Yash Kanoria

Unbalanced Random Matching Markets: The Stark Effect of Competition

We study competition in matching markets with random heterogeneous preferences and an unequal number of agents on either side. First, we show that even the slightest imbalance yields an essentially unique stable matching. Second, we give a tight description of stable outcomes, showing that matching markets are extremely competitive. Each agent on the short side of the market is matched with one of his top choices, and each agent on the long side either is unmatched or does almost no better than being matched with a random partner. Our results suggest that any matching market is likely to have a small core, explaining why small cores are empirically ubiquitous.

Efficient Dynamic Barter Exchange

We study dynamic matching policies in a stochastic marketplace for barter, with agents arriving over time. Each agent is endowed with an item and is interested in an item possessed by another agent homogeneously with probability p, independently for all pairs of agents. Three settings are considered with respect to the types of allowed exchanges: (a) only two-way cycles, in which two agents swap items, (b) two-way or three-way cycles, (c) (unbounded) chains initiated by an agent who provides an item but expects nothing in return. We consider the average waiting time as a measure of efficiency and find that the cost outweighs the benefit from waiting to thicken the market. In particular, in each of the above settings, a policy that conducts exchanges in a greedy fashion is near optimal. Further, for small p, we find that allowing three-way cycles greatly reduces the waiting time over just two-way cycles, and conducting exchanges through a chain further reduces the waiting time significantly. Thus, a centra...

Matching while Learning

We consider the problem faced by a service platform that needs to match supply with demand but also to learn attributes of new arrivals in order to match them better in the future. We introduce a benchmark model with heterogeneous workers and jobs that arrive over time. Job types are known to the platform, but worker types are unknown and must be learned by observing match outcomes. Workers depart after performing a certain number of jobs. The payoff from a match depends on the pair of types and the goal is to maximize the steady-state rate of accumulation of payoff. Our main contribution is a complete characterization of the structure of the optimal policy in the limit that each worker performs many jobs. The platform faces a trade-off for each worker between myopically maximizing payoffs (exploitation) and learning the type of the worker (exploration). This creates a multitude of multi-armed bandit problems, one for each worker, coupled together by the constraint on the availability of jobs of different types (capacity constraints). We find that the platform should estimate a shadow price for each job type, and use the payoffs adjusted by these prices, first, to determine its learning goals and then, for each worker, (i) to balance learning with payoffs during the exploration phase, and (ii) to myopically match after it has achieved its learning goals during the exploitation phase.

State Dependent Control of Closed Queueing Networks

We study the design of state dependent control for a closed queueing network model, inspired by shared transportation systems such as ridesharing. In particular, we focus on the design of assignment policies, wherein the platform can choose which supply unit to dispatch to meet an incoming customer request. The supply unit subsequently becomes available at the destination after dropping the customer. We consider the proportion of dropped demand in steady state as the performance measure. We propose a family of simple and explicit state dependent policies called Scaled MaxWeight (SMW) policies and prove that under the complete resource pooling (CRP) condition (analogous to a strict version of Halls condition for bipartite matchings), any SMW policy induces an exponential decay of demand-dropping probability as the number of supply units scales to infinity. Furthermore, we show that there is an SMW policy that achieves the optimal exponent among all assignment policies, and analytically specify this policy in terms of the matrix of customer-request arrival rates. The optimal SMW policy protects structurally under-supplied locations.

Convergence of the Core in Assignment Markets

We consider a two-sided assignment market with agent types and a stochastic structure, similar to models used in empirical studies. We characterize the size of the core in such markets. Each agent has a randomly drawn productivity with respect to each type of agent on the other side. The value generated from a match between a pair of agents is the sum of the two productivity terms, each of which depends only on the type (but not the identity) of one of the agents, and a third deterministic term driven by the pair of types. We prove, under reasonable assumptions, that when the number of agent types is kept fixed, the relative size of the core vanishes rapidly as the number of agents grows. Numerical experiments confirm that the core is typically small. Our results provide justification for the typical assumption of a unique core outcome in such markets, which is close to a limit point. Further, our results suggest that, given the market composition, wages are almost uniquely determined in equilibrium. The ...

Facilitating the Search for Partners on Matching Platforms: Restricting Agent Actions

Two-sided matching platforms, such as those for labor, accommodation, dating, and taxi hailing, can control and optimize over many aspects of the search for partners. To understand how the search for partners should be designed, we consider a dynamic model of search by strategic agents with costly discovery of pair-specific match value. We find that in many settings, the platform can mitigate wasteful competition in partner search via restricting what agents can see/do. For medium-sized screening costs (relative to idiosyncratic variation in utilities), the platform should prevent one side of the market from exercising choice (similar to Instant Book on Airbnb), whereas for large screening costs, the platform should centrally determine matches (similar to taxi hailing marketplaces). Surprisingly, simple restrictions can improve social welfare even when screening costs are small, and agents on each side are ex-ante homogeneous. In asymmetric markets where agents on one side have a tendency to be more selective (due to smaller screening costs or greater market power), the platform should force the more selective side of the market to reach out first, by explicitly disallowing the less selective side from doing so. This allows the agents on the less selective side to exercise more choice in equilibrium.When agents are vertically differentiated, forcing one side of the market to propose results in a significant increase in welfare even in the limit of vanishing screening costs. Furthermore, a Pareto improvement in welfare is possible in this limit: the weakest agents can be helped without hurting other agents. In addition, in this setting the platform can further boost welfare by hiding quality information.

Clearing Matching Markets Efficiently: Informative Signals and Match Recommendations

We study how to reduce congestion in two-sided matching markets with private preferences. We measure congestion by the number of bits of information that agents must (i) learn about their own preferences, and (ii) communicate with others before obtaining their final match. Previous results by Segal (2007) and Gonczarowski et al. (2015) suggest that a high level of congestion is inevitable under arbitrary preferences before the market can clear with a stable matching. We show that when the unobservable component of agent preferences satisfies certain natural assumptions, it is possible to recommend potential matches and encourage informative signals such that the market reaches a stable matching with a low level of congestion. This is desirable because the communication overhead is minimized while agents have negligible incentives to leave the marketplace or to look beyond the set of recommended partners. The main idea is to only recommend partners with whom the agent has a non-negligible chance of both liking and being liked by. The recommendations are based both on the observable component of preferences, and on the signals sent by agents on the other side that indicate interest.

Facilitating the Search for Partners on Matching Platforms

Two-sided matching platforms can control and optimize over many aspects of the search for partners. To understand how matching platforms should be designed, we introduce a dynamic two-sided search model with strategic agents who must bear a cost to discover their value for each potential partner, and can do so non-simultaneously. We characterize equilibria and find that, in many settings, the platform can mitigate wasted search effort by imposing suitable restrictions on agents. In unbalanced markets, the platform should force the short side of the market to initiate contact with potential partners, by disallowing the long side from doing so. This allows the agents on the long side to exercise more choice in equilibrium. When agents are vertically differentiated, the platform can significantly improve welfare even in the limit of vanishing screening costs by forcing the shorter side of the market to propose and by hiding information about the quality of potential partners. Furthermore, a Pareto improvement in welfare is possible in this limit.

Dynamic Matching in School Choice: Efficient Seat Reassignment after Late Cancellations

In the school choice market, where scarce public school seats are assigned to students, a key operational issue is how to reassign seats that are vacated after an initial round of centralized assignment. Practical solutions to the reassignment problem must be simple to implement, truthful and efficient while also alleviating costly student movement between schools. We propose and axiomatically justify a class of reassignment mechanisms, the Permuted Lottery Deferred Acceptance (PLDA) mechanisms. Our mechanisms generalize the commonly used Deferred Acceptance (DA) school choice mechanism to a two-round setting and retain its desirable incentive and efficiency properties. School choice systems typically run DA with a lottery number assigned to each student to break ties in school priorities. We show that under natural conditions on demand, the second round tie-breaking lottery can be correlated arbitrarily with that of the first round without affecting allocative welfare, and reversing the lottery order between rounds minimizes reassignment among all PLDA mechanisms. Empirical investigations based on data from NYC high school admissions support our theoretical findings.