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Patience, Fish Wars, rarity value & Allee effects

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  • Reinoud Joosten
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    Abstract

    In a Small Fish War two agents interacting on a body of water have essentially two options: they can Â…fish with restraint or without. Fishing with restraint is not harmful; Â…shing without yields a higher immediate catch, but may induce lower future catches. Inspired by recent work in biology, we introduce into this setting rarity value and Allee effects. Rarity value means that extreme scarcity of the Â…sh may affect its unit proÂ…t 'explosively'. An Allee effect implies that if the population size or density falls below a so-called Allee threshold, then only negative growth rates can occur from then on. We examine equilibrium behavior of the agents under the limiting average reward criterion and the sustainability of the common-pool resource system. Assuming Â…fixed prices at fiÂ…rst, we show that patience on the part of the agents is beneÂ…cial to both sustainable high catches and Â…fish stocks. An Allee effect can not influence the set of equilibrium rewards unless the Allee threshold is (unrealistically) high. A price mechanism reflecting effects of the resource's scarcity, is then imposed. We obtain a rather subtle picture of what may occur. Patience may be detrimental to the sustainability of a high Â…fish stock and it may be compatible with equilibrium behavior to exhaust the resource almost completely. However, this result does not hold in general but it depends on complex relations between the Allee threshold, the dynamics in the (interactive) resource and price systems, and the actual scarcity caused if the agents show no restraint.

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    File URL: ftp://papers.econ.mpg.de/evo/discussionpapers/2007-24.pdf
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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 2007-24.

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    Date of creation: Dec 2007
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    Handle: RePEc:esi:evopap:2007-24

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    Keywords: common pool resource systems; Â…fish wars; limiting average rewards; sustainability; rarity value; Allee effect; stochastic games Length 19 pages;

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    1. Erwin Bulte & Henk Folmer & Wim Heijman, 1995. "Open access, common property and scarcity rent in fisheries," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 6(4), pages 309-320, December.
    2. Reinoud Joosten & Thomas Brenner & Ulrich Witt, 2003. "Games with frequency-dependent stage payoffs," International Journal of Game Theory, Springer, vol. 31(4), pages 609-620, 09.
    3. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, April.
    4. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
    5. 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.
    6. 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).
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