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，通常假设战略局势中的参与者对该局势有相同的描述，即，他们有共同的语言 然而，在实践中，往往需要建立一种共同语言，这会推迟一个组织的决策，阻碍合同谈判，或者从积极的方面来说，防止市场上公司之间的勾结。这使得试图理解战略代理人如何学习发展共同语言变得非常重要。本研究从理论和实验两方面对这一学习过程进行了研究。 该赠款资助了一系列关于从部分语言中学习共同语言的相关项目。在理论研究中，我假设，作为一个基准，缺乏一个共同的语言是唯一的约束代理的学习行为，否则他们学习最佳。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作用。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，在其中调查部分语言，并快速学习现象，其中部分语言并不能保证立即协调，但允许一个完整的共同语言迅速建立。 第二个项目研究重复信息传递的简单模型中的最优学习范式。重点是学习是如何受到发送者和接收者之间的激励差异的影响，以及当前沟通的需要和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在交流中引起结构（部分语言）。相当直观的是，如果一种语言具有模块化结构，它就更容易学习，例如，在自然语言中，过去时态（几乎）总是以相同的方式表示，或者在会计惯例中有标准化的规则。然而，如何正式表达这种直觉并不那么明显。这里试图使用第一个项目中开发的概念框架，以确定合理的条件（例如，消息长度的成本，预先存在的部分语言），在这种情况下，效率需要模块化。 第四个项目将通过实验研究最优学习理论在最优学习规则是唯一的情况下的预测。这应该提供了一个有趣的对比，与目前的研究适应性学习规则，如刺激反应学习和虚构的发挥。 这项研究解决了博弈论中的基本问题，如理性，协调和学习。自适应学习模型、理性学习模型和学习实验是当前博弈论研究的核心。在部分语言环境中的最佳学习的研究建议增加了一个新的视角，这一研究议程。它对沟通、制度、契约、默契共谋等问题的研究具有重要意义。

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.