抽样惩罚下多人雪堆博弈模型的合作演化

Cooperative Evolution of Multi-Player Snowdrift Game Model under Sampling Punishment

摘要: 演化博弈中，惩罚已被证明是促进合作的关键机制，但其实施的有效性一直处于争论之中。在本文中，我们将抽样惩罚引入多人雪堆博弈模型中，基于愿景驱动规则，根据马尔科夫链的状态方程，推导出平稳概率分布，进而得出平均丰度、平均惩罚概率、平均惩罚成本的直观表达式，并且具体分析了它们受三个参数(惩罚强度、惩罚阈值、样本大小)的影响，同时结合具体案例研究了参数变化如何影响策略行为。研究结果表明，当惩罚强度相当大时，在低惩罚阈值和小样本情况下，合作水平可以得到有效提高。为了确定实施抽样惩罚的最优条件，我们观察惩罚概率和惩罚成本，我们研究发现，在一定的惩罚强度下，采用较低的惩罚阈值更有利于实施抽样惩罚，此时惩罚成本较低。

Abstract: Punishment has been proved to be a key mechanism to promote cooperation in evolutionary games, but the effectiveness of its implementation has been debated. In this paper, we introduce sampling punishment into the multi-player snowdrift game model. Based on the aspiration driven rule, we deduce the stationary probability distribution according to the state equation of Markov chain, and then get the intuitive expression of average abundance, average penalty probability and average penalty cost. Moreover, we analyze the influence of these three parameters (penalty intensity, penalty threshold and sample size). At the same time, how the parameter changes affect the policy behavior is studied with a case study. The results show that when the punishment intensity is quite large, the cooperation level can be effectively improved at low penalty thresholds and small sample sizes. In order to determine the optimal conditions for implementing sampling punishment, we observe the penalty probability and penalty cost. Our research finds that under a certain penalty intensity, a lower penalty threshold is more conducive to implementing sampling punishment, and the penalty cost is lower.