Working Papers:
Core of Convex Matching Games: A Scarf's Lemma Approach
[Full Text]
As a central solution concept of cooperative games, the notion of the core is widely studied and applied in the matching theory literature. A matching outcome is said to be in the core if no coalition of agents can find a profitable joint deviation. However, it is well known that the core may be empty with general contracting networks, multilateral contracts, or complementary preferences. Fortunately, recent studies including Hatfield and Kominers (2015), Azevedo and Hatfield (2018), and Che, Kim, and Kojima (2019) obtain nonempty core results under different assumptions despite those difficulties. In this paper, we identify a convexity structure of matching games that unifies our understanding of those nonempty core results and highlights their relation to a lemma of Scarf (1967). This approach also allows us to obtain a new nonempty core result after introducing peer preferences into the model of Che, Kim, and Kojima (2019).
A Characterization of Preference Domains that are Single-crossing and Maximal Condorcet (joint with Arkadii Slinko and Qinggong Wu)
[Full Text]
We show that a preference domain is single-crossing and maximal Condorcet if and only if it can be represented as a relay, a structure that is simple to construct and verify. Using this characterization, we find that there are at most two domains that are single-crossing and maximal Condorcet, and we also find another characterization of such domains in terms of inversion triples.
Work in Progress:
College Admissions with Flexible Major Quotas (joint with Dalin Sheng and Xiaohan Zhong)
A Foundation for Generalized Condorcet Domains (joint with Qinggong Wu)
Core of Convex Matching Games: A Scarf's Lemma Approach
[Full Text]
As a central solution concept of cooperative games, the notion of the core is widely studied and applied in the matching theory literature. A matching outcome is said to be in the core if no coalition of agents can find a profitable joint deviation. However, it is well known that the core may be empty with general contracting networks, multilateral contracts, or complementary preferences. Fortunately, recent studies including Hatfield and Kominers (2015), Azevedo and Hatfield (2018), and Che, Kim, and Kojima (2019) obtain nonempty core results under different assumptions despite those difficulties. In this paper, we identify a convexity structure of matching games that unifies our understanding of those nonempty core results and highlights their relation to a lemma of Scarf (1967). This approach also allows us to obtain a new nonempty core result after introducing peer preferences into the model of Che, Kim, and Kojima (2019).
A Characterization of Preference Domains that are Single-crossing and Maximal Condorcet (joint with Arkadii Slinko and Qinggong Wu)
[Full Text]
We show that a preference domain is single-crossing and maximal Condorcet if and only if it can be represented as a relay, a structure that is simple to construct and verify. Using this characterization, we find that there are at most two domains that are single-crossing and maximal Condorcet, and we also find another characterization of such domains in terms of inversion triples.
Work in Progress:
College Admissions with Flexible Major Quotas (joint with Dalin Sheng and Xiaohan Zhong)
A Foundation for Generalized Condorcet Domains (joint with Qinggong Wu)