(with Vikram Manjunath)
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.
Current Version: March 2017
WARP and Combinatorial Choice
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.
Current Version: May 2016
R&R at Journal of Economic Theory
When is manipulation all about the ones and twos?
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.
Current Version: May 2017
Stability and Matching with Aggregate Actors
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.
Pairwise Stability and Complementarity in Many-to-One Matching
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.
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)
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.
Version: September 2010
Papers In Preparation
Electoral Competition and Social Influence Networks: A Theory of Political Polarization
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.
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)