Evolutionary games defined at the network mesoscale: The Public Goods game

Abstract

The evolutionary dynamics of the Public Goods game addresses the emergence of cooperation within groups of individuals. However, the Public Goods game on large populations of interconnected individuals has been usually modeled without any knowledge about their group structure. In this paper, by focusing on collaboration networks, we show that it is possible to include the mesoscopic information about the structure of the real groups by means of a bipartite graph. We compare the results with the projected (coauthor) and the original bipartite graphs and show that cooperation is enhanced by the mesoscopic structure contained. We conclude by analyzing the influence of the size of the groups in the evolutionary success of cooperation.Evolutionary game dynamics on graphs has become a hot topic of research during the last years. The attention has been mainly focused on 2-players games, such as the Prisoner's Dilemma game, since the pairwise interactions can be easily implemented on top of networked substrates. However, for m-players game, such as the Public Goods game, the microscopic description about the pairwise interactions contained in the network is not enough, since m-players game are intrinsically defined at the mesoscopic network level. This mesoscopic level describes how individuals engage into groups where the Public Goods games are played. However, the actual group structure of networks has not been considered in the literature, being automatically substituted by a fictitious one. In this work, we study the emergence of cooperation in collaboration networks, by incorporating the real group structure to the evolutionary dynamics of the Public Goods game. Our results are compared with those obtained when the mesoscopic structure is ignored. We show that cooperation is actually enhanced when the group structure is taken into account, thus providing a novel structural mechanism, relying on the mesoscale level of large social systems, that promotes cooperation. Moreover, we further show that the particular characteristics of the group structure strongly influence the survival of cooperation.

Intergroup information exchange drives cooperation in the public goods game

“…Therefore, the bipartite formulation allows to study, e.g., different types of probability densities for the number of connections of the agents and for the number of elements of the groups. In particular, in [19,20] it is shown that the use of realistic patterns of connections for agents and groups leads to an increase of the cooperation with respect of the aforementioned case of scale-free networks. In brief, the recent works on the evolutionary dynamics of the PGG (see [25] for a recent comprehensive review) have tried to explain the emergence of cooperation by incorporating the actual structure of group interactions relying on real data about social and collaboration networks.…”

“…In fact, this assumption is somewhat unrealistic as it does not reflect the social structure of groups as revealed, for example, by real collaboration networks [22][23][24]. To incorporate the group structure into the formulation of the PGG in [19][20][21] the authors make use of bipartite graphs. In a bipartite graph there are two different types of nodes representing respectively, in the case of the PGG, agents and groups.…”

“…Another step further in the implementation of the evolutionary dynamics of the PGG have been recently proposed in [19][20][21]. In these works, the actual structure of social groups is taken into account, thus getting rid off the above assumption considering that groups are formed by each node together with its neighbors.…”

Conditional strategies and the evolution of cooperation in spatial public goods games

“…Inspired by the seminal paper introducing games on grids [18], evolutionary games on graphs and complex networks [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] have proven instrumental in raising the awareness of the fact that relaxing the simplification of well-mixed interactions may lead to qualitatively different results that are due to pattern formation and intricate organization of the competing strategies, which reveals itself in most unexpected ways. Specifically for the spatial public goods game [38,39], it has recently been shown that inhomogeneous player activities [40], appropriate partner selection [41,42], diversity [43][44][45], the critical mass [46], heterogeneous wealth distributions [47], the introduction of punishment [48,49] and reward [50], as well as both the joker [51] and the Matthew effect [52], can all substantially promote the evolution of public cooperation.…”

Eigenvector centrality of nodes in multiplex networks

“…This representation reflects the interaction of nodes through multiple layers of links, which cannot be captured by the classical singlelayer network representation. This multiplex representation has long been considered by sociologists (multiplex tie [6][7][8], and although some results concerning multiplex networks' modeling and structure have been recently proposed, [9][10][11][12][13][14][15][16][17] the study of centrality parameters in such networks has not yet been addressed satisfactorily. The aim of this paper is to propose a definition of centrality in multiplex networks, and illustrate potential applications.…”