Evolutionary Games and the Replicator Dynamics

This Element introduces the replicator dynamics for symmetric and asymmetric games where the strategy sets are metric spaces. Under this hypothesis the replicator dynamics evolves in a Banach space of finite signed measures. The authors provide a general framework to study the stability of the replicator dynamics for evolutionary games in this Banach space. This allows them to establish a relation between Nash equilibria and the stability of the replicator for normal a form games applicable to oligopoly models, theory of international trade, public good models, the tragedy of commons, and War of attrition game among others. They also provide conditions to approximate the replicator dynamics on a space of measures by means of a finite-dimensional dynamical system and a sequence of measure-valued Markov processes.

Author: Saul Mendoza-Palacios, On?imo Hern?dez-Lerma

Publisher: Cambridge University Press

Publication Date: Jun 06, 2024

Number of Pages: NA pages

Language: English

Binding: Paperback

ISBN-10: 1009472321

ISBN-13: 9781009472326