Optimal Learning in Games

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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.