Optimal Learning in Games

经济学、政治学和相关学科的许多领域都依赖于战略理论来研究市场结构、投票规则、法律、组织理论和商业战略等问题。在这一理论中，通常假设战略形势的参与者对该形势有相同的描述，即他们使用共同的语言。然而，在实践中，往往需要建立一种共同的语言来延迟组织中的决策，延长合同谈判，或者从积极的方面来说，防止市场中公司之间的勾结。这使得尝试理解战略代理如何学习开发一种共同语言变得非常重要。本项目从理论和实验两方面探讨了这一学习过程。该奖助金资助一系列从部分语言学习通用语言的相关项目。在理论研究中，作为基准，我假设缺乏共同语言是智能体学习行为的唯一约束，否则它们就会学习得最优。第一个项目的目标是开发一个概念框架，允许人们改变和研究部分语言的角色。这涉及到使用一些基本的群论作为一种手段，提供一个连贯的框架来研究部分语言，以及快速学习现象，其中部分语言不能保证立即协调，但允许快速建立一个完整的公共语言。第二个项目研究重复信息传递的简单模型中的最佳学习范式。重点是学习如何受到发送者和接收者之间动机差异的影响，以及当前交流的需要与为未来建立语言的愿望之间的紧张关系。第三个项目开始调查效率如何导致沟通中的结构（部分语言）。如果一门语言具有模块化结构，例如，如果在自然语言中，过去时（几乎）总是以相同的方式表示，或者如果有标准化的规则，如会计惯例，这是相当直观的。然而，如何正式地表达这种直觉并不是那么明显。在这里，我们尝试使用第一个项目中开发的概念框架，以确定可行的条件（例如，消息长度的成本，预先存在的部分语言），在这些条件下，效率需要模块化。第四个项目将实验研究在最优学习规则是唯一的情况下最优学习理论的预测。这与目前关于刺激反应学习和虚拟游戏等适应性学习规则的研究形成了有趣的对比。本研究探讨了博弈论的基本问题，如理性、协调和学习。适应性学习模型、理性学习模型和学习实验是当前博弈论研究的热点。在局部语言环境下的最佳学习研究为这一研究议程增加了一个新的视角。这对研究交往、制度、契约、心照不宣的串通等问题具有重要的启示意义。

Many areas of economics, political science and related disciplines rely on a theory of strategy to investigate issues such as market structure, voting rules, the law, the theory of organizations, and business strategy. In this theory it typically is assumed that the participants in a strategic situation have the same description of that situation, i.e., that they share a common language. In practice however, it is often the need for building a common language that delays decisions in an organization, prolongs contract negotiations, or, on a positive note, prevents collusion among firms in markets. This makes it important to try to understand how strategic agents learn to develop a common language. This project investigates this learning process both in theory and with experiments. The grant funds a set of related projects on learning a common language from a partial language. In the theoretical investigation, I assume, as a benchmark, that the lack of a common language is the only constraint on agents' learning behavior and that otherwise they learn optimally. The goal of the first project is to develop a conceptual framework that permits one to vary and study the role of a partial language. This involves the use of some elementary group theory as a means for providing a coherent framework in which to investigate partial languages, and of fast learning phenomena, where the partial language does not guarantee immediate coordination but permits a complete common language to be built rapidly. The second project investigates the optimal learning paradigm in simple models of repeated information transmission. The focus is on how learning is influenced by differences in incentives between sender and receiver, and on the tension between the need to communicate in the present and the desire to build a language for the future. The third project begins an investigation of how efficiency induces structure (a partial language) in communication. It is fairly intuitive that a language is easier to learn if it has a modular structure, e.g., if as in natural language the past tense is (almost) always indicated in the same way, or if there are standardized rules as in accounting conventions. However, it is not so obvious how to articulate this intuition formally. Here an attempt is made to use the conceptual framework developed in the first project in order to identify plausible conditions (e.g., costs of message length, preexistent partial languages) under which efficiency necessitates modularity. The fourth project will experimentally investigate the predictions of the optimal learning theory in instances where the optimal learning rule is unique. This should provide an interesting contrast with current research on adaptive learning rules such as stimulus response learning and fictitious play. This research addresses foundational issues in game theory such as rationality, coordination and learning. Adaptive learning models, rational learning models and experiments on learning are at the center of current game theoretic research. The proposed study of optimal learning in environments with a partial language adds a new perspective to this research agenda. It has important implications for the study of communication, institutions, contracting, tacit collusion etc.