Published work

"School Choice with Preference Rank Classes" with Nickesha Ayoade, Games and Economic Behavior, 2023, 137: 317-341.

We introduce and study a large family of rules for many-to-one matching problems, the Preference Rank Partitioned (PRP) rules. PRP rules are student-proposing Deferred Acceptance rules, where the schools select among applicants in each round taking into account both the students' preferences and the schools' priorities. In a PRP rule each school first seeks to select students based on priority rank classes, and subsequently based on preference rank classes. PRP rules include many well-known matching rules, such as the classic Deferred Acceptance rule, the Boston rule, the Chinese Application-Rejection rules of Chen and Kesten (2017), and the French Priority rules of Bonkoungou (2020), in addition to matching rules that have not been studied yet. We analyze the stability, efficiency and incentive properties of PRP rules in this unified framework.

"Preference Aggregation for Couples" with Rouzbeh Ghouchani, Social Choice and Welfare, 2022, 59: 889–923.

We study the aggregation of a couple’s preferences over their respective jobs when the couple enters a centralized labor market jointly, such as the market for hospital residencies. In such markets couples usually need to submit a joint preference ordering over pairs of jobs and thus we are interested in preference aggregation rules which start with two individual preference orderings over single jobs and produce a preference ordering of pairs of jobs. We first study the Lexicographic and the Rank-Based Leximin aggregation rules, as well as a large class of preference aggregation rules which contains these two rules. Then we propose a smaller family of parametric aggregation rules, the k-Lexi-Pairing rules, which call for a systematic way of compromising between the two partners. The parameter k indicates the degree to which one partner is prioritized, with the most equitable Rank-Based Leximin rule at one extreme and the least equitable Lexicographic rule at the other extreme. Since couples care about geographic proximity, a parametric family of preference aggregation rules which build on the k-Lexi-Pairing rules and express the couple’s preference for togetherness is also identified. We provide axiomatic characterizations of the proposed preference aggregation rules.

"Serial Rules in a Multi-Unit Shapley-Scarf Market" with Péter Biró and Flip Klijn, Games and Economic Behavior, 2022, 136: 428-453.

We study generalized Shapley-Scarf exchange markets where each agent is endowed with multiple units of an indivisible and agent-specific good and monetary compensations are not possible. An outcome is given by a circulation which consists of a balanced exchange of goods. We focus on circulation rules that only require as input ordinal preference rankings of individual goods, and agents are assumed to have responsive preferences over bundles of goods. We study the properties of serial dictatorship rules which allow agents to choose either a single good or an entire bundle sequentially, according to a fixed ordering of the agents. We also introduce and explore extensions of these serial dictatorship rules that ensure individual rationality. The paper analyzes the normative and incentive properties of these four families of serial dictatorships and also shows that the individually rational extensions can be implemented with efficient graph algorithms.

"Exchange in a General Market With Indivisible Goods" Journal of Economic Theory, 2007, 132: 208-235.

We examine properties of individual preferences (as opposed to preference profiles) for which there exists a stable hedonic coalition structure, and prove that an anonymous and rich preference domain guarantees the existence of a stable coalition structure if and only if it satisfies the Inclusion Property. The Inclusion Property requires that if a player ranks two non-singleton coalitions above any superset of their union then the intersection of these two coalitions should be ranked above at least one of these two coalitions.We show how to restrict trades in exchange markets with heterogeneous indivisible goods so that the resulting restricted exchange markets, the fixed deal exchange markets, have a unique core allocation. Our results on fixed deal exchange markets generalize classical results on the Shapley-Scarf housing market, in which each agent owns one good only. Furthermore, we define the class of fixed deal exchange rules for general exchange markets, and prove that these are the only exchange rules that satisfy strategyproofness, individual rationality, and a weak form of efficiency.

"Unique Stability in Simple Coalition Formation Games" Games and Economic Behavior, 2004, 48: 337-354.

We investigate the uniqueness of stable coalition structures in a simple coalition formation model, for which specific coalition formation games, such as the marriage and roommate models, are special cases that are obtained by restricting the coalitions that may form. The main result is a characterization of collections of permissible coalitions which ensure that there is a unique stable coalition structure in the corresponding coalition formation model. In particular, we show that only single-lapping coalition formation models have a unique stable coalition structure for each preference profile, where single-lapping means that two coalitions cannot have more than one member in common, and coalitions do not form cycles. We also give another characterization using a graph representation, explore the implications of our results for matching models, and examine the existence of strategyproof coalition formation rules.

"Strategyproof Exchange of Indivisible Goods" Journal of Mathematical Economics, 2003, 39: 931-959.

The exchange of heterogeneous indivisible goods is considered among agents with responsive preferences, who may be endowed with several goods. We introduce the segmented trading cycle rules which allow the agents to trade goods, one-for-one, subject to market segmentation. In particular, the market is divided into segments such that each agent in each segment may trade at most one good. The segmented trading cycle rules are characterized by four axioms: strategyproofness, nonbossiness, trade sovereignty, and strong individual rationality.

"Groves Sealed Bid Auctions of Heterogeneous Objects With Fair Prices" Social Choice and Welfare, 2003, 20: 371-385.

We study the allocation of heterogeneous indivisible objects to agents whose valuations of the objects depend on what other objects they are obtained with. We apply the envyfree criterion to Groves sealed bid auctions, which are value maximizing and dominant strategy incentive compatible for this multi-object allocation problem. First we show that if valuations are unrestricted then there is no Groves auction which ensures that the allocation is always envyfree. We obtain a positive result, however, if the valuations of the objects are superadditive, and give a complete characterization of Groves prices that guarantee envyfreeness for superadditive valuations.

"Strategy-Prooofness and Population-Monotonicity in House Allocation Problems" with Lars Ehlers and Bettina Klaus, Journal of Mathematical Economics, 2002, 38: 329-339.

We study a simple model of assigning indivisible objects to agents, such as dorm rooms to students, or offices to professors, where each agent receives at most one object and monetary compensations are not possible. For these problems population-monotonicity, which requires that agents are affected by population changes in the same way, is a compelling property because tentative assignments are made in many typical situations, which may have to be revised later to take into account the changing population. We completely describe the allocation rules satisfying population-monotonicity, strategy-proofness, and efficiency. The characterized rules assign the objects by an iterative procedure in which at each step no more than two agents "trade" objects from their hierarchically specified "endowments."

"Strategyproof Single Unit Award Rules" Social Choice and Welfare, 2001, 18: 785-798.

The problem of allocating a single indivisible unit to one of several agents is considered, where monetary compensations are not allowed, and the unit is not necessarily desirable to each agent. In addition to strategyproofness, three properties of social choice functions are considered: Pareto-optimality, nondictatorship, and nonbossiness. It is shown that these three additional criteria cannot be satisfied simultaneously. However, any two of the additional criteria can be satisfied. We give characterizations of the classes of strategyproof social choice functions satisfying these three pairs of properties.

"Strategyproof and Nonbossy Multiple Assignments" Journal of Public Economic Theory, 2001, 3: 257-271.

We consider the allocation of heterogeneous indivisible objects without using monetary transfers. Each agent may be assigned more than one object. We show that an allocation rule is strategyproof, nonbossy, and satisfies citizen sovereignty if and only if it is a sequential dictatorship. In a sequential dictatorship agents are assigned their favorite objects that are still available, according to a sequentially endogenously determined hierarchy of the agents. We also establish that replacing nonbossiness by a stronger criterion restricts the characterized class of allocation rules to serial dictatorships, in which the hierarchy of the agents is fixed a priori.

"Strategyproof Assignment by Hierarchical Exchange" Econometrica, 2000, 68: 1403-1433.

We give a characterization of the set of group-strategyproof, Pareto-optimal, and reallocation-proof allocation rules for the assignment problem, where individuals are assigned at most one indivisible object, without any medium of exchange. Although there are no property rights in the model, the rules satisfying the above criteria imitate a trading procedure with individual endowments, in which individuals exchange objects from their hierarchically determined endowment sets in an iterative manner. In particular, these assignment rules generalize Gale's top trading cycle procedure, the classical rule for the model in which each individual owns an indivisible good.

"Strategyproof Multiple Assignment Using Quotas" Review of Economic Design, 2000, 5: 91-105.

The allocation of heterogeneous and indivisible objects is considered where there is no medium of exchange. We characterize the set of strategyproof, nonbossy, Pareto-optimal, and neutral social choice functions when preferences are monotonic and quantity-monotonic. The characterized sets of social choice functions are sequential; agents are assigned their favorite objects among the objects not given to others before them, subject to a quota.