WARP and Combinatorial Choice
For combinatorial choice problems, I show that the Irrelevance of Rejected Items condition is equivalent
to the Weak Axiom of Revealed Preference (WARP), and is necessary and sufficient for the existence of
a complete, reflexive and antisymmetric rationalization of a combinatorial choice function.
I also show the equivalence of WARP to path independence and to other classical choice conditions when the
choice domain is combinatorial.
(with Vikram Manjunath)
Revise and Resubmit to Journal of Economic Theory
We consider a model where each agent has an outside option of privately known value. We show
that one strategy-proof and individually rational mechanism Pareto-improves another if and only
if it expands the set of participants. Corollaries include: a sufficient condition for a mechanism
to be on the Pareto-efficient frontier of strategy-proof mechanisms; uniqueness of strategy-proof
Pareto-improvements under true preferences over certain normatively meaningful benchmark allocation
rules; and a characterization of the pivotal mechanism.
Current Version: September 2018
When is manipulation all about the ones and twos?
Revise and Resubmit to Games and Economic Behavior
A rule 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: December 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.
The Impossibility of Strategy-proof, Pareto-efficient, and Individually Rational Rules for
(with Vikram Manjunath)
For a model of fractional matching with linear utility, interpreted as probabilistic
matching, we show that strategy-proofness, ex post Pareto-efficiency, and ex ante individual
rationality are incompatible. This result is robust to whether, or to what extent,
transfers are possible. Since we prove this impossibility for the domain of preferences
with linear utility representations and since ex post Pareto-efficiency is weaker than
Pareto-efficiency from the ex ante perspective, it implies an incompatibility for more
general fractional matching applications as well.
Current Version: July 2018
Stability and Complementarity in Matching
I define a notion of safety of a block, and propose a new notion of stability, safe-setwise stability.
Only unsafe blocks of a safe-setwise stable matching may remain. For each permutation of a classical versus
contractual and a many-to-one versus many-to-many model, I identify a condition on choice behavior,
depending upon the permutation, that is sufficient for the existence of a safe-setwise stable matching.
For classical matching, the condition is necessary in the typical sense of the literature.
The key feature of the choice condition is that some complementarities, those that are symmetric, are permitted.
This weakens the requirement that well-studied substitutes conditions impose.
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
Political Polarization and Social Influence Networks
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.
(with Vikram Manjunath)