Institutions selecting students, employees, or members value both about who is selected and the resulting group's composition. We study ``distributional'' preferences over group composition, and identify an upper-bound property and two exchange properties. With the upper-bound property, the exchange properties are necessary and sufficient for two results: the greedy rule is the unique choice rule that is non-wasteful, distributionally maximal, and free of justified envy; it is also path independent. In matching markets, deferred acceptance is the unique mechanism satisfying the three axioms, individual rationality, and strategy-proofness. Our framework accommodates intersectional identities and subsumes models based on reserves and matroids.
Given an initial matching and a policy objective on the distribution of agent types to institutions, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual rationality, and strategy-proofness. We show that such a mechanism need not exist in general. We introduce a new notion of discrete concavity, which we call pseudo M$^{\natural}$-concavity, and construct a mechanism with the desirable properties when the distributional objective satisfies this notion. We provide several practically relevant distributional obje…
We study two-sided many-to-one matching markets with transferable utilities, e.g., labor and rental housing markets, in which money can exchange hands between agents, subject to distributional constraints on the set of feasible allocations. In such markets, we establish the efficiency of equilibrium arrangements, specified by an assignment and transfers between agents on the two sides of the market, and study the conditions on the distributional constraints and agent preferences under which equilibria exist and can be computed efficiently. To this end, we first consider the setting when the nu…
The literature on centralized matching markets often assumes that a true preference of each player is known to herself and fixed, but empirical evidence casts doubt on its plausibility. To circumvent the problem, we consider evolutionary dynamics of preference revelation games in marriage problems. We formulate the asymptotic stability of a matching, indicating the dynamical robustness against sufficiently small changes in players' preference reporting strategies, and show that asymptotically stable matchings are stable when they exist. The simulation results of replicator dynamics are present…
Pseudo-Substitutability: A Maximal Domain for Pairwise Stability in Matching Markets with Contracts
Instituto de Matemática Aplicada San Luis (UNSL-CONICET)（圣路易斯应用数学研究所）；Departamento de Matemática, Universidad Nacional de San Luis（圣路易斯国立大学数学系）；Universidad Nacional de San Luis（圣路易斯国立大学）
We study a pure-exchange incomplete-market economy with heterogeneous agents. In each period, the agents choose how much to save (i.e., invest in a risk-free bond), how much to consume, and which bundle of goods to consume while their endowments are fluctuating. We focus on a competitive stationary equilibrium (CSE) in which the wealth distribution is invariant, the agents maximize their expected discounted utility, and both the prices of consumption goods and the interest rate are market-clearing. Our main contribution is to extend some general equilibrium results to an incomplete-market Bewl…
Results from the communication complexity literature have demonstrated that stable matching requires communication: one cannot find or verify a stable match without having access to essentially all of the ordinal preference information held privately by the agents in the market. Stated differently, these results show that stable matching mechanisms are not robust to even a small number of labeled inaccuracies in the input preferences. In practice, these results indicate that agents must go through the time-intensive process of accurately ranking each and every potential match candidate if they…
We introduce a new algorithm for finding stable matchings in multi-sided matching markets. Our setting is motivated by a PhD market of students, advisors, and co-advisors, and can be generalized to supply chain networks viewed as $n$-sided markets. In the three-sided PhD market, students primarily care about advisors and then about co-advisors (consistent preferences), while advisors and co-advisors have preferences over students only (hence they are cooperative). A student must be matched to one advisor and one co-advisor, or not at all. In contrast to previous work, advisor-student and stude…
In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. In this paper we show that in the case of strict preferences the unique strong core allocation (or competitive allocation) respects improvement: if an agent's object becomes more attractive for some other agents, then the agent's allotment in the unique strong core allocation weakly improves. We obtain a general result in case of ties in the preferences and provide n…
We study the stable marriage problem in two-sided markets with randomly generated preferences. We consider agents on each side divided into a constant number of "soft tiers", which intuitively indicate the quality of the agent. Specifically, every agent within a tier has the same public score, and agents on each side have preferences independently generated proportionally to the public scores of the other side. We compute the expected average rank which agents in each tier have for their partners in the men-optimal stable matching, and prove concentration results for the average rank in asympt…
Strategy Evolution in the Adoption of Conservation Tillage Technology under Time Preference Heterogeneity and Lemon Market: Insights from Evolutionary Dynamics
Northwest A&F University（西北农林科技大学）；Guilin Normal university（桂林师范学院）
University of California Berkeley（加州大学伯克利分校）；Caltech（加州理工学院）
We study the problem of online learning in competitive settings in the context of two-sided matching markets. In particular, one side of the market, the agents, must learn about their preferences over the other side, the firms, through repeated interaction while competing with other agents for successful matches. We propose a class of decentralized, communication- and coordination-free algorithms that agents can use to reach to their stable match in structured matching markets. In contrast to prior works, the proposed algorithms make decisions based solely on an agent's own history of play and…
The matching literature often recommends market centralization under the assumption that agents know their own preferences and that their preferences are fixed. We find counterevidence to this assumption in a quasi-experiment. In Germany's university admissions, a clearinghouse implements the early stages of the Gale-Shapley algorithm in real time. We show that early offers made in this decentralized phase, although not more desirable, are accepted more often than later ones. These results, together with survey evidence and a theoretical model, are consistent with students' costly learning abo…
School choice is the two-sided matching market where students (on one side) are to be matched with schools (on the other side) based on their mutual preferences. The classical algorithm to solve this problem is the celebrated deferred acceptance procedure, proposed by Gale and Shapley. After both sides have revealed their mutual preferences, the algorithm computes an optimal stable matching. Most often in practice, notably when the process is implemented by a national clearinghouse and thousands of schools enter the market, there is a quota on the number of applications that a student can subm…
