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Register a new userTopology dependent payoffs can lead to escape from prisoners dilemma
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The maintenance of cooperation in the presence of spatial restrictions has been studied extensively. It is well-established that the underlying graph topology can significantly influence the outcome of games on graphs. Maintenance of cooperation could be difficult, especially in the absence of spatial restrictions. The evolution of cooperation would naturally depend on payoffs. However, payoffs are generally considered to be invariant in a given game. A natural yet unexplored question is whether the topology of the underlying structures on which the games are played, possesses no role whatsoever in the determination of payoffs. Herein, we introduce the notion of cooperator graphs and defector graphs as well as a new form of game payoff, which is weakly dependent on the underlying network topology. These concepts are inspired by the well-known microbial phenomenon of quorum sensing. We demonstrate that even with such a weak dependence, the fundamental game dynamics and indeed the very nature of the game may be altered. Such changes in the nature of a game have been well-reported in theoretical and experimental studies.
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Standard epidemiological models for COVID-19 employ variants of compartment (SIR) models at local scales, implicitly assuming spatially uniform local mixing. Here, we examine the effect of employing more geographically detailed diffusion models based on known spatial features of interpersonal networks, most particularly the presence of a long-tailed but monotone decline in the probability of interaction with distance, on disease diffusion. Based on simulations of unrestricted COVID-19 diffusion in 19 U.S cities, we conclude that heterogeneity in population distribution can have large impacts on local pandemic timing and severity, even when aggregate behavior at larger scales mirrors a classic SIR-like pattern. Impacts observed include severe local outbreaks with long lag time relative to the aggregate infection curve, and the presence of numerous areas whose disease trajectories correlate poorly with those of neighboring areas. A simple catchment model for hospital demand illustrates potential implications for health care utilization, with substantial disparities in the timing and extremity of impacts even without distancing interventions. Likewise, analysis of social exposure to others who are morbid or deceased shows considerable variation in how the epidemic can appear to individuals on the ground, potentially affecting risk assessment and compliance with mitigation measures. These results demonstrate the potential for spatial network structure to generate highly non-uniform diffusion behavior even at the scale of cities, and suggest the importance of incorporating such structure when designing models to inform healthcare planning, predict community outcomes, or identify potential disparities.
Prisoners dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on aspiration, has been proved to be an effective model to promote cooperation in spatial prisoners dilemma game, which leads aspiration to receive lots of attention. But in many research the assumption that individuals aspiration is fixed is inconsistent with recent results from psychology. In this paper, according to Expected Value Theory and Achievement Motivation Theory, we propose a dynamic aspiration model based on Win-Stay-Lose-Learn rule in which individuals aspiration is inspired by its payoff. It is found that dynamic aspiration has a significant impact on the evolution process, and different initial aspirations lead to different results, which are called Stable Coexistence under Low Aspiration, Dependent Coexistence under Moderate aspiration and Defection Explosion under High Aspiration respectively. Furthermore, a deep analysis is performed on the local structures which cause cooperators existence or defectors expansion, and the evolution process for different parameters including strategy and aspiration. As a result, the intrinsic structures leading to defectors expansion and cooperators survival are achieved for different evolution process, which provides a penetrating understanding of the evolution. Compared to fixed aspiration model, dynamic aspiration introduces a more satisfactory explanation on population evolution laws and can promote deeper comprehension for the principle of prisoners dilemma.
The conventional wisdom is that scale-free networks are prone to cooperation spreading. In this paper we investigate the cooperative behaviors on the structured scale-free network. On the contrary of the conventional wisdom that scale-free networks are prone to cooperation spreading, the evolution of cooperation is inhibited on the structured scale-free network while performing the prisoners dilemma (PD) game. Firstly, we demonstrate that neither the scale-free property nor the high clustering coefficient is responsible for the inhibition of cooperation spreading on the structured scale-free network. Then we provide one heuristic method to argue that the lack of age correlations and its associated `large-world behavior in the structured scale-free network inhibit the spread of cooperation. The findings may help enlighten further studies on evolutionary dynamics of the PD game in scale-free networks.
The paradox of cooperation among selfish individuals still puzzles scientific communities. Although a large amount of evidence has demonstrated that cooperator clusters in spatial games are effective to protect cooperators against the invasion of defectors, we continue to lack the condition for the formation of a giant cooperator cluster that assures the prevalence of cooperation in a system. Here, we study the dynamical organization of cooperator clusters in spatial prisoners dilemma game to offer the condition for the dominance of cooperation, finding that a phase transition characterized by the emergence of a large spanning cooperator cluster occurs when the initial fraction of cooperators exceeds a certain threshold. Interestingly, the phase transition belongs to different universality classes of percolation determined by the temptation to defect $b$. Specifically, on square lattices, $1<b<4/3$ leads to a phase transition pertaining to the class of regular site percolation, whereas $3/2<b<2$ gives rise to a phase transition subject to invasion percolation with trapping. Our findings offer deeper understanding of the cooperative behaviors in nature and society.
We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node`s attractiveness. The developed model reveals that increasing either the network`s mean degree or the ``choosiness`` exercised during pair-formation increases the strength of positive assortative mating. That is, we note that attractiveness is correlated among mated nodes. Their total number also increases with mean degree and selectivity during pair-formation. By iterating over model mapping of parents onto offspring across generations, we study the evolution of attractiveness. Selection mediated by exclusion from reproduction increases mean attractiveness, but is rapidly balanced by skew in the offspring distribution of highly attractive mated pairs.
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