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A small Fish War: an example with frequency-dependent stage payoffs

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  • R. Joosten

Abstract

Two agents possess the fishing rights to a lake. Each period they have two options, to catch without restraint, e.g., to use a fine-mazed net, or to catch with some restraint, e.g., to use a wide-mazed net. The use of a fine-mazed net always yields a higher immediate catch than the alternative. The present catches depend on the behavior of the agents in the past. The more often the agents have used the fine-mazed net in the past, the lower the present catches are independent from the type of nets being used. We determine feasible rewards and provide (subgame perfect) equilibria for the limiting average reward criterion using methods inspired by the repeated-games literature. Our analysis shows that a `tragedy of the commons' can be averted, as sustainable Pareto-efficient outcomes can be supported by subgame perfect equilibria.

Suggested Citation

  • R. Joosten, 2005. "A small Fish War: an example with frequency-dependent stage payoffs," Papers on Economics and Evolution 2005-06, Philipps University Marburg, Department of Geography.
  • Handle: RePEc:esi:evopap:2005-06
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    References listed on IDEAS

    as
    1. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    2. repec:cor:louvrp:-636 is not listed on IDEAS
    3. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," CORE Discussion Papers 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Brenner, Thomas & Witt, Ulrich, 2003. "Melioration learning in games with constant and frequency-dependent pay-offs," Journal of Economic Behavior & Organization, Elsevier, vol. 50(4), pages 429-448, April.
    5. R. Joosten, "undated". "On Repeated Games with Vanishing Actions," Papers on Economics and Evolution 2001-11, Philipps University Marburg, Department of Geography.
    6. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Huang, Weihong, 2010. "On the complexity of strategy-switching dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 445-460, September.
    2. Reinoud Joosten, 2007. "Strategic Advertisement with Externalities: A New Dynamic Approach," Papers on Economics and Evolution 2007-02, Philipps University Marburg, Department of Geography.

    More about this item

    Keywords

    games with frequency-dependent stage payoffs; limiting average reward; equilibria; renewable common-pool resources;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery

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