On the elimination of dominated strategies in stochastic models of evolution with large populations

• Published in: Games and economic behavior Vol. 72; no. 2; pp. 452 - 466
• Main Author: Kuzmics, Christoph
• Format: Journal Article
• Language: English
• Published: Duluth Elsevier Inc 01.06.2011; Elsevier; Academic Press
• Series: Games and Economic Behavior
• Subjects: [formula omitted]-procedure; Dynamics; Evolution; Experimentation; Game theory; Iterated strict dominance; Learning; Learning Experimentation S[infinity]W-procedure Weak dominance Iterated strict dominance; Population; Sensitivity analysis; Stochastic models; Studies; Weak dominance; Learning; Experimentation; S ∞ W -procedure; Weak dominance; Iterated strict dominance; C62; C73; C72
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2010.10.002

A stochastic myopic best-reply dynamics is said to have property (W), for a given number of players n, if every pure weakly dominated strategy in every n-player game is eliminated in the long-run distribution of play induced by the dynamics. In this paper I give a necessary and sufficient condition that a dynamics has to satisfy in order for it to have property (W). The key determinant is found to be the sensitivity of the learning-rate to small payoff differences, inherent in the dynamics. If this sensitivity is higher than a certain cut-off, which depends on the number of players, then the dynamics satisfies property (W). If it is equal to or below that cut-off, then the dynamics does not satisfy property (W).