Is there switching for replicator dynamics and bimatrix games?

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Manuela Aguiar (Author) FEP

Journal

Title: Physica D: Nonlinear Phenomena

Vol. 240

Pages: 1475-1488

ISSN: 0167-2789

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 8 Citations

ISI Web of Science

Scopus - 8 Citations

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics

Other information

Authenticus ID: P-002-N0E

DOI: 10.1016/j.physd.2011.06.016

Abstract (EN): We consider heteroclinic networks for replicator dynamics and bimatrix games, that is, in a simplex or product of simplices, with equilibria at the vertices and connections at the edges - edge networks. Switching dynamics near a heteroclinic network occurs whenever every (infinite) sequence of connections in the network is shadowed by at least one trajectory in its neighborhood. Aguiar and Castro [MAD. Aguiar, S.B.S.D. Castro Chaotic switching in a two-person game, Physica D 239 (16), 1598-1609] prove switching near an edge network for the dynamics of the rock-scissors-paper game. Here we give conditions for switching dynamics in general bimatrix games and show that switching near an edge network can never occur for replicator dynamics.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14