Cooperation in costly-access environments

TL;DR

This paper introduces a model called Costly-Access Prisoner's Dilemma to analyze how voluntary participation with an access cost influences cooperation, revealing different behavioral phases in structured populations.

Contribution

It proposes a novel model that incorporates access costs into voluntary cooperation, providing a theoretical framework and simulation analysis for diverse population structures.

Findings

In well-mixed populations, the system tends to abstention.

Structured populations exhibit alternating phases of cooperation and defection.

Transitions between phases are explained by stability changes in strategic motifs.

Abstract

Understanding cooperative behavior in biological and social systems constitutes a scientific challenge, being the object of intense research over the past decades. Many mechanisms have been proposed to explain the presence and persistence of cooperation in those systems, showing that there is no unique explanation, as different scenarios have different possible driving forces. In this paper, we propose a model to study situations in which voluntary participation involves an access cost to the cooperative interaction, besides the cost associated with cooperation. The proposed Costly-Access Prisoner's Dilemma, a symmetric donation game with voluntary and costly participation, breaks the symmetry between abstainers and participants of the Voluntary Prisoner's Dilemma. A mean-field approach shows that, in well-mixed populations, the dynamic always leads the system to abstention. However, depending on the return parameter, numerical simulations in structured populations display an alternating behavior between mono-strategic, multi-stable, and coexistence phases. This behavior is fully explained through a theoretical analysis of the strategic motifs, the transitions being determined by the change in stability of those motifs.