Evolutionary Game Theory: A Generalization of the ESS Definition

Abstract

In this paper, we study the concept of Evolutionarily Stable Strategies (ESSs) for symmetric games with n = 3 players. The main properties of these games and strategies are analyzed and several examples are provided. We relate the concept of ESS with previous literature and provide a proof of finiteness of ESS in the context of symmetric games with n = 3 players. We show that unlike the case of n = 2, when there are more than two populations an ESS does not have a uniform invasion barrier, or equivalently, it is not equivalent to the strategy performing better against all strategies in a neighborhood. We also construct the extended replicator dynamics for these games and we study an application to a model of strategic planning of investment. © 2019 World Scientific Publishing Company.