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Resolution of the Stochastic Strategy Spatial Prisoners Dilemma by Means of Particle Swarm Optimization

机译:粒子群算法解决随机策略空间囚徒困境

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摘要

We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner's dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoner's dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.
机译:我们研究了随机策略空间囚徒困境游戏中自私个体之间合作的演变。我们为玩家提供了粒子群优化技术,发现即使对缺陷的诱惑力很强,它也可能导致高度合作的状态。粒子群优化的概念最初是在一个简单的社会动力学模型中引入的,该模型可以描述群的形成,即类似于蜜蜂寻找食物来源的群。本质上,粒子群优化预见了每个玩家的速度分布的变化,从而可以定位并最终占据最佳位置。在我们的案例中,每个玩家都跟踪在本地拓扑邻域中获得的最高收益及其个人最高收益。因此,玩家利用自己的记忆来保持先前行动中最有利可图的策略的得分,并利用整个群体所获得的知识为自己和社会找到最佳的可用策略。在对该设置进行广泛的模拟之后,我们发现针对各种参数的协作水平有了显着提高,并且可以完全解决囚徒的困境。当处理强烈支持缺陷扩散的环境时,我们还证明了优化算法的极高效率,这反过来表明,蜂拥而至可能是一种重要现象,即使在非常不利的条件下,也可以通过这种现象维持合作。因此,我们提出了另一种理解合作行为的演变及其在自然界中普遍存在的方式,我们希望这项研究对今后朝着这个方向的努力具有启发性。

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