Onur Kesten

On two competing mechanisms for priority-based allocation problems

We consider the priority-based allocation problem: there is a set of indivisible objects with multiple supplies (e.g., schools with seats) and a set of agents (e.g., students) with priorities over objects (e.g., proximity of residence area). We study two well-known and competing mechanisms. The agentoptimal stable mechanism (AOSM) allots objects via the deferred acceptance algorithm. The top trading cycles mechanism (TTCM) allots objects via Gale’s top trading cycles algorithm. We show that the two mechanisms are equivalent, or TTCM is fair (i.e., respects agents’ priorities), or resource monotonic ,o rpopulation monotonic, if and only if the priority structure is acyclic. Furthermore, if AOSM fails to be efficient (consistent) for a problem, TTCM also fails to be fair (consistent) for it. However, the converse is not necessarily true.

A Theory of School-Choice Lotteries

A new centralized mechanism was introduced in New York City and Boston to assign students to public schools in district school-choice programs. This mechanism was advocated for its superior fairness property, besides others, over the mechanisms it replaced. In this paper, we introduce a new framework for investigating school-choice matching problems and two ex-ante notions of fairness in lottery design, strong ex-ante stability and ex-ante stability. This frame- work generalizes known one-to-many two-sided and one-sided matching models. We first show that the new NYC/Boston mechanism fails to satisfy these fairness properties. We then propose two new mechanisms, the fractional deferred-acceptance mechanism, which is ordinally Pareto dominant within the class of strongly ex-ante stable mechanisms, and the fractional deferred- acceptance and trading mechanism, which satisfies equal treatment of equals and constrained ordinal Pareto efficiency within the class of ex-ante stable mechanisms.

Two axiomatic approaches to the probabilistic serial mechanism

This paper studies the problem of assigning a set of indivisible objects to a set of agents when monetary transfers are not allowed and agents reveal only ordinal preferences, but random assignments are possible. We offer two characterizations of the probabilistic serial mechanism, which assigns lotteries over objects. We show that it is the only mechanism satisfying non-wastefulness and ordinal fairness and the only mechanism satisfying sd-efficiency, sd-envy-freeness, and weak invariance or weak truncation robustness (where “sd” stands for first-order stochastic dominance).

Why do popular mechanisms lack efficiency in random environments

We consider the problem of randomly assigning n indivisible objects to n agents. Recent research introduced a promising mechanism, the probabilistic serial that has superior efficiency properties than the most common real-life mechanism random priority. On the other hand, mechanisms based on Gales celebrated top trading cycles method have long dominated the indivisible goods literature (with the exception of the present context) thanks to their outstanding efficiency features. We present an equivalence result between the three kinds of mechanisms, that may help better understand why efficiency differences among popular mechanisms might arise in random environments. This result also suggests that the probabilistic serial and the random priority mechanisms can be viewed as two top trading cycles based mechanisms that essentially differ in the initial conditions of the market before trading starts.

Coalitional strategy-proofness and resource monotonicity for house allocation problems

We consider the problem of allocating houses to agents when monetary compensations are not allowed. We present a simple and independent proof of a result due to Ehlers and Klaus (Int J Game Theory 32:545–560, 2004) that characterizes the class of rules satisfying efficiency, strategy-proofness, resource monotonicity and nonbossiness.

Chinese College Admissions and School Choice Reforms: A Theoretical Analysis

Each year approximately 10 million high school seniors in China compete for 6 million seats through a centralized college admissions system. Within the last decade, many provinces have transitioned from a “sequential” to a “parallel” mechanism to make their admissions decisions. In this study, we characterize a parametric family of application-rejection assignment mechanisms, including the sequential, deferred acceptance, and parallel mechanisms in a nested framework. We show that all of the provinces that have abandoned the sequential mechanism have moved toward less manipulable and more stable mechanisms. We also show that existing empirical evidence is consistent with our theoretical predictions.

Matching Markets with Mixed Ownership: The Case for A Real-life Assignment Mechanism

We consider a common indivisible good allocation problem in which agents have both social and private endowments. Popular applications include student assignment to on-campus housing, kidney exchange, and particular school choice problems. In a series of experiments Chen and Sonmez (American Economic Review 92: 1669-1686, 2002) have shown that a popular mechanism from recent theory, the Top Trading Cycles (TTC) mechanism, induces a significantly higher participation rate by agents with private endowments and leads to significantly more efficient outcomes than the most commonly used real-life mechanism, the Random Serial Dictatorship with Squatting Rights.We first show that a particular mechanism, the so-called New House 4 (NH4) mechanism, which has been in use at MIT since the 1980s, is in fact outcome-equivalent to a natural adaptation of the well-known Gale-Shapley mechanism of two-sided matching theory. This implies that the NH4 mechanism is the most efficient mechanism within the class of fair and individually rational mechanisms, and that it is essentially the only incentive compatible mechanism satisfying the two properties. We then experimentally compare NH4 and TTC. We find that under NH4, the participation rate is significantly higher than under TTC. We also propose a new efficiency test based on ordinal preference information and show that NH4 also outperforms TTC in terms of efficiency.

From Boston to Shanghai to Deferred Acceptance: Theory and Experiments on A Family of School Choice Mechanisms

School choice has been one of the most important and widely-debated education policies in the past two decades, with game theory playing a major role in the adoption of school choice mechanisms. Similarly, college admissions in China have gone through many local experimentations, with a rich variety of mechanisms used in various provinces.

More on the uniform rule: Characterizations without Pareto optimality

Abstract We consider the problem of allocating an infinitely divisible commodity to agents with single-peaked preferences. We propose various characterizations of the allocation rule known as the uniform rule without imposing Pareto optimality . We also present new computational characterizations of the rule.

An equilibrium analysis of the probabilistic serial mechanism

Two prominent mechanisms in the random assignment problem are the random priority (RP) and the probabilistic serial (PS). When agents are truthful, the outcomes obtained under PS have superior efficiency and fairness properties, but unlike RP, PS is vulnerable to strategizing. We study incentives of agents under PS. We find that when agents strategize, in equilibrium an outcome may be obtained under PS which is not efficient or fair and which is worse in some respects than the RP outcome. The results of our equilibrium analysis of PS call for caution when implementing it in “small” assignment problems.