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

Philosophy of Science 80 (5):783-795 (2013)
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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

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References found in this work

Equilibrium explanation.Elliott Sober - 1983 - Philosophical Studies 43 (2):201 - 210.
Deterministic Chaos and the Evolution of Meaning.Elliott O. Wagner - 2012 - British Journal for the Philosophy of Science 63 (3):547-575.
Chaos and the Explanatory Significance of Equilibrium: Strange Attractors in Evolutionary Game Dynamics.Brian Skyrms - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:374-394.

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