微观经济学workshop: Core of Convex Matching Games: A Scarf's Lemma Approach
题目： Core of Convex Matching Games: A Scarf's Lemma Approach
The core of a matching game is often empty when the market does not have a two-sided structure, contracts are multilateral, or agents have complementary preferences. In this paper, I use Scarf's lemma to show that the core of a matching game is always nonempty given a convexity structure, even if the game has an arbitrary contracting network, multilateral contracts, and complementary preferences. I provide three applications to show how the convexity structure is satisfied in different contexts by different assumptions. In the first application, I show that in large economies, the convexity structure is satisfied if the set of participants in each contract is small compared to the overall economy. Remarkably, no restriction on agents' preferences is needed beyond continuity. The second application considers finite economies, and I show that the convexity structure is satisfied if all agents have convex, but not necessarily substitutable, preferences. The third application considers a large-firm, many-to-one matching market with peer preferences, and I show that the convexity structure is satisfied under convexity of preferences and a competition aversion restriction on workers' preferences over colleagues. Because of the convexity structure, all three applications have a nonempty core.
Xingye Wu is an Assistant Professor from Department of Economics, School of Economics and Management, Tsinghua University. He received his Ph.D. in Economics from Columnbia University. His main research interests include Microeconomic Theory, Mechanism Design, Matching Theory.