Evolutionary Games and the Replicator Dynamics

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Saul Mendoza-Palacios (Centro de Investigación y Docencia Económicas) Onésimo Hernández-Lerma (Centro de Investigacion y de Estudios Avanzados del IPN)

Evolutionary Games and the Replicator Dynamics

Saul Mendoza-Palacios (Centro de Investigación y Docencia Económicas), Onésimo Hernández-Lerma (Centro de Investigacion y de Estudios Avanzados del IPN)

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English

Cambridge University Press
06 June 2024

Economics of industrial organisation; Economic growth; Game theory

Series: Elements in Evolutionary Economics

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.

By: Saul Mendoza-Palacios (Centro de Investigación y Docencia Económicas), Onésimo Hernández-Lerma (Centro de Investigacion y de Estudios Avanzados del IPN)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 8mm
Weight: 284g
ISBN: 9781009472302
ISBN 10: 1009472305
Series: Elements in Evolutionary Economics
Pages: 100
Publication Date: 06 June 2024
Audience: General/trade , ELT Advanced
Format: Hardback
Publisher's Status: Active

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.