Promotion of cooperation on networks? The myopic best response case

TL;DR

This paper investigates how network structures influence cooperation under myopic best response dynamics, revealing that such dynamics are largely unaffected by networks except in specific coordination game scenarios on lattices.

Contribution

The study introduces an extensive numerical analysis of best response dynamics, showing its limited impact on promoting cooperation across networks, with notable exceptions in lattice-based coordination games.

Findings

Best response dynamics are mostly unaffected by network topology.

Cooperation is not generally promoted by best response dynamics.

Coordination games on lattices show different behavior due to spatial clustering.

Abstract

We address the issue of the effects of considering 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.