Development of game theory and
fisheries
Marko Lindroos
JSS
Literature link
 http://www.mm.helsinki.fi/~mjlindro/gamefish.html
The history 1979 Methods:
 non-cooperative vs. cooperative
 single species vs. multi-species
 theoretical vs. empirical
 biomass vs. age-strcutured
 two-player vs. multi-player
 static vs. dynamic
 Equilibria and solutions used
 Games not (yet) applied
Munro 1979 Can J Ec
 First important contribution, background the UN Law of
the Sea negotiations
 Early Davenport 1960, game between fish and Jamaican
fishermen
 Two players, dynamic Nash bargaining game
 Countries different wrt discount rate, costs and consumer
preferences
 Side payments as a way to escape the tragedy of the
commons
Results
 Maximise the weighted sum of the objective functions of
the two countries, harvest shares constant in time
 Optimal biomass will be between the individually optimal
stock levels of the countries
 Critique: agreements not binding  Kaitala and Pohjola
NRM 1988
Kaitala and Pohjola NRM 1988
 Differential game with trigger (threat) strategies and
transfer (side) payments
 Non-cooperative equilibrium only the least cost country
harvests, for the other it is not profitable (entry deterring)
 Players monitor each other and compare this to the
agreement
 If discount rate and monitoring interval large, no
equilibrium
 Shows that cooperative equilibrium can be achieved
without the binding agreement assumption
Analysing straddling stocks
 New UN agreement 1995 on straddling and highly
migratory fish stocks
 Kaitala and Munro MRE 1993 and NRM 1997
 The new member problem:
 As the number of countries rises the bioeconomic
problems get worse
 Two solutions proposed: waiting period and transferable
membership
 Application: Pintassilgo and Duarte MRE 2000
 Coalitions not allowed  Kaitala and Lindros NRM 1998
Applying cooperative games
 Kaitala and Lindroos NRM 1998
 Bargaining strength defined also by coalitions, groups of
countries
 Values of coalitions computed from non-cooperative
games between coalition members and outside countries
 How to share benefits
 Three-player model applying Shapley value and nucleolus
 Endogenous coalition formation not allowed  Pintassilgo
NRM 2003
Multi-species games
 Fischer and Mirman JEDC 1992
 duopoly exploiting several areas
 fish move between areas
 Each country catches only one species
 Fischer and Mirman JEEM 1996
 Both countries can harvest both species
 Sumaila MRE 1997
 two-species predator-prey model
 age-structured model of cod and capelin
Differential games
 Clark 1980
 Basic non-cooperative equilibrium, applied in many
papers
 See McKelvey NRM 1999 for discussion
 Kaitala 1985
 Kaitala and Pohjola NRM 1988
 Kaitala and Munro NRM 1997
 Kaitala and Lindroos IGTR 2004
 When to sign fisheries agreements
Dynamic games
 Levhari and Mirman Bell J Ec 1980
 Levhari, Michener and Mirman AER 1981
 Okuguchi 1981
 Fischer and Mirman 1992 & 1996
 Kwon ERE 2006
 Coalitions in the Levhari-Mirman model
 McKelvey, Steinshamn and Sandal IGTR 2002 & 2003,
JEDC 2004
Stage games
 Ruseski JEEM 1998
 Quinn and Ruseski NRM 2001
 Kronbak and Lindroos ERE 2006
 Repeated games Hannesson JEEM 1997
Coalition games
 Kaitala and Lindroos 1998
 Arnason MRE 2000
 Spring-spawning herring fishery, Norway a veto
coalition
 Pintassilgo NRM 2003
 Burton JEEM 2003
 Kronbak and Lindroos MRE 2007
Stochastic games
 Kaitala EJOR 1993
 Cooperative periods vs non-cooperative periods in
fisheries games
 Jørgensen and Yeung JOTA 1996
 Laukkanen JEEM 2003
 Sequential game, with recruitment uncertainty
 Two-players using trigger-strategies
 Illustration for the Baltic Salmon case
 Uncertainty may trigger non-cooperative phases
 Lindroos IGTR 2004
 Bioeconomic reference points to maximise stability of
cooperation
Allocation
 White and Mace NRM 1988
 Armstrong ERE 1999
 Applying sharing rules
 Bjørndal and Lindroos ERE 2004
 Spatiality affects sharing of cooperative benefits
Reviews
 Kaitala 1986
 Sumaila MP 1999
 Bjørndal, Kaitala, Lindroos and Munro Ann OR 2000
 Kaitala and Lindroos 2001
 Lindroos, Kronbak and Kaitala 2007
Games to be played
 Use of mixed strategy equilibria where the equilibrium is
a probability distribution over the strategies
 Bayesian games with imperfect information
 Coopetition
 Uncertainty
International Management of North
Sea Herring
The North Sea herring fishery
 Consists of three spawning stocks in the UK waters
 Several harvesting nations: Norway and the EU
(Denmark, Scotland, the Netherlands)
 Stock close to extinction in 1970s
 Presently the stock is well above the safe minimum
biological level of 0.8 million tonnes
International management
 TAC management
 Norway receives 29% and the EU 71% of the TAC (total
harvest) based on geographical distribution of the stock
 Model the non-cooperative and cooperative games
between the two countries
 Equal sharing of cooperative benefits --> F% to Norway
and (1-F)% to the EU
Bioeconomic model
T
Both countries:
T
 phi  ci Ei 
max
Pi (t ) 

t 1 
1    
t 1
t 1 


Population dynamics:
 S (t ) 




S (t  1)  S (t )  rS (t ) 1 

q
E
FS
(
t
)

q
E
(
1

F
)
S
(
t
)
1 1
2 2

K


Biomass (million tonnes) in noncooperative
equilibrium
4
Total biomass in million tonnes
3.5
3
2.5
2
1.5
1
0.5
0
0
10
20
30
Time
40
50
60
Cooperative case
Maximise total benefits:
 phi  ci E coop 
i
Pi (t ) 


t 1
 1   

i 1 t 1
i 1 t 1 
2
T

2
T

TAC a constant fraction () of each year’s
biomass: TAC = S
 
h

qE
--> Norway’s allocation FS = 1
1 S
1
1  
coop  FS
E1


q


1
1  
coop  (1  F )S
E2



q

Biomass and harvest in cooperative case
Total biomass and harvest in million tonnes
4
3.5
3
S
2.5
2
1.5
1
0.5
h1+h2
0
10
20
30
Time
40
50
60
Sharing of benefits
Equal sharing of cooperative benefits:
e/2 for both, where e = Pcoop – P1 – P2
Number of vessels
Norwegian share
of vessels
F* (Norwegian share
of harvests)
Sharing of benefits (EU costs
1.12, 1.92)
417
409
(*=0.27)
(*=0.26)
39 %
36%
35 %
32%
Conclusions
 Effect of geographical location of fish stocks on
international management
 Non-cooperation leads to depletion of the stock and
economic benefits; Harvesting profitable for Norway only
for short period
 Cooperative management requires a higher share of TAC
to Norway (side payment)
NSSH
 Three-player coalitional game model
 Solution concept: Shapley value
 Effect of biological and economic uncertainties: Stability of
full cooperation?
Model framework
 Biological:
 discrete-time agestructured model with 17
age classes
 Ricker growth, BevertonHolt stock-recruitment with
 Economic:
 price 1.45 NOK /kg
 number of vessels (N)
related to maximum
fishing mortality (F)
 log-linear costs for
country i =
log-normal error
 fishing mortality (F) and
selectivity (0-1 type) as
controls
N i q i1 (Y i / N i Yv ) q 2
 country 1 has the
lowest costs
Game description
 Full cooperation:
 Country 1 buys out the fleets of the others and maximises
profits using a constant fishing mortality of 1.8 and first
fishing age of 8
 Non-cooperation:
 All countries harvest at maximum fishing mortality (0.97,
0.48, 0.35)
 Partial cooperation
 The most efficient member of two-player coalitions buys out
the fleet of the other
Solution: Shapley value
 Assumptions:
 all coalitions have an equal probability to form
 the contributions that the countries make to
coalitions define their bargaining strengths
 Shares (normalised Shapley values): 0.43, 0.31, 0.26
 Total cooperative benefit 20.593 billion NOK (for example
country 1 receives almost double the amount compared to noncooperation)
Biological uncertainty
 Stochastic recruitment (log-normal error)
 Value of grand coalition (cooperative benefits) varies a lot
 Uncertainty creates instability
 Modified cooperative strategy needed: f(t) = 0 if SSB(t) < 2.5
billion kg (Safe Minimum Biological Level = SMBL)
 Selectivity of fishing gear also affects stability
Instability of full cooperation and the effect of
selectivity
First
SMBL
fishing age
7
1%
no SMBL
6
3%
91 %
4
4%
100 %
3
1%
100 %
2
2%
100 %
53 %
Uncertainty type
core
stability
Biological
10.5
21
Biological, modified strategy
1
9.5
Price
20.5
28.5
Price, modified strategy
5.5
11.5
Both
20
29
Both, modified strategy
0.5
1.5
Table 4: Stability of full cooperation (violation percentages)
Conclusions
 Uncertainty creates instability so that full cooperation may
not be possible
 Simple modified cooperative strategies can reduce
instability in the presence of uncertainty
 Safe minimum biological level (SMBL) is also a safe
minimum economic level (SMEL)