论文标题
一维连续特质空间中具有双线性和二次回报功能的策略分布动力学
Dynamics of Strategy Distribution in a One-Dimensional Continuous Trait Space with a Bi-linear and Quadratic Payoff Functions
论文作者
论文摘要
游戏理论中策略分布的演变是一个有趣的问题，仅针对特定情况进行了研究。在这里，我开发了一种通用方法，以扩展对任何初始分布的双线性和二次收益功能的连续策略分布的演变的分析，以回答以下问题：鉴于游戏中策略的初始分布，它将如何随着时间的推移而发展？我查看了几个特定示例，包括整个线上的正态分布，正常的截短分布以及指数，均匀和伽马分布。我表明，对于具有双线性回报功能的游戏中的复制器动力学，指数分布类别是不变的。我还表明，在具有二次收益功能的游戏中，正常分布类在复制器动力学方面是不变的。现在，开发的方法可以应用于与具有不同回报功能和不同初始分布的游戏中策略演变有关的广泛问题。
Evolution of distribution of strategies in game theory is an interesting question that has been studied only for specific cases. Here I develop a general method to extend analysis of the evolution of continuous strategy distributions given bi-linear and quadratic payoff functions for any initial distribution to answer the following question: given the initial distribution of strategies in a game, how will it evolve over time? I look at several specific examples, including normal distribution on the entire line, normal truncated distribution, as well as exponential, uniform and Gamma distributions. I show that the class of exponential distributions is invariant with respect to replicator dynamics in games with bi-linear payoff functions. I show also that the class of normal distributions is invariant with respect to replicator dynamics in games with quadratic payoff functions. The developed method can now be applied to a broad class of questions pertaining to evolution of strategies in games with different payoff functions and different initial distributions.
