“(1) Understanding Stable Matchings: A Non-Cooperative Approach & (2) Tiers, Preference Similarity, and the Limits on Stable Partners” by Yosuke Yasuda
National Graduate Institute for Policy
National Graduate Institute for Policy Studies
University of Tokyo
Abstract for "Tiers, Preference Similarity, and the Limits on Stable Partners" We consider the one-to-one matching problem where agents on one side of the market have similar preferences over those on the other side. More specifically, we present two formalizations of the idea of preference similarity, called the tiers model and the distance model. In the tiers model, preferences can vary only within a fixed subset of agents. In the distance model, preferences are modified from the underlying common ranking within certain distance. In each model, we characterize the upper- bound of the number of possible partners in stable matchings. Abstract for "Understanding Stable Matchings: A Non-Cooperative Approach" We present a series of non-cooperative games with monotone best replies whose set of Nash equilibria coincides with the set of stable matchings. Key features of stable matchings are established as familiar properties of games with monotone best replies. Then we present a sense in which our method is necessary for the monotonicity approach. We also establish the connection of our approach with other monotone methods in the literature.