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

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  • R. Joosten
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    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.

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    Bibliographic Info

    Paper provided by Max Planck Institute of Economics, Evolutionary Economics Group in its series Papers on Economics and Evolution with number 2005-06.

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    Length: 18 pages
    Date of creation: May 2005
    Date of revision:
    Handle: RePEc:esi:evopap:2005-06

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

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    References

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    1. 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).
    2. 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.
    3. R. Joosten, . "On Repeated Games with Vanishing Actions," Papers on Economics and Evolution 2001-11, Max Planck Institute of Economics, Evolutionary Economics Group.
    4. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-85, November.
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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, Max Planck Institute of Economics, Evolutionary Economics Group.

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