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成功度不高，人们的注意力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自适应动力学——基于玩家学习和适应原则的动力学，因此“成功”策略的频率增加，而“不成功”策略的频率减少。不同的动力学理论在衡量“成功”、假设玩家拥有的复杂程度、选择错误的建模、玩家对策略空间的关注、抱负扮演的角色以及玩家模仿与实验的程度等方面存在差异。在本研究中，将研究一系列具有代表性的学习理论，包括简单的logit动态模型、渴望和模仿理论、强化学习模型、经验加权吸引学习模型和规则学习模型。在最近关于概率选择学习动态的研究中，我们很难找到能够做出完全不同的预测（基于类似游戏的参数估计）的模型。因此，不同的学习模式会根据它们与游戏路径的契合程度进行比较。拟合的度量要么基于均方误差，要么基于似然，并且存在各种缺点。由于成功的最终衡量标准是不同模型对最终结果的预测程度，因此有必要找到一个简单的游戏，在这个游戏中，不同模型对最终结果的预测成功程度存在根本差异。当最佳响应分离矩阵交叉时，最可能发生这种情况。此外，愿望和实验等问题可以在这样的环境中得到更好的解决。我们将重点关注归纳选择理论在具有分离矩阵交叉的多个纳什均衡博弈中的比较，我们将实证检验包含初始条件特征的扩展动态理论是否可以作为均衡选择的可靠理论。主要学习理论的表现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复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，这些结果揭示了哪种理论是最可靠的行为预测器（在传统标准下，如可能性和MSE，以及在预测最终结果的不太常见但更有信息量的成功率下）以及差异的实质性程度。该项目将资助一名研究生，为其提供博弈论前沿、先进统计方法和实验方法方面的宝贵培训。此外，本科生经常因接触实验而参与其中，并从他们的经历中获得灵感，撰写荣誉论文。事实证明，博弈论方法在分析从商业到政治再到国防等广泛的现实世界情况方面很有价值。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.