Cycles versus equilibrium in evolutionary games

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...

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Bibliographic Details
Published in:Theory and decision 2010-08, Vol.69 (2), p.167-182
Main Author: Norman, Thomas W. L.
Format: Article
Language:English
Subjects:
Applied sciences
Behavioral/Experimental Economics
Costs
Decision theory. Utility theory
Dynamic tests
Dynamics
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Equilibrium
Equilibrium models
Equilibrium theory
Evolution
Evolutionary
Evolutionary economics
Exact sciences and technology
Expected utility
Finance
Game Theory
Games
Insurance
Inventory control, production control. Distribution
Management
Mutation
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Population
Probability
Probability theory
Randomness
Social and Behav. Sciences
Statistics for Business
Stochastic models
Strategy
Studies
Switching
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Summary: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.
ISSN:0040-5833
1573-7187
DOI:10.1007/s11238-009-9190-y