Evolutionary prisoner’s dilemma games coevolving on adaptive networks

Abstract

We study a model for switching strategies in the Prisoner’s Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model wherein each player follows one strategy at a time (cooperate or defect) across all of its neighbors, changing that strategy and possibly changing partners in response to local changes in the network of player pairing and in the strategies used by connected partners. We compare and contrast numerical simulations with existing pair approximation differential equations for describing this system, as well as more accurate equations developed here using the framework of approximate master equations. We explore the parameter space of the model, demonstrating the relatively high accuracy of the approximate master equations for describing the system observations made from simulations. We study two variations of this partner-switching model to investigate the system evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two model variants.

Seasonal payoff variations and the evolution of cooperation in social dilemmas

“…They are kin selection [20], direct and indirect reciprocity [21,22], network reciprocity [23], and group selection [24], as reviewed in [25]. During the last decade, methods of statistical physics and network science [26][27][28][29] have been successfully integrated into the mainstream research concerning the evolution of cooperation, revealing that the structure of the interaction network can be crucial [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. It has also been thoroughly established that heterogeneity in general, for example in the form of heterogeneous networks, noisy payoff disturbances, or other individual properties like the teaching activity or the mobility to connect to additional other players, strongly promotes cooperation [45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Social clustering in epidemic spread on coevolving networks

“…We note in particular that with the additional variables and corresponding differential equations in AME, the triplet counts are precisely accounted for (cf. the closure approximations necessary to obtain triplet counts in PA) and that AME typically provides a more accurate approximation of such dynamics and can be highly stable around the critical point of the dynamics [1, 28, 34, 37, 38] (see also [28, 37, 39] for comparisons between AME and PA). We note that Ref.…”

“…for (cf. the closure approximations necessary to obtain triplet counts in PA) and that AME typically provides a more accurate approximation of such dynamics and can be highly stable around the critical point of the dynamics [1,28,34,37,38] (see also [28,37,39] for comparisons between AME and PA). We note that Ref.…”

Local Symmetry and Global Structure in Adaptive Voter Models

“…Adaptive networks [14,16,35] are characterized by dynamical coupling between node attributes and edge topology. Such models have been studied in contexts including epidemic spreading [9,15,20,24,26] and game theory [23,27], but are most commonly deployed as models of opinion dynamics [11,19,25,28,31,32,37]. In this setting, they often appear as adaptive (or coevolutionary) voter models (AVMs), which add opinionbased edge-rewiring to the opinion-adoption dynamics of the base voter model.…”