Inductive Equilibrium Selection in Games with Separatrix Crossing

由于演绎均衡选择理论在预测博弈结果方面的经验效果不佳，焦点已经转移到依赖于动态的均衡选择理论--也被称为归纳选择理论。归纳选择理论主要依赖于基于玩家学习和适应原理的自适应动力学，因此成功的策略增加了频率，而不成功的策略减少了频率。不同的动力学理论在“成功”的衡量标准、玩家被认为拥有的复杂程度、对选择错误的建模、玩家对策略空间的关注、抱负所扮演的角色以及模仿与玩家实验的程度等方面存在差异。在这项研究中，一系列具有代表性的学习理论将被研究，包括一个简单的Logit动态模型，一个渴望和模仿理论，一个强化学习模型，一个经验加权吸引学习模型，以及一个规则学习模型。在最近关于概率选择学习动力学的工作流中，很少发现做出完全不同预测的模型(使用类似游戏中的参数估计)。因此，根据不同的学习模式与游戏路径的匹配程度，对不同的学习模式进行了比较。拟合的衡量标准要么是基于均方误差，要么是基于似然，并且存在各种缺陷。由于成功的最终衡量标准是不同的模型对最终结果的预测有多好，因此有必要找到一个简单的游戏，其中对最终结果的预测在不同的模型之间存在根本性的差异。这最有可能发生在最佳响应分割线交叉时。此外，在这样的环境下，诸如渴望和实验等问题可以更好地被解决。我们将集中在具有显示分界线交叉的多个纳什均衡的博弈中的归纳选择理论的比较，并且我们将实证检验包含初始条件表征的扩展的动态理论是否可以作为均衡选择的可靠理论。主要学习理论的性能将在样本内和样本外进行比较。主要产品将是(I)为测试初始条件和学习动力学的综合理论而进行的一系列实验的数据，以及(Ii)这些测试结果的出版物，揭示哪种理论是行为的最佳稳健预测因素(在似然和MSE等传统标准下，以及在预测最终结果的不太常见但更具信息量的成功率下)以及差异有多大。这项建议将支持一名研究生，为他提供博弈论、高级统计方法和实验方法前沿的宝贵培训。此外，本科生经常因为接触到实验而参与进来，并根据他们的经验撰写荣誉论文。博弈论方法已被证明在分析从商业到政治再到国防的各种现实世界情况中都很有价值。因此，博弈论模型预测能力的重大改进将对社会产生广泛的影响。

Due to the poor empirical success of deductive equilibrium selection theories in predicting the outcomes of games, focus has shifted to equilibrium selection theories that rely on dynamics--also known as inductive selection theories. Inductive selection theories rely mainly on adaptive dynamics-dynamics based on the principle that players learn and adapt, so that "successful" strategies increase in frequency whereas "unsuccessful" strategies decrease in frequency. Different theories of dynamics differ in the measure of "success," the level of sophistication players are assumed to possess, the modeling of errors in choice, attention by players to the strategy space, the role that aspirations play, and the extent of imitation versus experimentation by players. In this research, a representative range of learning theories will be investigated including a simple logit dynamic model, a theory of aspiration and imitation, a model of reinforcement learning, a model of experience-weighted attraction learning, and a model of rule-learning.It is rare to find, in the recent stream of work on probabilistic choice learning dynamics, models that make radically different predictions (with parameter estimates from similar games). Hence, different learning models have been compared based on how well they fit the path of play. The measures of fit are based on either mean square error or likelihood, and suffer from a variety of shortcomings. Since the ultimate measure of success is how well different models predict final outcomes, it is necessary to find a simple game where the success in prediction of final outcomes radically differs among different models. This is most likely to occur when a best--response separatrix is crossed. Furthermore, issues such as aspiration and experimentation can better be addressed in such settings.We will focus on the comparisons of inductive selection theories in games with multiple Nash equilibria that exhibit separatrix crossings, and we will empirically test whether extended dynamic theories that incorporate characterization of initial conditions can serve as a reliable theory of equilibrium selection. The performance of the leading learning theories will be compared both in-sample and out-of-sample. The major products will be (i) data from a series of experiments conducted to test the composite theory of initial conditions and leaning dynamics, and (ii) publications of those test results revealing which theory is the best robust predictor of behavior (under traditional criteria such as likelihood and MSE as well as under the less common yet more informative rate of success in prediction of final outcome) and how substantial the differences are.This proposal will support one graduate student, providing him with valuable training in the frontiers of game theory, advanced statistical methods and experimental methods. In addition, undergraduate students frequently become involved due to exposure to experiments and have written Honors papers inspired by their experiences. Game theoretic approaches have proved valuable in the analysis of a wide range of real world situations from business to politics to defense. Consequently, a major improvement in the predictive power of game theoretic models will have wide ranging impacts on society.