June 26, 2019, Paper, "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."
Non-HKS Author Website - Scott Duke Kominers