A Compact, Logical Approach to Large-Market Analysis

Logic, Games, and Graphs Seminar

Meeting Details

For more information about this meeting, contact Stephanie Geyer, Andrew Belmonte, Jan Reimann, Linda Westrick, Kristin Berrigan, Christopher Griffin.

Speaker: Ran Shorrer, Penn State University

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.

Room Reservation Information

Room Number: 114 McAllister

Date: 10/02/2019

Time: 2:30pm - 3:30pm