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Stochastic games with endogenous transitions

Author

Listed:
  • Reinoud Joosten
  • Robin Meijboom

Abstract

We introduce a stochastic game in which transition probabilities depend on the history of the play, i.e., the players’ past action choices. To solve this new type of game under the limiting average reward criterion, we determine the set of jointly-convergent pure-strategy rewards which can be supported by equilibria involving threats. We examine the following setting for motivational and expository purposes. Each period, two agents exploiting a fishery choose between catching with restraint or without. The fish stock is in either of two states, High or Low, and in the latter each action pair yields lower payoffs. Restraint is harmless to the fish, but it is a dominated strategy in each stage game. Absence of restraint damages the resource, i.e., the less restraint the agents show, the higher the probabilities that Low occurs at the next stage of the play. This state may even become ‘absorbing’, i.e., transitions to High become impossible.

Suggested Citation

  • Reinoud Joosten & Robin Meijboom, 2010. "Stochastic games with endogenous transitions," Papers on Economics and Evolution 2010-24, Philipps University Marburg, Department of Geography.
  • Handle: RePEc:esi:evopap:2010-24
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    References listed on IDEAS

    as
    1. Reinoud Joosten & Thomas Brenner & Ulrich Witt, 2003. "Games with frequency-dependent stage payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(4), pages 609-620, September.
    2. Bulte, Erwin H., 2003. "Open access harvesting of wildlife: the poaching pit and conservation of endangered species," Agricultural Economics, Blackwell, vol. 28(1), pages 27-37, January.
    3. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    4. repec:cor:louvrp:-636 is not listed on IDEAS
    5. 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).
    6. Joosten Reinoud & Peters Hans & Thuijsman Frank, 1995. "Unlearning by Not Doing: Repeated Games with Vanishing Actions," Games and Economic Behavior, Elsevier, vol. 9(1), pages 1-7, April.
    7. 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)

    More about this item

    Keywords

    Stochastic games; endogenous transitions; limiting average rewards; equilibria; common pool resource dilemma Length 29 pages;

    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
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery
    • Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics

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