, Volume 19, Issue 1, pp 59-89

“Evolutionary” selection dynamics in games: Convergence and limit properties

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Abstract

This paper discusses convergence properties and limiting behavior in a class of dynamical systems of which the replicator dynamics of (biological) evolutionary game theory are a special case. It is known that such dynamics need not be well-behaved for arbitrary games. However, it is easy to show that dominance solvable games are convergent for any dynamics in the class and, what is somewhat more difficult to establish, weak dominance solvable games are as well, provided they are “small” in a sense to be made precise in the text. The paper goes on to compare dynamical solutions with standard solution concepts from noncooperative game theory.

This paper is a revision of Chapter 1 of my Ph.D. thesis. It owes much to the guidance of Andreu Mas-Colell, Eric Maskin, Vijay Krishna, and Dilip Abreu. I wish also to express my thanks for the comments of an anonymous referee. Naturally, all remaining shortcomings are my responsibility.