Cycles versus equilibrium in evolutionary games

Cycles versus equilibrium in evolutionary games

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Article ID: iaor20105393
Volume: 69
Issue: 2
Start Page Number: 167
End Page Number: 182
Publication Date: Aug 2010
Journal: Theory and Decision
Authors:
Abstract:

Mixed-strategy equilibria are typically rather unstable in evolutionary game theory. “Monocyclic” games, such as Rock– Paper– Scissors, have only mixed equilibria, some of which are “stable” in the sense that sequential best replies lead to them; yet, even these games are prone to stable cycles under discrete-time simultaneous best replies, giving an unusual equilibrium-selection problem. This article analyzes such games in a random-utility setting where changing strategies is costly, and the speed of the dynamic is, thus, endogenous. The stochastically stable outcome is determined by the cost of switching strategies; when switching costs are high, mixed equilibria are selected, whereas when switching costs are low, cycles are selected.

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