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Cooperation in costly-access environments

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.