Social dilemmas, network reciprocity and the small-world property

TL;DR

This paper explores how network structure, especially transitivity and small-world properties, influences cooperation in evolutionary games like Prisoner and Snowdrift dilemmas, revealing different effects on cooperation stability.

Contribution

It demonstrates the impact of network reciprocity and transitivity on cooperation dynamics in small-world networks, comparing these effects across different network types.

Findings

Transitivity increases and stabilizes with contacts per individual.

Snowdrift game converges to well-mixed behavior as network randomness increases.

Prisoner's Dilemma becomes less cooperative with higher network reciprocity.

Abstract

We revisit two evolutionary game theory models, namely the Prisoner and the Snowdrift dilemmas, on top of small-world networks. These dynamics on networked populations (individuals occupying nodes of a graph) are mainly concerning on the competition between to cooperate or to defect, by allowing some process of revision of strategies. Cooperators avoid defectors by forming clusters in a process known as network reciprocity. This defense strategy is based on the fact that any individual interact only with its nearest neighbors. The minimum cluster, in turn, is formed by a set of three completely connected nodes and the bulk of these triplets is associated with the transitivity property of a network. Particularly, we show that the transitivity increases eventually assuming a constant behavior when observed as a function of the number of contacts of an individual. We investigate the influence of the network reciprocity on that transitivity increasing regime on the promotion of a cooperative behavior. The dynamics on small-world networks are compared with those random regular, and annealed networks, the later typically studied as the well-mixed approach. We observe that the Snowdrift Game converge to an annealed scenario as randonness and coordination number increase, whereas the Prisoner's Dilemma becomes more severe against the cooperative behavior under the regime of an increasing network reciprocity.