Heterogeneous resource allocation can change social hierarchy in public goods games

Public Goods Games represent one of the most useful tools to study group interactions between individuals. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not able to reproduce some key features observed in social and economical interactions. The typical shape of wealth distribution - known as Pareto Law - and the microscopic organization of wealth production are two of them. Here, we introduce a modification to the classical formulation of Public Goods Games that allows for the emergence of both of these features from first principles. Unlike traditional Public Goods Games on networks, where players contribute equally to all the games in which they participate, we allow individuals to redistribute their contribution according to what they earned in previous rounds. Results from numerical simulations show that not only a Pareto distribution for the payoffs naturally emerges but also that if players don't invest enough in one round they can act as defectors even if they are formally cooperators. Finally, we also show that the players self-organize in a very productive backbone that covers almost perfectly the minimum spanning tree of the underlying interaction network. Our results not only give an explanation for the presence of the wealth heterogeneity observed in real data but also points to a conceptual change regarding how cooperation is defined in collective dilemmas.Comment: 8 pages, 5 figures, 55 reference

Dynamic instability of cooperation due to diverse activity patterns in evolutionary social dilemmas

Individuals might abstain from participating in an instance of an evolutionary game for various reasons, ranging from lack of interest to risk aversion. In order to understand the consequences of such diverse activity patterns on the evolution of cooperation, we study a weak prisoner's dilemma where each player's participation is probabilistic rather than certain. Players that do not participate get a null payoff and are unable to replicate. We show that inactivity introduces cascading failures of cooperation, which are particularly severe on scale-free networks with frequently inactive hubs. The drops in the fraction of cooperators are sudden, while the spatiotemporal reorganization of compact cooperative clusters, and thus the recovery, takes time. Nevertheless, if the activity of players is directly proportional to their degree, or if the interaction network is not strongly heterogeneous, the overall evolution of cooperation is not impaired. This is because inactivity negatively affects the potency of low-degree defectors, who are hence unable to utilize on their inherent evolutionary advantage. Between cascading failures, the fraction of cooperators is therefore higher than usual, which lastly balances out the asymmetric dynamic instabilities that emerge due to intermittent blackouts of cooperative hubs.Comment: 6 two-column pages, 6 figures; accepted for publication in Europhysics Letter

Dynamics of interacting diseases

Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place on a single level (be it a single population, a meta-population system or a network of contacts). In particular, interdependent contagion phenomena can only be addressed if we go beyond the scheme one pathogen-one network. In this paper, we propose a framework that allows describing the spreading dynamics of two concurrent diseases. Specifically, we characterize analytically the epidemic thresholds of the two diseases for different scenarios and also compute the temporal evolution characterizing the unfolding dynamics. Results show that there are regions of the parameter space in which the onset of a disease's outbreak is conditioned to the prevalence levels of the other disease. Moreover, we show, for the SIS scheme, that under certain circumstances, finite and not vanishing epidemic thresholds are found even at the thermodynamic limit for scale-free networks. For the SIR scenario, the phenomenology is richer and additional interdependencies show up. We also find that the secondary thresholds for the SIS and SIR models are different, which results directly from the interaction between both diseases. Our work thus solve an important problem and pave the way towards a more comprehensive description of the dynamics of interacting diseases.Comment: 24 pages, 9 figures, 4 tables, 3 appendices. Final version accepted for publication in Physical Review