Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics

Cars Hommes and Marius I. Ochea

Games and Economic Behavior, 2012, vol. 74, issue 1, 434-441

Abstract: This note shows, by means of two simple, three-strategy games, the existence of stable periodic orbits and of multiple, interior steady states in a smooth version of the Best-Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, occur under the Logit Dynamics, even for three-strategy games. We also show that the Logit Dynamics displays another bifurcation which cannot occur under the Replicator Dynamics: the fold bifurcation, with non-monotonic creation and disappearance of steady states.

Keywords: Evolutionary games; Logit dynamics; Hopf bifurcation; Fold bifurcation (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:74:y:2012:i:1:p:434-441

DOI: 10.1016/j.geb.2011.05.014

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