Development of game theory and fisheries Marko Lindroos JSS

Literature link

The history 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 Both countries: Population dynamics:

Biomass (million tonnes) in noncooperative equilibrium

Cooperative case Maximise total benefits: TAC a constant fraction ( ) of each year’s biomass: TAC = S --> Norway’s allocation F S =

Biomass and harvest in cooperative case

Sharing of benefits Equal sharing of cooperative benefits: e/2 for both, where e = P coop – P 1 – P 2

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 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 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

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 billion NOK (for example country 1 receives almost double the amount compared to non- cooperation)

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

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)