Equilibrium Breakdown and Equilibrium Selection in Evolutionary Game Theory

博弈论是经济学和其他社会科学中的基本建模工具，它通过策略性交互来模拟决策。 预测通常采取均衡的形式，即相互最优选择的集合。 一个最近引起广泛关注的问题是，在重复的互动中，代理人如何学习按照均衡预测进行游戏。 这个项目是对一个互补问题的第一次尝试：一个均衡的游戏如何打破，然后出现一个不同的均衡。 例如，在宏观经济背景下，经济的整体状态在繁荣和萧条之间移动;本项目开发的技术为理解这种转变提供了工具。具体而言，本项目研究近视代理人群体所玩的游戏中的均衡崩溃和均衡选择。 在我们的随机演化模型中，代理人通过应用噪声最佳响应规则来随时间更新他们的策略，在该规则下，次优选择的概率取决于其收益结果。 种群的聚集行为由单形中离散网格上的马尔可夫链描述。 从大偏差理论的发展方法，我们研究了这个过程的行为作为两个参数接近其极限值：作为代理的选择规则的噪声水平为零，并作为人口的规模趋于无穷大。 通过取这些极限中的任何一个，都有可能得到均衡崩溃和选择的特征，但是这些特征不允许人们解决最简单情况之外的具体例子。 但我们认为，采取这两个限制，在任何顺序，导致的特点是听话。 我们推测，从两个顺序的限制的预测是相同的，这意味着均衡的崩溃和选择的性质并不取决于是否罕见的错误或大量的平均效应驱动长期发挥。

Game theory, which models decision-making by strategically interacting agents, is a basic modeling tool in economics and other social sciences. Predictions typically take the form of equilibria, which are collections of mutually optimal choices. A question that has garnered much recent attention is how agents in a repeated interaction might learn to play in accordance with equilibrium predictions. This project is a first foray into a complementary question: how play of an equilibrium may break down, to be followed by the emergence of a different equilibrium. For instance, in macroeconomic contexts, the overall state of the economy moves between booms and busts; the techniques developed in this project offer tools for understanding such transitions.Specifically, this project studies equilibrium breakdown and equilibrium selection in games played by populations of myopic agents. In our stochastic evolutionary model, agents update their strategies over time by applying noisy best response rules, under which the probability of a suboptimal choice depends on its payoff consequences. The population's aggregate behavior is described by a Markov chain on a discrete grid in the simplex. Developing methods from the theory of large deviations, we study the behavior of this process as two parameters approach their limiting values: as the noise level in agents' choice rules goes to zero, and as the size of the population goes to infinity. By taking either one of these limits, it is possible to obtain characterizations of equilibrium breakdown and selection, but these characterizations do not allow one to solve specific examples beyond the simplest cases. But we argue that taking both limits, in either order, leads to characterizations that are tractable. We conjecture that the predictions from the two orders of limits are identical, implying that the nature of equilibrium breakdown and selection does not depend on whether rarity of mistakes or the averaging effects of large numbers drives long run play.