Journal
GAMES AND ECONOMIC BEHAVIOR
Volume 74, Issue 1, Pages 434-441Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.geb.2011.05.014
Keywords
Evolutionary games; Logit dynamics; Hopf bifurcation; Fold bifurcation
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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. (C) 2011 Elsevier Inc. All rights reserved.
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