Loss of skills in coordination games

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Abstract

This paper dealswith 2-player coordination games with vanishing actions, which are repeated games where all diagonal payoffs are strictly positive and all nondiagonal payoffs are zero with the following additional property: At any stage beyond r, if a player has not played a certain action for the last r stages, then he unlearns this action and it disappears from his action set. Such a game is called an r -restricted game. To evaluate the stream of payoffs we use the average reward. For r = 1 the game strategically reduces to a one-shot game and for r >= 3 in Schoenmakers ( Int Game Theory Rev 4: 119-126, 2002) it is shown that all payoffs in the convex hull of the diagonal payoffs are equilibrium rewards. In this paper for the case r = 2 we provide a characterization of the set of equilibrium rewards for 2 x 2 games of this type and a technique to find the equilibrium rewards in m xm games. We also discuss subgame perfection.

Original languageEnglish
Pages (from-to)769-789
Number of pages21
JournalInternational Journal of Game Theory
Volume40
Issue number4
DOIs
Publication statusPublished - Nov 2011

Keywords

  • Game theory
  • Repeated games
  • Coordination games
  • Nash equilibrium
  • Subgame perfect equilibrium
  • 2-PLAYER STOCHASTIC GAMES

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