Development of game theory and fisheries

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Development of game theory and fisheries

• Marko Lindroos
• JSS

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Literature link

• http//www.mm.helsinki.fi/mjlindro/gamefish.html

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Stage games

• Ruseski JEEM 1998
• Quinn and Ruseski NRM 2001
• Kronbak and Lindroos ERE 2006
• Repeated games Hannesson JEEM 1997

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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

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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

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Allocation

• White and Mace NRM 1988
• Armstrong ERE 1999
• Applying sharing rules
• Bjørndal and Lindroos ERE 2004
• Spatiality affects sharing of cooperative benefits

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Reviews

• Kaitala 1986
• Sumaila MP 1999
• Bjørndal, Kaitala, Lindroos and Munro Ann OR 2000
  
• Kaitala and Lindroos 2001
• Lindroos, Kronbak and Kaitala 2007

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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

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International Management of North Sea Herring
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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

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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 --gt F to
  Norway and (1-F) to the EU

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Bioeconomic model
Both countries
Population dynamics
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Biomass (million tonnes) in noncooperative
equilibrium
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Cooperative case
Maximise total benefits
TAC a constant fraction (l) of each
years biomass TAC lS --gt Norways allocation
FlS
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Biomass and harvest in cooperative case
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Sharing of benefits
Equal sharing of cooperative benefits e/2 for
both, where e Pcoop P1 P2
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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)

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NSSH

• Three-player coalitional game model
• Solution concept Shapley value
• Effect of biological and economic uncertainties
  Stability of full cooperation?

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Model framework

• Economic
• price 1.45 NOK /kg
• number of vessels (N) related to maximum fishing
  mortality (F)
• log-linear costs for country i
• country 1 has the lowest costs

• Biological
• discrete-time age-structured model with 17 age
  classes
• Ricker growth, Beverton-Holt stock-recruitment
  with log-normal error
• fishing mortality (F) and selectivity (0-1 type)
  as controls

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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

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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 non-cooperation)

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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) lt 2.5 billion kg (Safe Minimum
  Biological Level SMBL)
• Selectivity of fishing gear also affects stability

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Instability of full cooperation and the effect of
selectivity
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(No Transcript)
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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)