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Register a new userDynamic aspiration based on Win-Stay-Lose-Learn rule in Spatial Prisoners Dilemma Gam
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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.
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In recent years, Win-Stay-Lose-Learn rule has attracted wide attention as an effective strategy updating rule, and voluntary participation is proposed by introducing a third strategy in Prisoners dilemma game. Some researches show that combining Win-Stay-Lose-Learn rule with voluntary participation could promote cooperation more significantly under moderate temptation values, however, cooperators survival under high aspiration levels and high temptation values is still a challenging problem. In this paper, inspired by Achievement Motivation Theory, a Dynamic-Win-Stay-Lose-Learn rule with voluntary participation is investigated, where a dynamic aspiration process is introduced to describe the co-evolution of individuals strategies and aspirations. It is found that cooperation is extremely promoted and defection is almost extinct in our model, even when the initial aspiration levels and temptation values are high. The combination of dynamic aspiration and voluntary participation plays an active role since loners could survive under high initial aspiration levels and they will expand stably because of their fixed payoffs. The robustness of our model is also discussed and some adverse structures are found which should be alerted in the evolutionary process. Our work provides a more realistic model and shows that cooperators may prevail defectors in an unfavorable initial environment.
Evolutionary game theory assumes that players replicate a highly scored players strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someones strategy just by observing the behaviour. In this work, we consider players with memory-one stochastic strategies in the iterated prisoners dilemma, with an assumption that they cannot directly access each others strategy but only observe the actual moves for a certain number of rounds. Based on the observation, the observer has to infer the resident strategy in a Bayesian way and chooses his or her own strategy accordingly. By examining the best-response relations, we argue that players can escape from full defection into a cooperative equilibrium supported by Win-Stay-Lose-Shift in a self-confirming manner, provided that the cost of cooperation is low and the observational learning supplies sufficiently large uncertainty.
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 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.
In this Letter, we introduce an aspiration-induced reconnection mechanism into the spatial public goods game. A player will reconnect to a randomly chosen player if its payoff acquired from the group centered on the neighbor does not exceed the aspiration level. We find that an intermediate aspiration level can best promote cooperation. This optimal phenomenon can be explained by a negative feedback effect, namely, a moderate level of reconnection induced by the intermediate aspiration level induces can change the downfall of cooperators, and then facilitate the fast spreading of cooperation. While insufficient reconnection and excessive reconnection induced by low and high aspiration levels respectively are not conductive to such an effect. Moreover, we find that the intermediate aspiration level can lead to the heterogeneous distribution of degree, which will be beneficial to the evolution of cooperation.
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