Reducing Evolutionary Stability to Pure Strategies in Positive Semidefinite Games

This paper introduces a class of games called the positive semidefinite games, for which we show the absence of mixed and nonstrict ESS's. As a result, a strategy is an ESS if and only if it is strict Nash. One famous example in this class of games is Rock{Paper{Scissors. For a smaller class of games called the positive definite games, we prove a similar result forThis paper introduces a class of games called the positive semidefinite games, for which we show the absence of mixed and nonstrict ESS's. As a result, a strategy is an ESS if and only if it is strict Nash. One famous example in this class of games is Rock{Paper{Scissors. For a smaller class of games called the positive definite games, we prove a similar result for NSS's. This result opens the door to a corollary: for doubly symmetric games, the existence of an ESS is assured. This is an interesting result because of the stronger dynamic stability properties of ESS's as compared to NSS's. The coordination games played on the identity matrix are an example of games in this latter class. NSS's. This result opens the door to a corollary: for doubly symmetricgames, the existence of an ESS is assured. This is an interesting result because of the stronger dynamic stability properties of ESS's as compared to NSS's. The coordination games played on the identity matrix are anexample of games in this latter class.