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Stability and Explanatory Significance of Some Simple Evolutionary Models

Published online by Cambridge University Press:  01 April 2022

Brian Skyrms
Brian Skyrms*
Affiliation:
Logic and Philosophy of Science, University of California, Irvine
*
†Send requests for reprints to the author, Logic and Philosophy of Science, 3151 Social Science Plaza, University of California, Irvine, Irvine, Ca. 92697-5100.
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Abstract

The explanatory significance of equilibrium depends on the underlying dynamics. A number of questions of stability and robustness are relevant. Here I investigate these questions with respect to some simple evolutionary models from my book, Evolution of the Social Contract. These models use the replicator dynamics. In each of these models I identify the equilibria and characterize their local dynamic stability properties. In two of the models, I show that one equilibrium is globally asymptotically stable. I then show that the foregoing results are robust over a large class of adaptive dynamics that might be considered as alternatives to the replicator dynamics. I investigate the structural stability properties of the three models. The question of the structural stability of a model of bargaining with correlated encounters raised by D'Arms, Batterman, and Górny (1998) is answered in the affirmative. The other two models are not structurally stable. Modification of a structurally unstable signaling system to allow for correlated encounters results in a structurally stable model.

Type
Research Article
Information
Philosophy of Science , Volume 67 , Issue 1 , March 2000 , pp. 94 - 113
Copyright
Copyright © 2000 by the Philosophy of Science Association

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Footnotes

‡

I would like to thank Bruce Bennett for a tutorial on structural stability and Morse-Smale systems, and two anonymous referees for helpful suggestions.

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