Peer Effects and Stability in Matching Markets (original) (raw)

Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In the these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings. In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social net- work. Our model captures peer effects and complementarities using utility functions rather than traditional preference ordering. With this model and considering pairwise stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. We also give distributed algorithms that are guaranteed to converge to a stable matching. To assess the competitive ratio of these algorithms and to more generally characterize the efficiency of matching markets with externalities, we prove general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

Many-to-one matching with complementarities and peer effects

This paper studies many-to-one matching problems such as between students and colleges, and workers and firms in the general case, in which both peer effects and complementarities are allowed. In a matching, an agent on one side, say a firm, employs a subset of agents from the other side (workers), thus forming a coalition. The paper interprets an agent's payoff in a matching as determined by a division rule applied to the value created by the agent's coalition. The main results relate stability to pairwise alignment. A matching is stable if no group of agents can profitably deviate. Agents' preferences are pairwise aligned if any two agents in the intersection of any two coalitions prefer the same one of the two coalitions. The results say that under mild regularity conditions (i) if the division rule generates pairwise-aligned preferences then there exists a stable matching, and (ii) if there exists a stable matching for all profiles of coalitional values then the divi...

Efficiency and stability in large matching markets

We study efficient and stable mechanisms in matching markets when the number of agents is large and individuals' preferences and priorities are drawn randomly. When agents' preferences are uncorrelated, then both efficiency and stability can be achieved in an asymptotic sense via standard mechanisms such as deferred acceptance and top trading cycles. When agents' preferences are correlated over objects, however, these mechanisms are either inefficient or unstable even in an asymptotic sense. We propose a variant of deferred acceptance that is asymptotically efficient, asymptotically stable and asymptotically incentive compatible. This new mechanism performs well in a counterfactual calibration based on New York City school choice data.

Three remarks on the many-to-many stable matching problem

Mathematical Social Sciences, 1999

We propose a general definition of stability, setwise-stability, and show that it is a stronger requirement than pairwise-stability and core. We also show that the core and the set of pairwise-stable matchings may be non-empty and disjoint and thus setwise-stable matchings may not exist. For many labor markets the effects of competition can be characterized by requiring only pairwise-stability. For such markets we define substitutability and we prove the existence of pairwise-stable matchings. The restriction of our proof to the College Admission Model is simple and short and provides an alternative proof for the existence of stable matchings for this model.

A Theory of Stability in Many-to-many Matching Markets

SSRN Electronic Journal, 2000

We develop a theory of stability in many-to-many matching markets. We give conditions under wich the setwisestable set, a core-like concept, is nonempty and can be approached through an algorithm. The setwise-stable set coincides with the pairwise-stable set, and with the predictions of a non-cooperative bargaining model. The set-wise stable set possesses the canonical conflict/coincidence of interest properties from many-to-one, and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

Matching through decentralized markets

2007

Abstract. We study a simple model of a decentralized market game in which firms make directed offers to workers. We identify three components of the market game that are key in determining whether stable matches can arise as equilibrium outcomes. The first is related to the structure of preferences of agents. The second pertains to the agentslinformation on preferences. The third is whether there are frictions in the market, which in this paper take the form of discounting.

Instability of matchings in decentralized markets with various preference structures

International Journal of Game Theory, 2008

In any two-sided matching market, a stable matching can be found by a central agency using the deferred acceptance procedure of Gale and Shapley. But if the market is decentralized and information is incomplete then stability of the ensuing matching is not to be expected. Despite the prevalence of such matching situations, and the importance of stability, little theory exists concerning instability. We discuss various measures of instability and analyze how they interact with the structure of the underlying preferences. Our main result is that even the outcome of decentralized matching with incomplete information can be expected to be "almost stable" under reasonable assumptions.

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