CAREER: A Theory of Mechanisms with Unstructured Beliefs

这个项目将机制理论扩展到具有非结构化信念的环境。更具体地说，计算机科学研究的是数据在手时的优化问题，而机制设计研究的是数据在理性参与者手中时的优化问题，如果符合他们的利益，他们可能会在战略上对自己拥有的数据撒谎。对机制设计的需求出现在计算机科学和经济学的许多环境中，例如分布式计算、拍卖、社会网络、医疗保健和多代理系统。在一个机制中，玩家对其他玩家的信念是他所拥有的关于他们的信息：这被称为“信念”而不是“知识”，以反映信息可能并不总是正确或一致的。玩家的信念构成了他们推理的基础，并在很大程度上影响着机制的结构和性能。信念可以是空的，纯可能性的，或者纯概率的；但是，它们通常是非结构化的：玩家的信念可能介于一系列可能性和完全成熟的概率分布之间。尽管机制设计取得了巨大进步，但玩家拥有非结构化信念的广阔空间仍未被探索。本项目研究关于这些设置的基本问题，旨在发展一种分析和利用非结构化信念的机制理论。如果成功，它将对计算机科学和经济学做出深远的贡献，并有望对逻辑学、多智能体系统和博弈论产生持久的影响。本项目的技术部分由两个关键部分组成。一方面，它将为不同的信息结构建立逻辑基础，并表征相应的合理性概念。另一方面，它将为机制设计开发新的工具和标准，并为拍卖等战略设置提供新的机制。该项目将为具有非结构化信念的机制建立坚实的科学基础，使机制设计更接近于逻辑和认知博弈论，进一步加强计算机科学与经济学的联系。该项目的成果将在计算机科学、经济学和运筹学领域广泛传播。倡议将鼓励妇女和代表性不足的少数群体成员参与这一项目。此外，新的研究生和本科课程将在此项目基础上开发。

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.