CAREER: A Theory of Mechanisms with Unstructured Beliefs

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This project expands the theory of mechanisms to settings with unstructured beliefs. More specifically, computer science studies optimization problems when the data is at hand, and mechanism design studies optimization problems when the data is in the hands of rational players, who may strategically lie about the data in their possession if this is in their interest. The need for mechanism design arises in many contexts in both computer science and economics, such as distributed computation, auctions, social networks, healthcare, and multiagent systems at large. A player's belief about other players in a mechanism is the information he has about them: it's called "belief" rather than "knowledge" to reflect that the information may not always be correct or consistent. Players' beliefs form the basis of their reasoning, and largely affect the mechanism's structure and performance. Beliefs can be null, purely possibilistic, or purely probabilistic; but, very often, they are unstructured: a player's belief can be anywhere between a set of possibilities and a fully-fledged probability distribution. Despite the tremendous progress made in mechanism design, the vast space where players have unstructured beliefs remains highly unexplored. This project studies fundamental questions about such settings and aims at developing a theory of mechanisms for analyzing and leveraging unstructured beliefs. If successful, it will make profound contributions to both computer science and economics, and is expected to have a long-lasting impact on logic, multiagent systems, and game theory. The technical part of this project consists of two key components. On the one hand, it will establish the logical foundation for different information structures and characterize corresponding notions of rationality. On the other hand, it will develop new tools and criteria for mechanism design, and provide new mechanisms for strategic settings such as auctions. This project will establish a solid scientific foundation for mechanisms with unstructured beliefs, bring mechanism design closer to logic and epistemic game theory, and further strengthen the connections between computer science and economics. Results from this project will be broadly disseminated in computer science, economics, and operations research. The PI will encourage the participation of women and members of underrepresented minority groups in this project. Moreover, new graduate and undergraduate curriculums will be developed based on this project.