Games with frequency-dependent stage payoffs

Reinoud A.M.G. Joosten, Thomas Brenner, Ulrich Witt

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Games with frequency-dependent stage payoffs (FD-games), are infinitely repeated non-cooperative games played at discrete moments in time called stages. The stage payo¤s depend on the action pair actually chosen, and on the relative frequencies with which all actions were chosen before. We assume that players wish to maximize their expected (limiting) average rewards over the entire time-horizon. We prove an analogy to, as well as an extension of the (perfect) Folk Theorem. Each pair of rewards in the convex hull of all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Moreover, each pair of rewards in same set giving each player strictly more than the threat-point-reward, can be supported by a subgame-perfect equilibrium. Under a pair of jointly-convergent strategies, the relative frequency of each action pair converges in the long run.
Original languageUndefined
Pages (from-to)609-620
Number of pages12
JournalInternational journal of game theory
Issue number4
Publication statusPublished - 2002


  • METIS-213079
  • jointly-convergent strategies
  • Frequency-dependent stage payoffs
  • limiting average rewards
  • IR-58682

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