Strict and Symmetric Correlated Equilibria are the Distributions of the ESS’s of Biological Conflicts with Asymmetric Roles

Abstract

We investigate the ESS’s of payoff-irrelevant asymmetric animal conflicts in Selten’s (1980) model. We show that these are determined by the symmetric and strict correlated equilibria of the underlying (symmetric) two-person game. More precisely, the set of distributions (on the strategy space) of ESS’s coincides with the set of strict and symmetric correlated equilibria (described as distributions). Our result enables us to predict all possible stable payoffs in payoff-irrelevant asymmetric animal conflicts using Aumann’s correlated equilibria. It also enables us to interpret correlated euqilibria as solutions to biological conflicts: Nature supplies the correlation device as a phenotypic conditional behavior.

This work was supported by Volkswagen Foundation Grant I/63691 to ECO-RATIO group. We would like to thank the Institute of Advanced Studies of The Hebrew University of Jerusalem for its hospitality which contributed to our “coordination”. We acknowledge helpful conversations with R. Aumann, S. Ellner, U. Motro, R. Selten, J. Sobel, and P. Young. We thank S. Zamir and D. Goldberg for comments on the manuscript. A.S. would like to thank especially R. Selten, A. Neyman and M. Maschler for introducing him to the intriguing world of game theory and competitive interactions.