Dynamics of social systems. PACS. 89.75.-k -Complex systems. PACS. 05.70.Ln -Nonequilibrium and irreversible thermodynamics.Abstract. -We investigate how the topology of small-world networks affects the dynamics of the voter model for opinion formation. We show that, contrary to what occurs on regular topologies with local interactions, the voter model on small-world networks does not display the emergence of complete order in the thermodynamic limit. The system settles in a stationary state with coexisting opinions whose lifetime diverges with the system size. Hence the nontrivial connectivity pattern leads to the counterintuitive conclusion that long-range connections inhibit the ordering process. However, for networks of finite size, for which full uniformity is reached, the ordering process takes a time shorter than on a regular lattice of the same size.

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.

An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the WattsStrogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale τ separates a quasistationary disordered state with coexisting domains from a fully ordered frozen configuration. τ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.

We study the one-dimensional behavior of a cellular automaton aimed at the description of the formation and evolution of cultural domains. The model exhibits a non-equilibrium transition between a phase with all the system sharing the same culture and a disordered phase of coexisting regions with different cultural features. Depending on the initial distribution of the disorder the transition occurs at different values of the model parameters. This phenomenology is qualitatively captured by a mean-field approach, which maps the dynamics into a multi-species reaction-diffusion problem.

Abstract. -In this Letter we present a new perspective for the study of the Public Goods games on complex networks. The idea of our approach is to consider a realistic structure for the groups in which Public goods games are played. Instead of assuming that the social network of contacts self-defines a group structure with identical topological properties, we disentangle these two interaction patterns so to deal with systems having groups of definite sizes embedded in social networks with a tunable degree of heterogeneity. Surpisingly, this realistic framework, reveals that social heterogeneity may not foster cooperation depending on the game setting and the updating rule.