Stubbornness,Power, and Equilibrium Selection in Repeated Games with Multiple Equilibria |
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Authors: | Kjell Hausken |
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Institution: | (1) Faculty of Social Sciences, University of Stavanger, 4036 Stavanger, Norway |
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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.
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Keywords: | conflict discounting equilibrium refinement equilibrium selection power index repeated game stubbornness incentive |
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