Note: I have graduated from MIT and am no longer maintaining this site. Find my current website at Microsoft Research.
Job Market Paper
Abstract: We present a general approach to quantifying a mechanism’s susceptibility to strategic manipulation, based on the premise that agents report their preferences truthfully if the potential gain from behaving strategically is small. Susceptibility is defined as the maximum amount of expected utility an agent can gain by manipulating. We apply this measure to anonymous voting rules, by making minimal restrictions on voters’ utility functions and beliefs about other voters’ behavior. We give two sets of results. First, we offer bounds on the susceptibility of several specific voting rules. This includes considering several voting systems which have been previously identified as resistant to manipulation; we find that they are actually more susceptible than simple plurality rule by our measure. Second, we give asymptotic lower bounds on susceptibility for any voting rule, under various combinations of efficiency, regularity, and informational conditions. These results illustrate the tradeoffs between susceptibility and other properties of the voting rule.
Abstract: We study the question of whether local incentive constraints are sufficient to imply full incentive-compatibility, in a variety of mechanism design settings, allowing for probabilistic mechanisms. We give a unified approach that covers both continuous and discrete type spaces. On many common preference domains — including any convex domain of cardinal or ordinal preferences, single-peaked ordinal preferences, and successive single-crossing ordinal preferences — local incentive-compatibility (suitably defined) implies full incentive-compatibility. On domains of cardinal preferences that satisfy a strong nonconvexity condition, local incentive-compatibility is not sufficient. Our sufficiency results hold for dominant-strategy and Bayesian Nash solution concepts and allow for some interdependence in preferences.
An Efficiency Theorem for Incompletely Known Preferences (Journal of Economic Theory 145 (6) (2010), 2463-2470)
Abstract: There are n agents who have von Neumann-Morgenstern utility functions on a finite set of alternatives A. Each agent i’s utility function is known to lie in the nonempty, convex, relatively open set Ui. Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist utility functions ui in Ui for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case.
Abstract: Defaults often have a large influence on consumer decisions. We identify an overlooked but practical alternative to defaults: requiring individuals to make explicit choices for themselves. We study such “active decisions” in the context of 401(k) saving. We find that compelling new hires to make active decisions about 401(k) enrollment raises the initial fraction that enroll by 28 percentage points relative to a standard opt-in enrollment procedure, producing a savings distribution three months after hire that would take thirty months to achieve under standard enrollment. We also present a model of 401(k) enrollment and derive conditions under which the optimal enrollment regime is automatic enrollment (i.e., default enrollment), standard enrollment (i.e., default nonenrollment), or active decisions (i.e., no default and compulsory choice). Active decisions are optimal when consumers have a strong propensity to procrastinate and savings preferences are highly heterogeneous. Financial illiteracy, however, favors default enrollment over active decision enrollment.
Abstract: We consider the tradeoff between efficiency and incentives in large double auction environments with weak budget balance. No mechanism simultaneously gives agents perfect incentives to be truthful and ensures first-best efficiency, but a planner designing a mechanism may be willing to compromise on either of these dimensions for improvements along the other. She would then naturally wish to find where the possibility frontier lies with respect to incentives and efficiency. We make inroads on this question: our main result locates the frontier to within a factor that is logarithmic in the size of the market.
Abstract: We consider mechanism design for agents who know their own ordinal preferences, but whose preferences over lotteries may be uncertain. We ask whether this uncertainty gives a reason to use mechanisms that only elicit agents' ordinal preferences. Our main theorem formalizes such a justification, as long as agents' preferences over pure outcomes are strict: If a planner is to implement her goals (in ex-post equilibrium) using a mechanism that is robust to interdependence of arbitrary form in agents' cardinal preferences, then there must exist such a mechanism that elicits only ordinal preferences. The strictness assumption can be dropped if we further enlarge the space of uncertainty to allow non-expected-utility preferences over lotteries. Examples show that the hypotheses in these results, including the modeling assumption of interdependence, are not superfluous.
Abstract: We consider markets in which n indivisible objects are to be allocated to n agents. A number of recent papers studying such markets have shown various interesting equivalences between randomized mechanisms based on trading and randomized mechanisms based on serial dictatorship. We prove a very general equivalence theorem from which many previous equivalence results immediately follow, and we give several new applications. Our general result also sheds some light on why these equivalences hold by presenting the existing serial-dictatorship-based mechanisms as randomizations of a general mechanism which we call serial dictatorship in groups. The proof technique, a hybrid of explicit bijective and enumerative methods, is cleaner than previous bijective proofs.