Inductive Equilibrium Selection in Games with Separatrix Crossing

分界线交叉博弈中的归纳均衡选择

• 批准号: 9986379
• 负责人: Dale Stahl
• 金额: $ 4.5万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-02-15 至 2002-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9986379&HistoricalAwards=false
• 关键词: Inductive; Equilibrium; Selection; Games; Separatrix

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.

由于演绎均衡选择理论在预测博弈结果方面的经验成功率很低，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适应性动态--基于参与者学习和适应原则的动态，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、玩家对策略空间的注意力、愿望所起的作用以及玩家模仿与实验的程度等方面有所不同。 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，愿望和模仿理论，强化学习模型，经验加权吸引学习模型和规则学习模型。在最近的概率选择学习动态工作流中，这些模型做出完全不同的预测（使用类似游戏的参数估计）。 因此，不同的学习模型已经根据它们是否适合游戏的路径进行了比较。 拟合的度量是基于均方误差或似然，并且具有各种缺点。 由于成功的最终衡量标准是不同模型对最终结果的预测效果，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效果有着根本的不同。 这是最有可能发生时，最佳对策分界线交叉。 此外，问题，如愿望和实验，可以更好地解决在这样的setting.We将集中在多个纳什均衡，表现出分界线交叉博弈的归纳选择理论的比较，我们将实证检验是否扩展的动态理论，包括初始条件的表征可以作为一个可靠的理论均衡选择。 领先的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）为检验初始条件和倾斜动力学的复合理论而进行的一系列实验的数据，以及（ii）揭示哪种理论是行为的最佳稳健预测器的那些测试结果的出版物（根据可能性和MSE等传统标准，以及在预测最终结局方面不太常见但信息量更大的成功率）以及差异有多大。这个建议将支持一个研究生，为他提供有价值的培训，在前沿的博弈论，先进的统计方法和实验方法。 此外，本科生经常因为接触实验而参与其中，并在他们的经验启发下撰写了荣誉论文。 博弈论方法在分析从商业到政治到国防的广泛的真实的世界局势中被证明是有价值的。 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。