Cycles versus equilibrium in evolutionary games |
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Authors: | Thomas W L Norman |
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Institution: | (1) European University Institute, Villa San Paolo, Via della Piazzuola, 43, 50133 Firenze, Italy |
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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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