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Repeated two-person zero-sum games with unequal discounting and private monitoring

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  • Carmona, Guilherme
  • Carvalho, Luís

Abstract

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.

Suggested Citation

  • Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    • Handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:131-138
    DOI: 10.1016/j.jmateco.2016.02.005
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    1. Romulus Breban, 2016. "A mathematical model for a gaming community," Papers 1607.03161, arXiv.org.

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    Repeated games; Two-person zero-sum games;

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