full cooperation stable in both fisheries

• C = 34 & F = 32 total benefits 34 (compared to 30)

Case III: One stock, countries may be part of several agreements

• Countries may e.g. sign bilateral agreements on various issues concerning same stock

• Example: Countries 1,2 agree on technology, countries 2,3 on biology, countries 1,3 on enforcement, all countries on research

• Implications for Regional Fisheries Management Organisations: What should we agree on? Who should agree? Optimal structures of RFMOs, e.g. how many RFMOs should there be?

Discussion

• Realism in the game-theoretic models, e.g. national and international level negotiations

• Effect of species interactions

• Case III needs a new more complicated model

A Coalition Game of the Baltic Sea Cod Fishery

Lone Grønbæk Kronbak Department of Environmental and Business Economics

University of Southern Denmark

Marko Lindroos Department of Economics and Management

University of Helsinki

Literature

• Kaitala & Munro (1993): Need for coalition modelling in high seas fisheries management

• Kaitala & Munro (1995): First analysis on coalitions and high seas fisheries

• Followed by Kaitala & Lindroos (1998), Arnason et al. (2000), Duarte et al. (2000), Gallastegui et al. (2002), Kennedy (2003), Pham Do et al. (2003), Pintassilgo (2003)

Motivation• Previous empirical studies applying c-games:

- Lindroos & Kaitala (2000)

- Arnason, Magnusson & Agnarsson (2000)

- Costa Duarte, Brasão & Pintassilgo (2000)

- Brasão, Costa Duarte & Cunha-e-Sá (2000)

determine sharing rules, but these sharing rules does not satisfy all players.

• Kronbak & Lindroos (2003) shows cooperation in the Baltic Sea cod fishery should be encouraged.

Determine a stable sharing rule for the cooperative Baltic Sea cod fishery

Our Goal

The Baltic Sea

• Remote Area with no international waters

• Cod most valuable fishery in the Baltic Sea

• All Parties exploiting cod are members on IBSFC

• IBSFC sets TACs for cod

• TAC measures are often exceeded

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B otnian S eaG ulf of F in lan d

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Bio-Economic Model

• Discrete time

• Single species

• Age-structured model (6 cohorts)

• Beverton-Holt stock-recruitment relationship (ICES 2000)

• Simulation length: 50 years (1997-2046)

Bio-Economic Model (cont’d)

• 3 players/groups of countries

• Players commit to fishing mortality only in the beginning of the game

• Players move simultaneously

• Cost function squared in harvest and inverse in stock; players differ in cost parameter c1>c2>c3

• Prices are assumed identical and constant

Optimal Strategy and Benefits Playe

rStrategy

(f)NB

(1010 DKR)

FR value

(1010 DKR)

Norm. C-function

1 0.35 2.31 0

2 0.29 1.67 0

3 0.27 1.56 0

1,2 0.46 4.26 2.03 (f3=0.26) 0.1428

1,3 0.46 4.13 2.11 (f2=0.28) 0.1333

2,3 0.41 3.35 2.85 (f1=0.35) 0.0621

1,2,3 0.35 7.47 6.98 (sum) 1

Sharing Rules

Shapley Value• The potential to

change the worth of the coalition by joining or leaving it

• The expected marginal contribution

Nucleolus• Minimize the

dissatisfaction of the coalition

• Finding the lexicographic centre of the core

Sharing Rules

Percentage of cooperative benefits received

Player Shapley Nucleolus Free Rider

1 35.9 % 33.3 % 38.1 %

2 32.3 % 33.3 % 28.2 %

3 31.8 % 33.3 % 27.1 %

Satisfactory nucleolus

• A cooperative sharing imputation which is stable to free rider values

Player Sat. nucleolus Free Rider

1 40.3 % 38.1 %

2 30.4 % 28.2 %

3 29.3 % 27.1 %

Our Contribution

• To apply the c-game in the Baltic Sea environment

• To allow all members of a coalition to be active in the fishery

• Determining a sharing rule which takes the free rider values into consideration

Critique & Limitations

• No fluctuations in the stock.

• Fixed fishing mortality over the simulation period.

• No development in prices and costs over the 50 years simulation.

• The number of players is limited to three (encourage POs in the Baltic Sea).

• No species interaction included.

Concluding Remarks

• Enough benefits in the Baltic Sea cod fishery to achieve a stable cooperative solution.

• Shapley value and nucleolus does not satisfy all players.

• The satisfactory nucleolus is a stable sharing rule for distributing the cooperative benefits in the Baltic Sea cod fishery.