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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 Philipps University Marburg, Department of Geography 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, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 54(6), pages 1375-85, November.
    3. HART, Sergiu, . "Nonzerosum two-person repeated games with incomplete information," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -636, 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, Elsevier, vol. 50(4), pages 429-448, April.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521637329.
    6. R. Joosten, . "On Repeated Games with Vanishing Actions," Papers on Economics and Evolution, Philipps University Marburg, Department of Geography 2001-11, Philipps University Marburg, Department of Geography.
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    Cited by:
    1. Reinoud Joosten, 2007. "Strategic Advertisement with Externalities: A New Dynamic Approach," Papers on Economics and Evolution, Philipps University Marburg, Department of Geography 2007-02, Philipps University Marburg, Department of Geography.
    2. Huang, Weihong, 2010. "On the complexity of strategy-switching dynamics," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 75(3), pages 445-460, September.

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