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Stochastic games with endogenous transitions

  • Reinoud Joosten
  • Robin Meijboom
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    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.

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    File URL: ftp://137.248.191.199/RePEc/esi/discussionpapers/2010-24.pdf
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    Paper provided by Philipps University Marburg, Department of Geography in its series Papers on Economics and Evolution with number 2010-24.

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    Date of creation: 25 Nov 2010
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    Handle: RePEc:esi:evopap:2010-24
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    1. 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.
    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. HART, Sergiu, . "Nonzerosum two-person repeated games with incomplete information," CORE Discussion Papers RP -636, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. F. Forges, 2010. "An Approach to Communication Equilibrium," Levine's Working Paper Archive 516, David K. Levine.
    5. 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.
    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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