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Stubbornness, Power, and Equilibrium Selection in Repeated Games with Multiple Equilibria

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  • Kjell Hausken

Abstract

Axelord’s [(1970), Conflict of Interest, Markham Publishers, Chicago] index of conflict in 2 × 2 games with two pure strategy equilibria has the property that a reduction in the cost of holding out corresponds to an increase in conflict. This article takes the opposite view, arguing that if losing becomes less costly, a player is less likely to gamble to win, which means that conflict will be less frequent. This approach leads to a new power index and a new measure of stubbornness, both anchored in strategic reasoning. The win probability defined as power constitutes an equilibrium refinement which differs from Harsanyi and Selten’s [(1988), A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge] refinement. In contrast, Axelrod’s approach focuses on preferences regarding divergences from imaginary outmost rewards that cannot be obtained jointly. The player who is less powerful in an asymmetric one-shot game becomes more powerful in the repeated game, provided he or she values the future sufficiently more than the opponent. This contrasts with the view that repetition induces cooperation, but conforms with the expectation that a more patient player receives a larger share of the pie. Copyright Springer Science+Business Media, LLC 2007

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  • Kjell Hausken, 2007. "Stubbornness, Power, and Equilibrium Selection in Repeated Games with Multiple Equilibria," Theory and Decision, Springer, vol. 62(2), pages 135-160, March.
  • Handle: RePEc:kap:theord:v:62:y:2007:i:2:p:135-160
    DOI: 10.1007/s11238-006-9020-4
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    More about this item

    Keywords

    conflict; discounting; equilibrium refinement; equilibrium selection; power index; repeated game; stubbornness incentive; C72; D74;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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