论文标题
混合策略中的进化游戏理论：从微观相互作用到动力学方程
Evolutionary game theory in mixed strategies: from microscopic interactions to kinetic equations
论文作者
论文摘要
在这项工作中，当代理使用混合策略时，我们为零和游戏的进化游戏理论提出了动力学公式。我们从一个简单的自适应规则开始，在遇到遇到后，每个代理都会增加比赛中使用的成功纯策略的概率。我们得出了描述该显微镜规则的宏观效应的Boltzmann方程，并在概率变化为零时获得了一阶，非局部，部分微分方程为极限。 我们研究了该方程与众所周知的复制器方程之间的关系，显示了NASH均衡的概念，部分微分方程的固定解和复制器方程的平衡之间的等效性。最后，我们将解决方案的长时间行为与部分微分方程和复制器方程的稳定性联系起来。
In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play the successful pure strategy used in the match. We derive the Boltzmann equation which describes the macroscopic effects of this microscopical rule, and we obtain a first order, nonlocal, partial differential equation as the limit when the probability change goes to zero. We study the relationship between this equation and the well known replicator equations, showing the equivalence between the concepts of Nash equilibria, stationary solutions of the partial differential equation, and the equilibria of the replicator equations. Finally, we relate the long time behavior of solutions to the partial differential equation and the stability of the replicator equations.
