MASSACHUSETTS INSTITUTE OF TECHNOLOGY

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY GABRIEL CARROLL OFFICE CONTACT INFORMATION 50 Memorial Drive, E HOME CONTACT INFORMATION 1534 Cambridge Street, #1 Cambridge, MA Mobile: MIT PLACEMENT OFFICER Professor Ben Olken MIT PLACEMENT ADMINISTRATOR Ms. Beata Shuster DOCTORAL STUDIES Massachusetts Institute of Technology (MIT) Ph.D., Economics, Expected completion June 2012 DISSERTATION: Non-Equilibrium Approaches to Mechanism Design DISSERTATION COMMITTEE AND REFERENCES Professor Parag Pathak 50 Memorial Drive, E52-391C Professor Daron Acemoglu 50 Memorial Drive, E52-380B Professor Glenn Ellison 50 Memorial Drive, E52-380A PRIOR EDUCATION Harvard University, B.A., summa cum laude, Mathematics and Linguistics, 2005 CITIZENSHIP USA GENDER M YEAR OF BIRTH 1982 LANGUAGES FIELDS TEACHING EXPERIENCE English (native); Mandarin Chinese (competent); French, Spanish (basic) Primary: Microeconomic Theory Secondary: Political Economy, Behavioral Economics TEACHING ASSISTANTSHIPS AT MIT: Game Theory (graduate intermediate-level, ), Spring 2010, 2011 Game Theory (graduate core-level, ), Fall 2010

2 Gabriel Carroll, October 2011 Page 2 Strategy and Information (undergraduate, 14.16), Spring 2011 OTHER EXPERIENCE: Instructor at Mathematical Olympiad Summer Program, Summer 2008, 2009, 2010 Volunteer English teacher at Chaling #1 Middle School, Chaling, Hunan, China, RELEVANT POSITIONS FELLOWSHIPS, HONORS, AND AWARDS PROFESSIONAL ACTIVITIES Research Assistant to Professor Jean Tirole, 2010 Research Assistant to Professors James Choi, David Laibson, and Brigitte Madrian at NBER, Yahoo! Key Scientific Challenges fellowship, 2011 NSF Graduate Research Fellowship, 2007 David Mumford Prize (outstanding mathematics student at Harvard), 2005 Thomas T. Hoopes Prize (outstanding undergraduate thesis), 2005 Junior Phi Beta Kappa (top 2% of graduating class), 2004 Putnam Fellow, 2000, 2001, 2002, 2003 CONFERENCE PRESENTATIONS: An Expected-Utility Measure of Incentives (poster), Yahoo! Key Scientific Challenges Summit, Santa Clara, 2011 When are Local Incentive Constraints Sufficient? Workshop in Prior-Free Mechanism Design, CIMAT, Guanajuato, Mexico, 2010 How to Allocate Indivisible Objects to People, MathFest, Pittsburgh, 2010 Participant in RSF Summer Institute in Behavioral Economics, 2010 Referee for B. E. Journal of Theoretical Economics; Journal of Economic Theory; Journal of Law, Economics, and Organization; Journal of Mathematical Economics PUBLICATIONS When are Local Incentive Constraints Sufficient? Econometrica, forthcoming 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),

3 Gabriel Carroll, October 2011 Page 3 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 U i. 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 u i U i for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case. Optimal Defaults and Active Decisions (with James J. Choi, David Laibson, Brigitte Madrian, and Andrew Metrick), Quarterly Journal of Economics 124 (4) (2009), 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. RESEARCH PAPERS A Quantitative Approach to Incentives: Application to Voting Rules (Job Market Paper) 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 bound 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. The Efficiency-Incentive Tradeoff in Double Auction Environments We consider the tradeoff between efficiency and incentives in large double auction environments. No mechanism simultaneously gives agents perfect incentives to be

4 Gabriel Carroll, October 2011 Page 4 truthful and ensures first-best efficiency under truthfulness; but if agents are willing to be truthful when the gains to strategic behavior are sufficiently small, then the optimal mechanism should compromise between these two criteria. We give a first stab at quantifying the tradeoff between the two, providing asymptotic lower bounds on either the inefficiency or the susceptibility to manipulation that any mechanism must possess. On Direct Mechanisms with Ordinal Preferences We consider dominant-strategy implementation of social choice correspondences, where the set of acceptable outcomes depends only on the agents ordinal preferences, and where mechanisms may prescribe lotteries over outcomes. We investigate the possibility of providing theoretical foundations for restricting attention to mechanisms that only elicit ordinal preferences. Specifically, we address the following question: if a social choice correspondence is implementable for all possible preferences over lotteries that the agents may have, is it necessarily implementable by a mechanism that only elicits ordinal preferences? We can obtain affirmative answers if there is a single agent and the social choice correspondence takes a simple form; or if there are multiple agents, each agent s cardinal preferences are subjectively correlated with others preferences, and either all ordinal preferences are strict or agents are allowed to have non-expected-utility preferences over lotteries. Under weaker combinations of assumptions, the answer to our question is negative. A General Equivalence Theorem for Allocation of Indivisible Objects, revise and resubmit, Theoretical Economics 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. Public Projects under Dual Utility We perform a case study in mechanism design under non-expected utility. Specifically, we consider the public projects problem, and study whether the well-known AGV mechanism can be generalized to the dual utility framework, where the value of a lottery is linear in money but nonlinear in probabilities. In this problem, there are M projects under consideration. Each of N agents has a valuation for each project; agents preferences are independently distributed and the distributions are common knowledge. An AGV-type mechanism asks each agent to report his valuations, pays him an amount that depends on his report, finances this payment by an equal charge to all other agents,

5 Gabriel Carroll, October 2011 Page 5 and then carries out the project for which the aggregate valuation is highest. In our main model, there may not exist any AGV-type mechanism that is Bayesian incentivecompatible. However, if there are only two projects and the agents probability weighting functions are of the inverse-s-shaped form, then existence is guaranteed via a fixed-point argument. If there are more than two projects, then we have a negative result: no restriction on the weighting functions, short of linearity, is sufficient to ensure that the desired mechanism exists. RESEARCH IN PROGRESS Information Acquisition and Mechanism Robustness We consider a Bayesian mechanism design setting in which agents may be able to engage in costly acquisition of information about each other s types before entering the mechanism. A welfare-oriented mechanism designer should take the social costs of such spying into account. A dominant-strategy mechanism gives no incentives for spying; but a priori, non-dominant-strategy mechanisms may be better if the improvement in the outcome outweighs the costs of spying. We formalize the comparison in the context of a bilateral trade model, where a designer has a correct prior over agents valuations but knows nothing about the spying technology. In a two-type model, we determine the maximum level of expected welfare that the designer can guarantee, no matter what the spying technology is. For some parameter values, a dominant-strategy mechanism achieves the best possible guarantee. For other values, it is possible to do better. An Approach to Describing Strategic Complexity We propose a framework for quantifying the complexity of decision problems, in terms of how much the agent s optimization problem depends on information that is difficult to think about. After presenting the framework, we discuss applications to mechanism design, centering on the problem of eliciting a probability distribution from an agent who can introspect about it at a cost. We discuss the complexity of various mechanisms, and offer some bounds on the resulting utility costs to the principal. ADDITIONAL PAPERS MINOR PAPERS: Efficient Random Assignment with Constrained Rankings Foundations for Large-Population Mechanisms NON-ECONOMICS: The Cube Recurrence (with David Speyer), Electronic Journal of Combinatorics 11 (1) (2004), #R73 Two New Combinatorial Models for the Ptolemy Recurrence (with Gregory Price)