In several two-sided markets, including labor and dating, agents typically have limited information about their preferences prior to mutual interactions. This issue can result in matching frictions, as arising in the labor market for medical residencies, where high application rates are followed by a large number of interviews. Yet, the extensive literature on two-sided matching primarily focuses on models where agents know their preferences, leaving the interactions necessary for preference discovery largely overlooked. This paper studies this problem using an algorithmic approach, extending Gale-Shapley’s deferred acceptance to this context. Two algorithms are proposed. The first is an adaptive algorithm that expands upon Gale-Shapley’s deferred acceptance by incorporating interviews between applicants and positions. Similar to deferred acceptance, one side sequentially proposes to the other. However, the order of proposals is carefully chosen to ensure an interim stable matching is found. Furthermore, with high probability, the number of interviews conducted by each applicant or position is limited to O(log² n). In many seasonal markets, interactions occur more simultaneously, consisting of an initial interview phase followed by a clearing stage. We present a non-adaptive algorithm for generating a single stage set of in tiered random markets. The algorithm finds an interim stable matching in such markets while assigning no more than O(log³ n) interviews to each applicant or position.

School choice mechanism designers use discrete choice models to understand and predict families' preferences. The most widely-used choice model, the multinomial logit (MNL), is linear in school and/or household attributes. While the model is simple and interpretable, it assumes the ranked preference lists arise from a choice process that is uniform throughout the ranking, from top to bottom. In this work, we introduce two strategies for rank-heterogeneous choice modeling tailored for school choice. First, we adapt a context-dependent random utility model (CDM), considering down-rank choices as occurring in the context of earlier up-rank choices. Second, we consider stratifying the choice modeling by rank, regularizing rank-adjacent models towards one another when appropriate. Using data on household preferences from the San Francisco Unified School District (SFUSD) across multiple years, we show that the contextual models considerably improve our out-of-sample evaluation metrics across all rank positions over the non-contextual models in the literature. Meanwhile, stratifying the model by rank can yield more accurate first-choice predictions while down-rank predictions are relatively unimproved. These models provide performance upgrades that school choice researchers can adopt to improve predictions and counterfactual analyses.

In many centralized labor markets candidates interview with potential employers before matches are formed through a clearinghouse. One prominent example is the market for medical residencies and fellowships, which in recent years has had a large increase in the number of interviews. There have been numerous efforts to reduce the cost of interviewing in these markets using a variety of signalling mechanisms, however, the theoretical properties of these mechanisms have not been systematically studied in models with rich preferences. In this paper we give theoretical guarantees for a variety of mechanisms, finding that these mechanisms must properly balance competition in both sides of the market.

We study the welfare structure in two-sided matching markets when agents have latent preferences generated according to observed characteristics. Specifically, we are interested in the empirical welfare distribution of agents on each side of the market under stable outcomes as well as the relation between the outcomes of each side of the market.

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We study centralized dynamic matching markets with finitely many agent types and heterogeneous match values. Delaying actions to accumulate "inventory" creates a positive externality from forming future matches that generate high value. This delay, however, inevitably compromises short-term value. The goal of this paper is to shed light on this tension within the family of two-way matching networks.

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 asymptotically large markets. Furthermore, we show that despite having a significant effect on ranks, public scores do not strongly influence the probability of an agent matching to a given tier of the other side. This generalizes results of [Pittel 1989] which correspond to uniform preferences. The results quantitatively demonstrate the effect of competition due to the heterogeneous attractiveness of agents in the market, and we give the first explicit calculations of rank beyond uniform markets.

Motivated by the high discard rate of donated organs in the United States, we study an allocation problem in the presence of learning and strategic incentives. We consider a setting where a benevolent social planner decides whether and how to allocate a single indivisible object to a queue of strategic agents. The object has a common true quality, good or bad, which is ex-ante unknown to everyone. Each agent holds an informative, yet noisy, private signal about the quality. To make a correct allocation decision the planner attempts to learn the object quality by truthfully eliciting agents' signals. Under the commonly applied sequential offering mechanism, we show that learning is hampered by the presence of strategic incentives as herding may emerge. This can result in incorrect allocation and welfare loss. To overcome these issues, we propose a novel class of incentive-compatible mechanisms. Our mechanism involves a batch-by-batch, dynamic voting process using a majority rule. We prove that the proposed voting mechanisms improve the probability of correct allocation whenever agents are sufficiently well informed. Particularly, we show that such an improvement can be achieved via a simple greedy algorithm. We quantify the improvement using simulations.

We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent's value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. We analyze direct-revelation mechanisms that elicit agents' types and assign them to objects over time. We identify the welfare-maximizing mechanism and show that it can be implemented by a first-come first-served wait-list with deferrals when the marketmaker can design the information disclosed to agents about the objects. The optimal disclosure policy pools adjacent object types.

Consider a seller that intends to auction some item. The seller can invest money and effort in advertising in different market segments in order to recruit n bidders to the auction. Alternatively, the seller can have a much cheaper and focused marketing operation and recruit the same number of bidders from a single market segment. Which marketing operation should the seller choose?

Waiting lists are common mechanisms for allocating scarce items without monetary transfers. Examples include the allocation of cadaver organs to patients in need of a transplant, public housing apartments to applicants, health care services to patients, and even spots at childcare centers to parents. In all these markets waiting times play the role of prices in guiding the allocation and rationing items. But while prices are set by the designer, waiting times are endogenously determined by the number of agents waiting. Moreover, waiting times are not fixed, and continuously adjust as items arrive or agents join. When agents and items arrive stochastically over time, waiting times stochastically adjust over time.

The increasing popularity of online two-sided markets such as ride-sharing, accommodation and freelance labor platforms, goes hand in hand with new socioeconomic challenges. One major issue remains the existence of bias and discrimination against certain social groups. We study this problem using a two-sided large market model with employers and workers mediated by a platform. Employers who seek to hire workers face uncertainty about a candidate worker's skill level. Therefore, they base their hiring decision on learning from past reviews about an individual worker as well as on their (possibly misspecified) prior beliefs about the ability level of the social group the worker belongs to. Drawing upon the social learning literature with bounded rationality and limited information, uncertainty combined with social bias leads to unequal hiring opportunities between workers of different social groups. Although the effect of social bias decreases as the number of reviews increases (consistent with empirical findings), minority workers still receive lower expected payoffs. Finally, we consider a simple directed matching policy (DM), which combines learning and matching to make better matching decisions for minority workers. Under this policy, there exists a steady-state equilibrium, in which DM reduces the discrimination gap.

We study the assignment problem of objects to agents with heterogeneous preferences under distributional constraints. Each agent is associated with a publicly known type and has a private ordinal ranking over objects. We are interested in assigning as many agents as possible. Our first contribution is a generalization of the well-known and widely used serial dictatorship. Our mechanism maintains several desirable properties of serial dictatorship, including strategyproofness, Pareto efficiency, and computational tractability while satisfying the distributional constraints with a small error. We also propose a generalization of the probabilistic serial algorithm, which finds an ordinally efficient and envy-free assignment, and also satisfies the distributional constraints with a small error. We show, however, that no ordinally efficient and envy-free mechanism is also weakly strategyproof. Both of our algorithms assign at least the same number of students as the optimum fractional assignment.

In the min-cost bipartite perfect matching with delays (MBPMD) problem, requests arrive online at points of a finite metric space. Each request is either positive or negative and has to be matched to a request of opposite polarity. As opposed to traditional online matching problems, the algorithm does not have to serve requests as they arrive, and may choose to match them later at a cost. Our objective is to minimize the sum of the distances between matched pairs of requests (the connection cost) and the sum of the waiting times of the requests (the delay cost). This objective exhibits a natural tradeoff between minimizing the distances and the cost of waiting for better matches. This tradeoff appears in many real-life scenarios, notably, ride-sharing platforms. MBPMD is related to its non-bipartite variant, min-cost perfect matching with delays (MPMD), in which each request can be matched to any other request. MPMD was introduced by Emek et al. (STOC'16), who showed an O(log^2(n)+log(Delta))-competitive randomized algorithm on n-point metric spaces with aspect ratio Delta. Our contribution is threefold. First, we present a new lower bound construction for MPMD and MBPMD. We get a lower bound of Omega(sqrt(log(n)/log(log(n)))) on the competitive ratio of any randomized algorithm for MBPMD. For MPMD, we improve the lower bound from Omega(sqrt(log(n))) (shown by Azar et al., SODA'17) to Omega(log(n)/log(log(n))), thus, almost matching their upper bound of O(log(n)). Second, we adapt the algorithm of Emek et al. to the bipartite case, and provide a simplified analysis that improves the competitive ratio to O(log(n)). The key ingredient of the algorithm is an O(h)-competitive randomized algorithm for MBPMD on weighted trees of height h. Third, we provide an O(h)-competitive deterministic algorithm for MBPMD on weighted trees of height h. This algorithm is obtained by adapting the algorithm for MPMD by Azar et al. to the apparently more complicated bipartite setting.

We study how much communication is needed to find a stable matching in a two-sided matching market with private preferences. Segal (2007) and Gonczarowski et al.~(2015) showed that in the worst case, any protocol that computes a stable matching requires the communication cost per agent to scale linearly in the total number of agents. In real-world markets with many agents, this communication requirement is implausibly high. This casts doubts on whether stable matching can arise in large markets. We study markets with realistic structure on the preferences and information of agents, and show that in "typical" markets, a stable matching can be found with much less communication effort. In our model, the preferences of workers are unrestricted, and the preferences of firms follow an additively separable latent utility model. Our efficient communication protocol modifies workers-proposing DA, by having firms signal workers they especially like, while also broadcasting qualification requirements to discourage other workers who have no realistic chances from applying. In the special case of tiered random markets, the protocol can be modified to run in two-rounds and involve only private messages. Our protocols have good incentive properties and give insights on how to mediate large matching markets to reduce congestion.

We study dynamic matching in an infinite-horizon stochastic networked market, in which some agents are a priori more difficult to match than others. Agents have compatibility-based preferences and can match either bilaterally, or indirectly through chains. We study the effect matching technologies and matching policies have on efficiency in markets with different compositions of hard and easy-to-match agents. First, we analyze myopic matching policies and identify a strong connection between market thickness and the efficiency driven by the matching technology. We show that when "hard-to-match" agents join the market more frequently than "easy-to-match" ones, moving from bilateral matchings to chains significantly increases efficiency. Otherwise, the difference between matching bilaterally or through a chain is negligible. Second, we show that the lack of thickness cannot be compensated by non-myopic matching policies implying that the only way to thicken the market fruitfully is by attracting more agents.

How should one sell an item to a buyer whose value for the item will only be realized next week? E.g. consider selling a flight to some executive who may or may not have a meeting with a client next week. Suppose that both the seller and the buyer only know a distribution, F, from which the buyer's value, v, for the item will be drawn. One way the seller could go about this sale is to make a take-it-or-leave-it offer today. The offer reads "pay the expected value today to get the item next week". A risk-neutral buyer would find this offer attractive, hence the seller would extract the full surplus.

School districts that adopt the Deferred Acceptance (DA) mechanism to assign students to schools face the tradeoff between fairness and efficiency when selecting how to exogenously break ties among equivalent students. We analyze a model with random generated preferences for students and compare two tie-breaking rules: a single lottery (STB) and DA with a separate lottery for each school (MTB). We consider three different notions for this comparison: stochastic dominance of rank distributions, variance of students' ranks, and number of Pareto improving pairs (pairs of students whom would be better off by swapping their positions).

School choice districts that implement stable matchings face various design issues that impact students' assignments to schools. We study properties of the rank distribution of students with random preferences, when schools use different tiebreaking rules to rank equivalent students. We find that under a multiple tiebreaking rule a vanishing fraction of students match to one of their top choices, in contrast to a single tiebreaking rule under which a constant fraction of students are assigned to one of their top choices. We find that when students can submit only a relatively short preference list, the multiple tiebreaking rule allows a constant fraction of students to match to one of their top choices, with only a "small" fraction of students remaining unmatched.

We consider the problem of efficient operation of a barter exchange platform for indivisible goods. We introduce a dynamic model of barter exchange where in each period one agent arrives with a single item she wants to exchange for a different item. We study a homogeneous and stochastic environment: an agent is interested in the item possessed by another agent with probability p, independently for all pairs of agents. We consider two settings with respect to the types of allowed exchanges: a) Only two-way cycles, in which two agents swap their items, b) Two or three-way cycles. The goal of the platform is to minimize the average waiting time of an agent. Somewhat surprisingly, we find that in each of these settings, a policy that conducts exchanges in a greedy fashion is near optimal, among a large class of policies that includes batching policies. Further, we find that for small p, allowing three-cycles can greatly improve the waiting time over the two-cycles only setting. Specifically, we find that a greedy policy achieves an average waiting time of Θ(1/p2) in setting a), and Θ(1/p3/2) in setting b). Thus, a platform can achieve the smallest waiting times by using a greedy policy, and by facilitating three cycles, if possible. Our findings are consistent with empirical and computational observations which compare batching policies in the context of kidney exchange programs.

We study the optimal allocation of heterogeneous services without using monetary transfers. Agents have private, multi-dimensional utilities over the services, and a social planner has arbitrary priors on the utilities, which may depend on the agents' observable characteristics. The social planner's goal is to maximize a public objective, which may be complex, taking into account diverse considerations such as social welfare, equity, and system costs. Potential applications include the allocation of seats to public schools, spaces in college dorms or courses, and spots in subsidized housing.

We describe a model for competitive online scheduling algorithms. Two servers, each with a single observable queue, compete for customers. Upon arrival, each customer strategically chooses the queue with minimal expected wait time. Each scheduler wishes to maximize its number of customers, and can strategically select which scheduling algorithm, such as First-Come-First-Served (FCFS), to use for its queue. This induces a game played by the servers and the customers. We consider a non-Bayesian setting, where servers and customers play to maximize worst-case payoffs. We show that there is a unique subgame perfect safety-level equilibrium and we describe the associated scheduling algorithm (which is not FCFS). The uniqueness result holds for both randomized and deterministic algorithms, with a different equilibrium algorithm in each case. When the goal of the servers is to minimize competitive ratio, we prove that it is an equilibrium for each server to apply FCFS: each server obtains the optimal competitive ratio of 2.

The need for kidney exchange arises when a healthy person wishes to donate a kidney but is incompatible with her intended recipient. Two main factors determine compatibility of a donor with a patient: blood-type compatibility and tissue-type compatibility. Two or more incompatible pairs can form a cyclic exchange so that each patient can receive a kidney from a compatible donor. In addition, an exchange can be initiated by a non-directed donor (an altruistic donor who does not designate a particular intended patient), and in this case, a chain of exchanges need not form a closed cycle.

We analyze large random matching markets with unequal numbers of men and women. Agents have complete preference lists that are uniformly random and independent, and we consider stable matchings under the realized preferences. We find that being on the short side of the market confers a large advantage.

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for large random markets the algorithm will find a stable matching with high probability. In our model we allow the number of couples to grow at a near-linear rate. Furthermore, truth-telling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists.

As multi-hospital kidney exchange clearinghouses have grown, the set of players has grown from patients and surgeons to include hospitals. Hospitals have the option of enrolling only their hard-to-match patient-donor pairs, while conducting easily arranged exchanges internally. This behavior has already started to be observed.

Previous work on machine scheduling has considered the case of agents who control the scheduled jobs and attempt to minimize their own completion time. We argue that in cloud and grid computing settings, different machines cannot be considered to be fully cooperative as they may belong to competing economic entities, and that agents can easily move their jobs between competing providers. We therefore consider a setting in which the machines are also controlled by selfish agents, and attempt to maximize their own gains by strategically selecting their scheduling policy. We analyze the equilibria that arise due to competition in this 2-sided setting. In particular, not only do we require that the jobs will be in equilibrium with one another, but also that the schedulers' policies will be in equilibrium. We also consider different mixtures of classic deterministic scheduling policies and random scheduling policies.

Consider a matching problem on a graph where disjoint sets of vertices are privately owned by self-interested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to maximize the number of matches despite self-interest, with agents that each want to maximize the number of their own vertices that match. Each agent can choose to hide some of its vertices, and then privately match the hidden vertices with any of its own vertices that go unmatched by the mechanism. A prominent application of this model is to kidney exchange, where agents correspond to hospitals and vertices to donor-patient pairs. Here hospitals may game an exchange by holding back pairs and harm social welfare.

We consider the problem of designing truthful mechanisms to minimize the makespan on m unrelated machines. In their seminal paper, Nisan and Ronen [14] showed a lower bound of 2, and an upper bound of m, thus leaving a large gap. They conjectured that their upper bound is tight, but were unable to prove it. Despite many attempts that yield positive results for several special cases, the conjecture is far from being solved: the lower bound was only recently slightly increased to 2.61 [5,10], while the best upper bound remained unchanged.

Correlated equilibrium generalizes Nash equilibrium to allow correlation devices. Correlated equilibrium captures the idea that in many systems there exists a trusted administrator who can recommend behavior to a set of agents, but can not enforce such behavior. This makes this solution concept most appropriate to the study of multi-agent systems in AI. Aumann showed an example of a game, and of a correlated equilibrium in this game in which the agents' welfare (expected sum of players' utilities) is greater than their welfare in all mixed-strategy equilibria. Following the idea initiated by the price of anarchy literature this suggests the study of two major measures for the value of correlation in a game with nonnegative payoffs: 1. The ratio between the maximal welfare obtained in a correlated equilibrium to the maximal welfare obtained in a mixed-strategy equilibrium. We refer to this ratio as the mediation value. 2. The ratio between the maximal welfare to the maximal welfare obtained in a correlated equilibrium. We refer to this ratio as the enforcement value. In this work we initiate the study of the mediation and enforcement values, providing several general results on the value of correlation as captured by these concepts. We also present a set of results for the more specialized case of congestion games, a class of games that received a lot of attention in the recent literature.

A mediator is a reliable entity, which can play on behalf of agents in a given game. A mediator however can not enforce the use of its services, and each agent is free to participate in the game directly. In this paper we introduce a study of mediators for games with incomplete information, and apply it to the context of position auctions, a central topic in electronic commerce. VCG position auctions, which are currently not used in practice, possess somenice theoretical properties, such as the optimization of social surplus and having dominant strategies. These properties may not be satisfied by current position auctions and their variants. We therefore concentrate on the search for mediators that will allow to transform current position auctions into VCG position auctions. We require that accepting the mediator services, and reporting honestly to the mediator, will form an ex post equilibrium, which satisfiesthe following rationality condition: an agent's payoff can not be negative regardless of the actions taken by the agents who did not choose the mediator's services, or by the agents who report false types to the mediator. We prove the existence of such desired mediators for the next-price (Google-like) position auctions, as well as for a richer class of position auctions, including k-price position auctions, k>1. For k=1, the self-price position auction, we show that the existence of such mediator depends on the tie breaking rule used in the auction.