标题： 随机游戏中冻结无序的临界性和Griffiths相 显示英文标题

标题： Criticality and Griffiths phases in random games with quenched disorder

摘要： 对于特定情况的感知风险和回报会根据资源可用性、积累的财富和其他外在因素如个人背景而有所不同。 基于日常生活中这一普遍方面，我们在这里使用演化博弈论来模拟一个具有随机扰动收益的囚徒困境游戏场景。 通过在收益条目中添加一个平均值为零的随机噪声来建模感知多样性，并使用蒙特卡洛模拟来获得种群动力学。 这种收益异质性可以在原本只有背叛者能够生存的竞争场景中促进并维持合作。 在这项工作中，我们进一步研究了异质性的作用，通过调查淬火无序对随机博弈关键性质的影响。 我们观察到收益波动会引起非常缓慢的动力学，使得合作衰减表现为幂律，而不是临界点之后的常规指数衰减，这表明出现了Griffiths相。 我们还发现在存在波动时，在背叛者的灭绝点附近出现对称的Griffiths相，这表明Griffiths相可能在演化博弈动力学中很常见，并在不同策略的共存中发挥作用。 显示英文摘要

摘要： The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte-Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.