Hommes, C. and Ochea, M. (2012). Multiple equilibria and limit cycles in evolutonary games with Logit Dynamics Games and Economic Behavior, 74(1):434--441.
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Affiliated author
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Publication year2012
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JournalGames and Economic Behavior
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.