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Register a new userEvolutionary dynamics of cooperation in a population with probabilistic corrupt enforcers and violators
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Pro-social punishment is a key driver of harmonious and stable society. However, this institution is vulnerable to corruption since law-violators can avoid sanctioning by paying bribes to corrupt law-enforcers. Consequently, to understand how altruistic behavior survives in a corrupt environment is an open question. To reveal potential explanations here we introduce corrupt enforcers and violators into the public goods game with pool punishment, and assume that punishers, as corrupt enforcers, may select defectors probabilistically to take a bribe from, and meanwhile defectors, as corrupt violators, may select punishers stochastically to be corrupted. By means of mathematical analysis, we aim to study the necessary conditions for the evolution of cooperation in such corrupt environment. We find that cooperation can be maintained in the population in two distinct ways. First, cooperators, defectors, and punishers can coexist by all keeping a steady fraction of the population. Second, these three strategies can form a cyclic dominance that resembles a rock-scissors-paper cycle or a heteroclinic cycle. We theoretically identify conditions when the competing strategies coexist in a stationary way or they dominate each other in a cyclic way. These predictions are confirmed numerically.
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In the framework of the evolutionary dynamics of the Prisoners Dilemma game on complex networks, we investigate the possibility that the average level of cooperation shows hysteresis under quasi-static variations of a model parameter (the temptation to defect). Under the discrete replicator strategy updating rule, for both Erdos-Renyi and Barabasi-Albert graphs we observe cooperation hysteresis cycles provided one reaches tipping point values of the parameter; otherwise, perfect reversibility is obtained. The selective fixation of cooperation at certain nodes and its organization in cooperator clusters, that are surrounded by fluctuating strategists, allows the rationalization of the lagging behind behavior observed.
A network effect is introduced taking into account competition, cooperation and mixed-type interaction amongst agents along a generalized Verhulst-Lotka-Volterra model. It is also argued that the presence of a market capacity enforces an indubious limit on the agents size growth. The state stability of triadic agents, i.e., the most basic network plaquette, is investigated analytically for possible scenarios, through a fixed point analysis. It is discovered that: (i) market demand is only satisfied for full competition when one agent monopolizes the market; (ii) growth of agent size is encouraged in full cooperation; (iii) collaboration amongst agents to compete against one single agent may result in the disappearance of this single agent out of the market, and (iv) cooperating with two rivals may become a growth strategy for an intelligent agent.
Networks determine our social circles and the way we cooperate with others. We know that topological features like hubs and degree assortativity affect cooperation, and we know that cooperation is favoured if the benefit of the altruistic act divided by the cost exceeds the average number of neighbours. However, a simple rule that would predict cooperation transitions on an arbitrary network has not yet been presented. Here we show that the unique sequence of degrees in a network can be used to predict at which game parameters major shifts in the level of cooperation can be expected, including phase transitions from absorbing to mixed strategy phases. We use the evolutionary prisoners dilemma game on random and scale-free networks to demonstrate the prediction, as well as its limitations and possible pitfalls. We observe good agreements between the predictions and the results obtained with concurrent and Monte Carlo methods for the update of the strategies, thus providing a simple and fast way to estimate the outcome of evolutionary social dilemmas on arbitrary networks without the need of actually playing the game.
We study the evolution of cooperation in spatial Prisoners dilemma games with and without extortion by adopting aspiration-driven strategy updating rule. We focus explicitly on how the strategy updating manner (whether synchronous or asynchronous) and also the introduction of extortion strategy affect the collective outcome of the games. By means of Monte Carlo (MC) simulations as well as dynamical cluster techniques, we find that the involvement of extortioners facilitates the boom of cooperators in the population (and whom can always dominate the population if the temptation to defect is not too large) for both synchronous and asynchronous strategy updating, in stark contrast to the otherwise case, where cooperation is promoted for intermediate aspiration level with synchronous strategy updating, but is remarkably inhibited if the strategy updating is implemented asynchronously. We explain the results by configurational analysis and find that the presence of extortion leads to the checkerboard-like ordering of cooperators and extortioners, which enable cooperators to prevail in the population with both strategy updating manners. Moreover, extortion itself is evolutionary stable, and therefore acts as the incubator for the evolution of cooperation.
Recent empirical studies suggest that heavy-tailed distributions of human activities are universal in real social dynamics [Muchnik, emph{et al.}, Sci. Rep. textbf{3}, 1783 (2013)]. On the other hand, community structure is ubiquitous in biological and social networks [M.~E.~J. Newman, Nat. Phys. textbf{8}, 25 (2012)]. Motivated by these facts, we here consider the evolutionary Prisoners dilemma game taking place on top of a real social network to investigate how the community structure and the heterogeneity in activity of individuals affect the evolution of cooperation. In particular, we account for a variation of the birth-death process (which can also be regarded as a proportional imitation rule from social point of view) for the strategy updating under both weak- and strong-selection (meaning the payoffs harvested from games contribute either slightly or heavily to the individuals performance). By implementing comparative studies, where the players are selected either randomly or in terms of their actual activities to playing games with their immediate neighbors, we figure out that heterogeneous activity benefits the emergence of collective cooperation in harsh environment (the action for cooperation is costly) under strong selection, while it impairs the formation of altruism under weak selection. Moreover, we find that the abundance of communities in the social network can evidently foster the fixation of cooperation under strong-selection, in contrast to the games evolving on the randomized counterparts. Our results are therefore helpful for us to better understand the evolution of cooperation in real social systems.
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