The Robustness of Hybrid Equilibria in Costly Signaling Games
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Recent work on costly signaling games has identified new Nash equilibria in addition to the standard costly signaling equilibrium as a possible explanation for signaling behavior. These so-called hybrid equilibria are Liapunov stable, but not asymptotically stable for the replicator dynamics. Since some eigenvalues of the hybrid equilibria have zero real part, this result is not structurally stable. The purpose of this paper is to show that under one reasonable perturbation of the replicator dynamics—the selection–mutation dynamics—rest points close to the hybrid equilibrium exist and are asymptotically stable. Moreover, for another plausible version of the replicator dynamics—Maynard Smith’s adjusted replicator dynamics—the same is true. This reinforces the significance of hybrid equilibria for signaling.
KeywordsCostly signaling games Hybrid equilibrium Replicator dynamics Structural stability Selection–mutation dynamics
We would like to thank Josef Hofbauer and Carl Bergstrom for helpful comments. This material is based upon work supported by the National Science Foundation under Grant No. EF 1038456. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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