Fish Wars with Changing Area for a Fishery

  • Anna Rettieva
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)


In this paper, a discrete-time game model related to a bioresource management problem (fish catching) is considered. The center (referee) shares a reservoir between the competitors, the players (countries) harvest the fish stock on their territory.We consider power population’s growth function and logarithmic players’ profits. Both cases of finite and infinite planning horizon are investigated. The Nash and cooperative equilibria are derived. We investigate a new type of equilibrium – cooperative incentive equilibrium.Hence, the center punishes players for a deviation from the cooperative equilibrium by changing the harvesting territory. A numerical illustration is carried out and results are compared.


Nash Equilibrium Planning Horizon Nash Equilibrium Strategy Punishment Strategy Cooperative Equilibrium 
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The research was supported by the Russian Fund for Basic Research, projects 10-01-00089-a and 08-01-98801-r-sever-a.


  1. 1.
    Basar, T., Olsder G.J.: Dynamic noncooperative game theory. Academic, New York (1982)MATHGoogle Scholar
  2. 2.
    Ehtamo, H., Hamalainen, R.P.: A cooperative incentive equilibrium for a resource management problem. J. Econ. Dyn. Control 17, 659–678 (1993)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Levhari, D., Mirman, L.J.: The great fish war: an example using a dynamic Cournot-Nash solution. Bell J. Econ. 11(1), 322–334 (1980)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Mazalov, V.V., Rettieva, A.N.: A fishery game model with migration: reserved territory approach. Int. J. Math. Game Theor. Algebra 15(3), 243–256 (2005)MathSciNetGoogle Scholar
  5. 5.
    Mazalov, V.V., Rettieva, A.N.: Nash equilibrium in bioresource management problem. Math. Model. 18(5), 73–90 (2006) (in russian)Google Scholar
  6. 6.
    Mazalov, V.V., Rettieva, A.N.: Bioresource management problem with changing area for fishery. Game Theor. Appl. 13, 101–110 (2008)MathSciNetGoogle Scholar
  7. 7.
    Nowak, A.: A note on an equilibrium in the great fish war game. Econ. Bull. 17(2), 1–10 (2006)Google Scholar
  8. 8.
    Osborn, D.K.: Cartel problems. Am. Econ. Rev. 66, 835–844 (1976)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of Applied Mathematical ResearchKarelian Research Center of RASPetrozavodskRussia

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