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The Explanatory Relevance of Nash Equilibrium: One-Dimensional Chaos in Boundedly Rational Learning

Published online by Cambridge University Press:  01 January 2022

Elliott Wagner
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Abstract

Game theory is often used to explain behavior. Such explanations often proceed by demonstrating that the behavior in question is a Nash equilibrium. Agents are in Nash equilibrium if each agent’s strategy maximizes her payoff given her opponents’ strategies. Nash equilibriums are fundamentally static, but it is usually assumed that equilibriums will be the outcome of a dynamic process of learning or evolution. This article demonstrates that, even in the most simple setting, this need not be true. In two-strategy games with just a single equilibrium, a family of imitative learning dynamics does not lead to equilibrium.

Type
General Philosophy of Science
Information
Philosophy of Science , Volume 80 , Issue 5 , December 2013 , pp. 783 - 795
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

This material is based on work supported by the National Science Foundation under grant EF 1038456. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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