Working Papers

Strategy-proof Pareto-improvement
(with Vikram Manjunath)
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We consider a general model for the allocation of discrete resources, or objects. It encompasses most allocation problems where each agent consumes at most one object, including object allocation with or without priorities, multi-item auctions, and matching with contracts. Our main result is that each individually rational and weakly non-wasteful allocation rule is weakly Pareto-dominated by at most one strategy-proof rule. So if a mechanism designer's choice of a strategy-proof rule is constrained to Pareto-dominate an individually rational and weakly non-wasteful status quo or normative benchmark, then there is a unique solution to his problem, if there is one at all. We also show that individual rationality and weak non-wastefulness impose a particular structure on the set of allocations: if two allocations satisfy these properties and are Pareto-comparable, then the same agents are assigned objects by either. To demonstrate the strength and applicability of our results, we present some novel implications for the above mentioned special cases of the model.
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Current Version: March 2017
WARP and Combinatorial Choice
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I show that in combinatorial choice environments the Weak Axiom of Revealed Preference (WARP) is equivalent to the Irrelevance of Rejected Items (IRI), a choice consistency condition whose importance for familiar results in matching theory is demonstrated by Aygun and Sonmez (2013). Moreover, WARP is necessary and sufficient for there to exist a complete and reflexive rationalization of a single-valued combinatorial choice function. I also study the connection between IRI and other important choice conditions in the classical choice framework, including independence of irrelevant alternatives, the Chernoff property, and Plott path independence. Each of these conditions is equivalent to IRI and WARP in single-valued combinatorial choice settings. I extend the definition of IRI for multi-valued combinatorial choice and show that the equivalence with WARP continues to hold. These results rely upon a faithful representation of a combinatorial model as a classical choice model.
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Current Version: May 2016
R&R at Journal of Economic Theory
When is manipulation all about the ones and twos?
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A mechanism is pairwise strategy-proof if groups of size one and two never have an incentive to manipulate. When agents have strict preferences over their own outcomes, I show that pairwise strategy-proofness even eliminates incentives for any group of agents to manipulate, therefore implying group strategy-proofness. It is also equivalent to Maskin monotonicity. I obtain the equivalence results assuming preference domains satisfy a richness condition. Decomposing richness into two parts, I explore what brings about the equivalence. The results apply to school choice and matching with contracts, indivisible object allocation, and economies with private or public goods with single-peaked preferences.
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Current Version: May 2017
Stability and Matching with Aggregate Actors
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Many real-life problems involve the matching of talented individuals to institutions such as firms, hospitals, or schools, where these institutions are simply treated as individual agents. In this paper, I study many-to-one matching with contracts that incorporates a theory of choice of institutions, which are aggregate actors, composed of divisions that are enjoined by an institutional governance structure (or mechanism). Conflicts over contracts between divisions of an institution are resolved by the institutional governance structure, whereas conflicts between divisions across institutions are resolved, as is typically the case, by talents' preferences. Noting that hierarchies are a common organizational structure in institutions, I offer an explanation of this fact as an application of the model, where stability is a prerequisite for the persistence of organizational structures. I show that stable market outcomes exist whenever institutional governance is hierarchical and divisions consider contracts to be bilaterally substitutable. In contrast, when governance in institutions is non-hierarchical, stable outcomes may not exist. Since market stability does not provide an impetus for reorganization, the persistence of markets with hierarchical institutions can thus be rationalized. Hierarchies in institutions also have the attractive incentive property that in a take-it-or-leave-it bargaining game with talents making offers to institutions, the choice problem for divisions is straightforward and realized market outcomes are pairwise stable, and stable when divisions have substitutable preferences.
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Pairwise Stability and Complementarity in Many-to-One Matching
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I provide new sufficient conditions for the existence of pairwise stable matchings in the many-to-many matching with contracts model. These conditions generalize the substitutes condition by allowing for symmetric complements. However, the existence of a lattice structure or even a side-optimal matching is not necessary. A separate, weaker condition on the domain of choice is necessary for the guaranteed existence of a pairwise stable matching.
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New version coming soon
The Impact of a DROP Program on the Age of Retirement and Employer Pension Costs
(with Norma Coe and Tony Webb)
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We investigate the impact of a Deferred Retirement Option Plan (DROP) on the age of retirement of employees covered by defined benefit pension plans provided by the City of Philadelphia. We show that the program results in significant and substantial increases in the age of retirement: 1.25 years on average for municipal employees. Employees make use of the program in ways that maximize the expected present value of their pension benefits, with municipal employees entering the program an average 2.1 years before the age at which they would otherwise have retired. Consequently, the program results in a substantial increase in pension cost. We estimate that the program has cost the city around $258 million over the period to 31 December 2009. We construct an indicator of employee quality and find that some classes of high-quality employees are disproportionately likely to delay retirement as a result of the program.
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Version: September 2010

Papers In Preparation

Electoral Competition and Social Influence Networks: A Theory of Political Polarization
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I examine electoral competition in which two parties compete through policy and persuasion, using a tractable two-dimensional framework with social learning, and provide an explanation for increasing political polarization at both the party and the population level. Voters and parties have policy preferences that depend upon the state of the world, which is known to parties but not known to voters, and are connected through a social influence network that determines through a learning process the final opinion of voters, where the voters' initial opinions and the persuasion efforts of the parties affect final opinions, and so voting behavior. Equilibrium level of polarization in policy and opinion (of the parties and the population) increases when persuasion cost decreases. An increase in homophily increases the equilibrium level of policy polarization and population opinion polarization. These comparative static results help explain the evidence of increased polarization in both the policy and opinion dimensions in the United States in parties and in the population.
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An Analysis of Substitutes Conditions in Matching

Current Research Projects

Strategyproofness and Weakened Substitutes in Matching with Contracts
Matching in supply chains with complementary inputs
(with Alex Teytelboym)