Evolutionary Games and the Replicator Dynamics

This Element introduces the replicator dynamics for symmetric and asymmetric games where the strategy sets are metric spaces. The authors 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.

List of contents

1. Introduction and technical preliminaries; 2. Normal form games; 3. Evolutionary games: the asymmetric case; 4. Evolutionary games: symmetric case; 5. Finite dimensional approximations; 6. The replicator dynamics as a deterministic approximation; 7. Conclusions and suggestions for future research; Symbols; Abbreviations; Appendix; Bibliography.

Summary

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.

Product details

• Authors: Onésimo Hernández-Lerma, Saul Mendoza-Palacios, Saul (Centro De Investigacion Y Mendoza-Palacios
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 06.06.2024
• EAN: 9781009472326
• ISBN: 978-1-0-0947232-6
• No. of pages: 75
• Series: Elements in Evolutionary Economics
• Subjects: Social sciences, law, business > Business > Economics; BUSINESS & ECONOMICS / Economics / General, economic growth, game theory, Economics of industrial organisation, Economics of industrial organization