To Infinity and Beyond: Scaling Economic Theories via Logical Compactness (joint with Scott Duke Kominers and Ran Shorrer)

Abstract: Many economic-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example, they may depend upon edge effects or artificial boundary conditions. Here, we present a unified method that enables us to remove finiteness assumptions, such as those on market sizes, time horizons, and datasets.

The key to our approach is Logical Compactness, a core result from Propositional Logic. We demonstrate our approach by showing that it applies equally well to settings as varied as revealed preferences, matchings, and exchange economies. We concisely reprove celebrated results ranging from Reny’s infinite-data version of Afriat’s theorem to large-market stable-matching existence results implied by Fleiner’s analysis. We then use the same approach to newly prove results ranging from generalizations of finite-data results by McFadden and Richter and by Masatlioglu et al. to the strategy-proofness of the man-optimal stable matching mechanism in infinite markets and an infinite-market version of Nguyen and Vohra’s existence result for near-feasible stable matchings with couples.

Bio: Yannai is a faculty member at Harvard Economics and Harvard Computer Science. His main research interests lie in the interface between economic theory, theoretical computer science, and game theory. In particular, Yannai is interested in various aspects of complexity in mechanism design (where mechanisms are deļ¬ned broadly from auctions to matching markets), including the interface between mechanism design and machine learning. A high-level introduction to some of Yannai's main research interests is given in the half-hour ACM SIGecom Dissertation Award Talk given at EC'19. He has also applied his research to the design of real-life matching markets. The 20-minute inaugural Rothkopf Prize Lecture he gave at INFORMS 2020 discusses such an applied market-design project.