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Demented Prisoners

Author

Listed:
  • Klaus Kultti

    (Department of Economics, University of Helsinki)

  • Hannu Salonen

    (Department of Economics, University of Turku)

Abstract

We study infinitely repeated Prisoners' Dilemma, where one of the players may be demented. If a player gets demented in period t after his choice of action, he is stuck to this choice for the rest of the game. So if his last choice was ``cooperate'' just before dementia struck him, then he's bound to cooperate always in the future. Even though a demented player cannot make choices any more he enjoys the same payoffs from strategy profiles as he did when healthy. A player may prove he is still healthy by showing a (costly) health certificate. This is possible only as long as the player really is healthy: a demented player cannot get a clean bill of health. We study an asymmetric information game where it is known that player 1 cannot get demented but player 2 may be either a ``healthy'' type who will never be demented or a ``dementible'' type who eventually will get demented. We study when cooperation can be maintained in a perfect Bayesian equilibrium with at most health check.

Suggested Citation

  • Klaus Kultti & Hannu Salonen, 2009. "Demented Prisoners," Discussion Papers 43, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp43
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    File URL: http://www.ace-economics.fi/kuvat/dp43.pdf
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    References listed on IDEAS

    as
    1. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
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    More about this item

    Keywords

    prisoners' dilemma; dementia; co-operation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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