Making Auctions Work in Practice Is Worth a Nobel
Citation:
Kominers, Scott Duke. "Making Auctions Work in Practice Is Worth a Nobel." Bloomberg Opinion (October 12, 2020). View Details|
Working Paper HBS Working Paper Series 2020 To Infinity and Beyond: Scaling Economic Theories via Logical Compactness |
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 rely on edge effects or artificial boundary conditions. Here, we present a unified method that enables us to remove finiteness assumptions, such as those on datasets, market sizes, and time horizons. We then apply our approach to a variety of revealed preference, matching, and exchange economy settings. The key to our approach is Logical Compactness, a core result from Propositional Logic. Building on Logical Compactness, in a revealed-preference setting, we reprove Reny's infinite-data version of Afriat's theorem and (newly) prove an infinite-data version of McFadden and Richter's characterization of rationalizable stochastic datasets. In a matching setting, we reprove large-market existence results implied by Fleiner's analysis and prove both the strategy-proofness of the man-optimal stable mechanism in infinite markets and an infinite-market version of Nguyen and Vohra's existence result for near-feasible stable matchings with couples. In a trading-network setting, we prove that the Hatfield et al. result on the existence of Walrasian equilibria extends to infinite markets. Finally, we prove that Pereyra's existence result for dynamic two-sided matching markets extends to a doubly infinite time horizon.
Keywords: Markets; Analysis; Game Theory;
Citation:
Gonczarowski, Yannai A., Scott Duke Kominers, and Ran I. Shorrer. "To Infinity and Beyond: Scaling Economic Theories via Logical Compactness." Harvard Business School Working Paper, No. 19-127, June 2019. (Revised March 2020.)
