Efficiency and stability in large matching markets (original) (raw)

Incentives in Two-sided Matching Markets with Prediction-enhanced Preference-formation

ArXiv, 2021

Two-sided matching markets have long existed to pair agents in the absence of regulated exchanges. A common example is school choice, where a matching mechanism uses student and school preferences to assign students to schools. In such settings, forming preferences is both difficult and critical. Prior work has suggested various prediction mechanisms that help agents make decisions about their preferences. Although often deployed together, these matching and prediction mechanisms are almost always analyzed separately. The present work shows that at the intersection of the two lies a previously unexplored type of strategic behavior: agents returning to the market (e.g., schools) can attack future predictions by interacting short-term non-optimally with their matches. Here, we first introduce this type of strategic behavior, which we call an adversarial interaction attack. Next, we construct a formal economic model that captures the feedback loop between prediction mechanisms designed...

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.

Non-Standard Choice in Matching Markets

2021

We explore the possibility of designing matching mechanisms that can accommodate non-standard choice behavior. We pin down the necessary and sufficient conditions on participants’ choice behavior for the existence of stable and incentive compatible mechanisms. Our results imply that well-functioning matching markets can be designed to adequately accommodate a plethora of choice behaviors, including the standard behavior that is consistent with preference maximization. To illustrate the significance of our results in practice, we show that a simple modification in a commonly used matching mechanism enables it to accommodate non-standard choice behavior.

Peer Effects and Stability in Matching Markets

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.

Large Matching Markets as Two-Sided Demand Systems

Econometrica, 2015

This paper studies two-sided matching markets with non-transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

A MARKET WITH FRICTIONS IN THE MATCHING PROCESS: AN EXPERIMENTAL STUDY

International Economic Review, 2007

We construct a laboratory market with the structure of the theoretical model of Burdett, Shi, and Wright (2001). The model is a simple and natural way to represent a market in which there is a friction in the matching process between buyers and sellers. Sellers first simultaneously post prices at which they are willing to sell their single unit of a good. Buyers then simultaneously choose a seller from whom to attempt to purchase a unit. If more than one buyer chooses the same seller, the good is randomly sold to one of the buyers. If a seller is not chosen by any buyer, his unit is not sold. Our experimental results show a broad consistency with the model of Burdett et al. and less support for an alternative model, which is analogous to Montgomery (1991), and which has different assumptions on the strategic interaction between sellers. The main departure that we observe from the Burdett et al. model is that prices exceed the equilibrium level when there are only two sellers.

Stability in dynamic matching markets

Games and Economic Behavior, 2005

A dynamic two-sided matching market is considered. We examine two existing notions of stability-the core and recursive core-for this multi-period market and argue that they both have limitations. We define two new notions of stability and label them, self-sustaining stability and strict self-sustaining stability. Both concepts can be viewed as the recursive core with more stringent conditions for when deviating coalitions are effective. We show that these concepts overcome some of the weaknesses of the core and the recursive core. We also provide conditions for the existence of our concepts. ď›™ 2004 Elsevier Inc. All rights reserved.

Matching in Dynamic Imbalanced Markets

SSRN Electronic Journal, 2018

We study dynamic matching in exchange markets with easy-and hard-to-match agents. A greedy policy, which attempts to match agents upon arrival, ignores the positive externality that waiting agents generate by facilitating future matchings. We prove that this trade-off between a "thicker" market and faster matching vanishes in large markets; A greedy policy leads to shorter waiting times, and more agents matched than any other policy. We empirically confirm these findings in data from the National Kidney Registry. Greedy matching achieves as many transplants as commonly-used policies (1.6% more than monthly-batching), and shorter patient waiting times (23 days faster than monthly-batching).