A Compact, Logical Approach to Large-Market Analysis

28 Pages Posted: 27 Jun 2019

See all articles by Yannai A. Gonczarowski

Yannai A. Gonczarowski

The Blavatnik School of Computer Science, Tel Aviv University

Scott Duke Kominers

Harvard University

Ran I. Shorrer

Pennsylvania State University

Date Written: June 25, 2019

Abstract

In game theory, we often use infinite models to represent "limit" settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

Suggested Citation

Gonczarowski, Yannai A. and Kominers, Scott Duke and Shorrer, Ran I., A Compact, Logical Approach to Large-Market Analysis (June 25, 2019). Harvard Business School Entrepreneurial Management Working Paper No. 19-127, June 2019. Available at SSRN: https://ssrn.com/abstract=3409828 or http://dx.doi.org/10.2139/ssrn.3409828

Yannai A. Gonczarowski

The Blavatnik School of Computer Science, Tel Aviv University ( email )

Ramat Aviv
Tel-Aviv, 6997801
Israel

Scott Duke Kominers (Contact Author)

Harvard University ( email )

Rock Center
Harvard Business School
Boston, MA 02163
United States

HOME PAGE: http://www.scottkom.com/

Ran I. Shorrer

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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