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Stochastic Stability and Disagreements between Dynamics

Published online by Cambridge University Press:  01 January 2022

Aydin Mohseni
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Abstract

The replicator dynamics and Moran process are the main deterministic and stochastic models of evolutionary game theory. The models are connected by a mean-field relationship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad class of games, demonstrates a novel domain of agreement between the dynamics, and indicates a broader moral for evolutionary modeling.

Type
Articles
Information
Philosophy of Science , Volume 86 , Issue 3 , July 2019 , pp. 497 - 521
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

*

To contact the author, please write to: University of California, Irvine, Irvine, CA 92697; e-mail: amohseni@uci.edu.

†

I am indebted to Simon Huttegger, Brian Skyrms, Cailin O’Connor, Hannah Rubin, Cole Williams, and two anonymous referees for invaluable feedback on earlier drafts. Special thanks to audiences at the Generalized Theory of Evolution conference in Düsseldorf and the Infinite Idealizations in Science conference at the Munich Center for Mathematical Philosophy and participants in the Social Dynamics seminar in Irvine for helpful discussions.

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