Stability of the replicator dynamics for games in metric spaces

Saul Mendoza-Palacios; Onésimo Hernández-Lerma

doi:10.3934/jdg.2017017

Article Contents

2017, Volume 4, Issue 4: 319-333. Doi: 10.3934/jdg.2017017

This issue Previous Article Game theoretical modelling of a dynamically evolving network Ⅰ: General target sequences Next Article Nonlinear dynamics from discrete time two-player status-seeking games

Stability of the replicator dynamics for games in metric spaces

Saul Mendoza-Palacios^1, , and
Onésimo Hernández-Lerma^2,

1.
Centro de Estudios Económicos, El Colegio de México, Entronque Picacho-ajusco 20, Fuentes del Pedregal, 10740 México City, México
2.
Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México City 07000, México

* Corresponding author: Saul Mendoza-Palacios
* Corresponding author: Saul Mendoza-Palacios

Received: March 2017

Revised: June 2017

Published online: September 2017

This research was partially supported by CONACYT Grant 221291.

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Abstract

In this paper we study the stability of the replicator dynamics for symmetric games when the strategy set is a separable metric space. In this case the replicator dynamics evolves in a space of measures. We study stability criteria with respect to different topologies and metrics on the space of probability measures. This allows us to establish relations among Nash equilibria (of a certain normal form game) and the stability of the replicator dynamics in different metrics. Some examples illustrate our results.

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Mathematics Subject Classification: Primary: 91A22, 91A10; Secondary: 34A34, 34G20.

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