Home Address:
  123 York St., Apt. 11-B
  New Haven, CT 06510

Telephone: (203) 285-5609 (cell)
                   (203) 785-8321 (home)

Microeconomic Theory
Game Theory
Industrial Organization

Microeconomics
Game Theory
Industrial Organization

2003 (Oral): Microeconomic Theory (with distinction), Industrial Organization
2002 (Written): Microeconomic Theory, Macroeconomic Theory

Quantile Maximization in Decision Theory

Professor Benjamin Polak
Professor Stephen Morris
Professor Itzhak Gilboa
Professor Dino Gerardi

May 2006

Yale University, Ph.D., Economics, expected May 2006
M.Phil., Economics, 2004, M.A., Economics, 2003
Tinbergen Institute, University of Amsterdam, The Netherlands, M.Phil., Economics, 2001
Catholic University of Leuven, Belgium, M.Sc., Economics, Magna Cum Laude, 2000
Warsaw University, Poland, B.A., Economics, 1999

Winner of the Raymond Powell Teaching Prize, Yale University, 2003–2004
Yale University Dissertation Fellowship, 2005
Cowles Foundation Prize, Yale University, 2001-2005
Graduate School of Arts and Sciences Fellowship, Yale University, 2001–2006
Fellowship of the Department of Economics and Econometrics, University of Amsterdam, 2000–2001
Erasmus-Socrates Scholarship, 1999–2000
Award of the Ministry of Education, Poland, 1991
Excellence Award, Department of Economics, Warsaw University, Poland, 1998
Scholarship for Outstanding Achievement, Department of Economics, Warsaw University, Poland, 1997 and 1998
Third Prize in the Regional Mathematics Olympiad, Poland, 1996

Instructor:
  Introduction to Microeconomics (Undergraduate level), 2004
Teaching Assistant:
  Game Theory (Undergraduate level), Professor Benjamin Polak, 2003 and 2004
  Intermediate Microeconomics (Undergraduate level), Professor Dirk Bergemann, 2004

CUNY, Department of Computer and Information Science, December 2005 (invited)
Midwest Economic Theory Conference, Lawrence, Kansas, October 2005
XVI International Conference on Game Theory, Stony Brook, New York, July 2005
X Spring Meeting of Young Economists, Geneva, April 2005
Yale University, Department of Economics, Micro Theory Lunch (multiple presentations), Summer Workshop

Workshop on Uncertainty in Economic Theory, Yale University, October 2004
NSF Workshop on Classroom Economics, College of William and Mary, May 2004
IX IFREE Graduate Student Workshop, George Mason University, August 2002
II Mannheim Empirical Research Summer School, June 2002
IV European Science Days, "Social and Psychological Foundations of Economic Life," Steyr, Austria, July 2002
Amsterdam Symposium, Department of Psychology, Amsterdam, The Netherlands, June 2001
III European Science Days, "Growth, Values and Welfare," Steyr, Austria, July 2001
International Meeting of ESA, Barcelona, June 2001

Referee for X SMYE conference, Referee for Games and Economic Behavior

Professor Benjamin Polak
Department of Economics
Yale University
PO Box 208268
New Haven, CT 06520-8268
Phone: (203) 432-9926
Fax: (203) 432-5779
E-mail: benjamin.polak@yale.edu

Professor Itzhak  Gilboa
Eitan Berglas School of Economics and Recanati Business School, Tel-Aviv University
Cowles Foundation for Research in Economics
Yale University
PO Box 39040
Ramat Aviv, Tel Aviv, 69978
Israel
Phone: (+972) 3-640-6423
Fax: (+972) 3-640-9908
E-mail: igilboa@post.tau.ac.il

Professor Stephen Morris
Department of Economics
Princeton University
Contact address for the 2005–2006 academic year:
Center for Advanced Studies in Behavioral Sciences
75 Alta Road
Stanford, CA 94305
Phone: (650) 321-2052
Fax: (650) 321-1192
E-mail: smorris@princeton.edu

Professor Dino Gerardi
Department of Economics
Yale University
PO Box 208281
New Haven, CT 06520-8281
Phone: (203) 432-6519
Fax: (203) 432-6167
E-mail: donato.gerardi@yale.edu

My dissertation consists of two projects. The first introduces Quantile Maximization, an ordinal framework for modeling individual decision making under uncertainty. The second project analyzes strategic interactions in which the customary assumptions about knowledge of utilities and beliefs are not a good approximation.

PROJECT I: Quantile Maximization

Virtually all models of choice under uncertainty characterize preferences that imply cardinal properties of utility functions.  In many economic settings, however, preferences associated with a cardinal representation are not likely to be observed.   There are two important ordinal models of choice:  maxmin (choosing an alternative with the highest minimal outcome) and maxmax (choosing an alternative with the highest maximal outcome).  These models have been used in a wide range of economic applications, including games, bargaining, social choice and voting.  Nevertheless, the preferences they represent, are exclusively based on extreme outcomes.   Surprisingly, there does not exist an ordinal framework that captures less-extreme choice behavior.  In "Quantile Maximization in Decision Theory" (Job Market Paper), I model choice of an individual whose preferences lie between maxmin and maxmax.  Maxmin and -max can be viewed as maximizing, respectively, the lowest and the highest quantile of beliefs distributions.  Building on this insight, the model generalizes the choice rules to any intermediate quantile.  At the same time, decisions are robust to outliers and remain invariant to arbitrary increasing transformations of payoffs. 

Although largely ignored in decision theory literature, quantiles are present in many applied areas of economics: finance (Value at Risk, VaR), econometrics (robust estimation and quantile regression), measurement (population-based poverty lines, Lorenz curves), order statistics, practical applications of stochastic dominance theory (production, agriculture) and others.

The main contributions of the paper are as follows.

Identification and Testability: I examine which actions will be observed if individuals are quantile maximizers. I investigate whether the unobservables of the model can be identified from the data (payoff structure and choices). When agents make choices facing known probabilities, for instance in the lab, I show that one can identify the quantile exactly from observing a single decision. A subtler problem involves inferring the quantile without knowing the agent’s beliefs about the likelihood of events. For this problem, I show how to place bounds on the unobservable quantile and on the beliefs from data, and I investigate how these bounds vary with the decision problem and the richness of the data set.

Axiomatization: I provide an axiomatic foundation for Quantile Maximization in a Savage setting. That is, taking preferences over acts as a primitive, I find conditions that are necessary and sufficient for those preferences to admit the quantile representation. I derive probability measure(s) representing subjective beliefs, and a unique quantile that is maximized by the induced preferences over probability distributions. Importantly, the probability measure is unique for all levels of quantile strictly between 0 and 1.

Probabilistic Sophistication: The recently emerged line of research on probabilistic sophistication characterizes agents whose choices are based on probabilistic beliefs, independently of the hypothesized model of decision making. In stark contrast to subjective expected utility and its variants, I establish probabilistic sophistication without assuming any (cardinal or other) numerical representation of preferences over outcomes.

Applications: Distinct theoretical properties of Quantile Maximization (robustness, ordinality, one-dimensional information about preferences) make it a complementary tool to choice rules based on expectation, such as expected utility. Its policy implications do not hinge on concavity of utilities, but I show that the model still yields meaningful risk attitudes. Given its tractability and much weaker requirements about the knowledge of utility functions, it can serve as an attractive alternative in applied work. I discuss applications to insurance, pricing discrimination between short-run vs. long-run consumers, career choices, savings decisions and risk measures. The model naturally incorporates context-dependence, experience and framing, thus allowing for a rich set of applications.

PROJECT II: REASONING IN GAMES

Economic models of strategic interactions typically assume that information about payoffs and beliefs is available to and used by the players. Nonetheless, vast experimental evidence demonstrates that the subjects consistently underuse this information when making choices in one-shot games. Since many economic interactions are inherently one-shot, it seems essential to relax the stringent conditions on payoffs and beliefs to predict outcomes in those interactions. The following three papers study different aspects specific to one-shot games.

Two commonly used restrictions to describe equilibrium outcomes in games are that each player knows (i) which subset of the available actions may possibly be played by her opponents, and (ii) what is the exact distribution of their choices in that subset. Admittedly, these assumptions are not plausible in one-shot interactions. In the paper "P-Dominant Sets," I investigate how the predictions are affected when a player (i) is only certain with probability at least p_i about the subset of actions that might be played by others, and (ii) does not know how they choose in and outside of that subset. I obtain a rich framework that can also be used as a tool to examine how the game outcomes change with varying epistemic requirements.

The paper "Uncertainty about Rationality" is motivated by the question: What is the impact of people’s perception of others' rationality on equilibrium outcomes? The very notion of equilibrium used in economics implicitly assumes that the impact is none: equilibrium outcomes are always weakly within the rationalizable set (where rationality is common knowledge). And yet, this type of uncertainty is prevalent, arguably at least in one-shot interactions. Using the language of the hierarchy of beliefs, I formulate a model in which the players hold perceptions about the level of rationality of their opponents and, given those perceptions, respond optimally to their beliefs about actions. This permits uncertainty about rationality and allows me to parameterize the size of the derived set of outcomes by the actual levels of reasoning that the players use.

In the paper "Do Players Use Strategic Information in One-Shot Games? An Experimental Study of Decision Making," I report results of an experiment that investigates whether and how strategic information is used in one-shot games. This study contributes to the theoretical debate initiated by Luce and Raiffa [1954] and later by Kadane and Larkey [1982], who argued that players in games can be modeled as if they were making a non-strategic decision under uncertainty. Despite its conceptual and modeling implications, this conjecture has never been tested empirically. I develop a design that controls the information about an opponent (Nature or another subject), payoffs (all payoffs or own payoffs only), and varies the order in which it is presented to different treatment groups. I find that the data largely support the hypothesis qualified to one-shot interactions: the subjects appear to ignore strategic information.