Eur. Phys. J. B 71, 587-595 (2009)
https://doi.org/10.1140/epjb/e2009-00189-0

Promotion of cooperation on networks? The myopic best response case

¹ Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
² Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, 28006 Madrid, Spain
³ Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza, Spain

Corresponding author: ^a anxo@math.uc3m.es

Received: 23 December 2008
Revised: 29 April 2009
Published online: 3 June 2009

Abstract

We study the effect of a network of contacts on the emergence of cooperation on social dilemmas under myopic best response dynamics. We begin by summarizing the main features observed under less intellectually demanding dynamics, pointing out their most relevant general characteristics. Subsequently we focus on the new framework of best response. By means of an extensive numerical simulation program we show that, contrary to the rest of dynamics considered so far, best response is largely unaffected by the underlying network, which implies that, in most cases, no promotion of cooperation is found with this dynamics. We do find, however, nontrivial results differing from the well-mixed population in the case of coordination games on lattices, which we explain in terms of the formation of spatial clusters and the conditions for their advancement, subsequently discussing their relevance to other networks.