Games with frequency-dependent stage payoffs

Games with frequency-dependent stage payoffs (FD-games), are infinitely repeated non-cooperative games played at discrete moments in time called stages. The stage payoffs 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.

Authors and Affiliations

1. School of Business, Public Administration and Technology, Financial Engineering Laboratory, University of Twente, no street, P.O. Box 217, 7500 AE, Enschede, The Netherlands

   Reinoud Joosten

2. Max Planck Institute for Research into Economic Systems, Evolutionary Economics Group, Kahlaische Strasse 10, 000, 07745, Jena, Germany

   Thomas Brenner

3. Max Planck Institute for Research into Economic Systems, Evolutionary Economics Group, no orgname, Kahlaische Strasse 10, 000, 07745, Jena, Germany

   Ulrich Witt

Corresponding authors

Correspondence to Reinoud Joosten, Thomas Brenner or Ulrich Witt.

Received: March 2002/Revised: January 2003

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