The Classification of Continuation Probabilities

Michael A. Jones

No 1137, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

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.

Date: 1995-07
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