多人雪堆演化博弈在愿景驱动规则下的扩展平均丰度函数

随着博弈理论的深入研究,演化博弈模型在许多社会现象和经济问题的分析中得到了广泛应用.演化博弈模型将策略更新规则引入状态转移方程,得到相应的马尔可夫链,从而研究种群演化状态.当此马尔可夫链无吸收态时,采用平均丰度函数来研究种群演化状态.采用策略更新规则中的愿景驱动规则,通过分析马尔可夫链的平稳分布导出了扩展平均丰度函数.同时,通过将多人演化博弈模型应用于雪堆演化博弈中,得到了多人雪堆演化博弈模型的扩展平均丰度函数.采用数字分析的方式,计算分析了相应参数对平均丰度函数的影响,结合具体案例研究了参数变化如何影响企业在博弈中的行为.研究表明可以通过改变相关参数来提高合作者的占比,这一结论为在实际应用中如何调控相应参数以促进合作指出了方向.

Extended average abundance function of multi-player snowdrift evolutionary game under aspiration driven rule

With further study of game theory, evolutionary game model has been widely used in the analysis of many social phenomena and economic problems. In evolutionary game model, strategy updating rule is introduced into the state transition equation, and the corresponding Markov chain is obtained to study the evolutionary state of population. When the Markov chain has no absorbing states, the average abundance function is used to study the evolutionary state of population. The extended average abundance function is derived by analyzing the stationary distribution of Markov chain using aspiration driven rule in the strategy updating rules. At the same time, by applying the multi-player evolutionary game model to snowdrift evolutionary game, extended average abundance function of multi-player snowdrift evolutionary game model is obtained. By means of numerical analysis, the influence of corresponding parameters on the average abundance function is calculated and analyzed, and how the variation of parameters affects the behavior of enterprises in the game is studied with a specific case. The research shows that the proportion of cooperators will be increased by changing relevant parameters, and this conclusion points out the direction for how to regulate the corresponding parameters to promote cooperation in practical application.