### 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 probablities that Low occurs at the next stage of the play. This state may even become 'absorbing', i.e., transitions to High become impossible.

Original language | English |
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Place of Publication | Jena, Germany |

Publisher | Max Planck Gesellschaft |

Number of pages | 29 |

Publication status | Published - Nov 2010 |

### Publication series

Name | Papers on economics & evolution, ISSN 1430-4716 |
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Publisher | Max Planck Gesellschaft |

No. | 2010-24 |

### Keywords

- IR-76562
- common pool resource dilemma
- Equilibria
- Stochastic games
- endogenous transitions
- limiting average rewards

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## Cite this

Joosten, R. A. M. G., & Meijboom, R. (2010).

*Stochastic games with endogenous transitions*. (Papers on economics & evolution, ISSN 1430-4716; No. 2010-24). Jena, Germany: Max Planck Gesellschaft.