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The Classification of Continuation Probabilities

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  • Michael A. Jones

Abstract

It is known that the only subgame perfect equilibrium for finitely repeated Prisoner's Dilemna games consists of "defecting" in every round. Finitely repeated games are only representative of a class of indefinitely repeated games where the sole subgame perfect equilibrium is noncooperative. This broader class of repeated games with "quasifinite" continuation probabilities is defined. A matrix inequality is recalled that when solved by a cooperation vector, induces a subgame perfect equilibrium. A condition for continuation probabilities indicates when this matrix inequality can be satisfied at equality by a cooperation vector. The associated strategy is a cooperative subgame perfect equilibrium.

Suggested Citation

  • Michael A. Jones, 1995. "The Classification of Continuation Probabilities," Discussion Papers 1137, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1137
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    Cited by:

    1. Steven Brams & D. Kilgour, 1998. "Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem," Theory and Decision, Springer, vol. 45(3), pages 263-289, December.

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