Stubbornness, power, and equlibrium selection in repeated games with multiple equilibra
Journal article, Peer reviewed
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Original versionHausken, K. (2007) Stubbornness, power, and equlibrium selection in repeated games with multiple equilibra. Theory and Decision, 62(2), pp. 135-160 10.1007/s11238-006-9020-4
Axelrod’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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