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Dynamic Games and Applications

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01.09.2016

The Robustness of Hybrid Equilibria in Costly Signaling Games

verfasst von: Simon M. Huttegger, Kevin J. S. Zollman

Erschienen in: Dynamic Games and Applications | Ausgabe 3/2016

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Abstract

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.

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The order of the publications is somewhat misleading since Wagner was actually the first to recognize the significance of hybrid equilibria for evolutionary games.

In the context of signaling games, see [12] and [13] for a general selection–mutation dynamics.

The Jacobian matrix of the replicator dynamics is the matrix of partial derivatives of (1) with respect to \(x_1, \ldots , x_4,y_1, \ldots , y_4\). A rest point of the replicator dynamics (2) is hyperbolic if no eigenvalue of the Jacobian matrix of (1) evaluated at the rest point has zero real part.

By the eigenvalues of the selection–mutation dynamics, we mean the eigenvalues of the Jacobian matrix of (2). The role of the implicit function theorem is explained in, e.g., [6].

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Titel: The Robustness of Hybrid Equilibria in Costly Signaling Games
verfasst von: Simon M. Huttegger
Kevin J. S. Zollman
Publikationsdatum: 01.09.2016
Verlag: Springer US
Erschienen in: Dynamic Games and Applications / Ausgabe 3/2016
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-015-0159-x

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