Research

Overview | (Jump to Papers)

Life is a never-ending series of decisions under uncertainty. Understanding how people make, or should make, these decisions, is fundamental to economic analysis. My goal is to shed what light I can on key aspects of this inexhaustible problem. The bulk of my work bifurcates naturally into the study of two kinds of uncertainty:

I. Strategic uncertainty, or uncertainty about the beliefs and actions of others, is a central topic of game theory. My joint work with Muhamet Yildiz has dealt, more specifically, with the strategic implications of higher-order beliefs. A first-order belief is a belief about the key aspects of the external environment, without reference to other players. A second-order belief is a belief about the first-order beliefs of other players and the environment. And so on: an (n+1)st-order belief is a belief about the nth-order beliefs of other players and the environment. For ordinary humans, second and third-order beliefs are necessary to navigate everyday interactions (What does Bob think I believe? What does Ann think about Sally?), while higher-order beliefs are progressively less likely to form clearly in one's mind. In standard economic models, players deal effortlessly with infinite hierarchies of beliefs. We illuminate this tension by classifying models whose predictions are sensitive to the specification of higher-order beliefs (it is much more common than you would think, and much more common than we suspected when we began this program!) In such cases we believe that outcomes are extremely sensitive to fine details of how the players receive and assess their information about the environment. Applying such models then requires great care in specifying the informational assumptions. Our work on this topic is contained in (3), (4), (8) and (9) below, and our main results have also been extended by other researchers; see our most recent paper for an up-to-date list.

II. Statistical uncertainty confronts a decison-maker who does not know the best statistical model for making inferences from a stream of data. A recent literature on "expert testing" concerns experts who claim to know the best model, but my in fact be strategically manipulating a test to fool a client as to their worth. In general this manipulation can be very difficult to combat, but in (7) Nabil Al-Najjar and I showed that the problem can be mitigated when we compare multiple experts. In (5) (with Alvaro Sandroni and Rann Smorodinsky) we further showed that manipulation can be prevented if the expert is restricted to certain models with statistically desirable properties.

In (12), Nabil and I survey the literature on "ambiguity aversion." This literature argues that a decision-maker faced with uncertainty should (or at least, does) exhibit preferences which are contrary to the classic probability-based nodels of Savage and de Finetti. We argue that instead, uncertainty can be encompassed within standard models of Bayesian inference and game theory. We follow up on this argument in the working paper (1) where we analyze the impact of financial uncertainty on a Bayesian decision-maker.

In (2), I offer a resolution to the following dilemma: Classic results tell us that Bayesian inference is the only consistent way to assimilate information, and hence, in a sense, the most rational. But, unless our prior belief accounts for every possible pattern we might see in the data, there are sequences of data we may observe which will cry out for us to change our beliefs to account for the new pattern, rather than continuing to blindly follow Bayes' rule. I call such an occurence, which is equivalent to a classical statistician rejecting his model and choosing a new one, a paradigm shift. Paradigm shifts seem to be an essential component of good statistics, but they lead inevitably to inconsistency and the existence of arbitrage opportunities against the decision-maker. My resolution to this dilemma is that if paradigm shifts are rare, then arbitrage opportunities will be small. I will defer to the paper for formal definitions of these concepts.

III. Miscellaneous: A brief description of my other papers, starting with the most recent: In (11) I made a foray into the public debate on tax policy, writing an official reply to an address by Gregory Mankiw (2010) concerning the methodology of choosing a tax code. Mankiw noted that while classic economic theories of optimal taxation proceed by optimizing a utilitarian social welfare function, many people would prefer to live in a world governed by “Just Deserts,” where one’s earnings are proportional to one’s contributions to society. He argued that this principle favored a very flat marginal tax rate. I noticed some problems, both formal and intuitive, with his argument. In brief: He argues that high earners should not be heavily taxed, because in perfectly competitive markets each worker earns their marginal product, a fair outcome. I respond that this argument is self-defeating, because in a perfectly competitive market there are no high earners, but a large population of each kind of individual, each of whom earns identically. My response makes clear the relationship of this debate to the classic market efficiency theorems. I suggest a line of research where fair outcomes can be explored through coalitional game theory, and hope to produce a more formal paper along these lines.

In (6), Attila Ambrus and I contributed to the literature on price dispersion, the phenomenon that different prices may be charged for a single good. Unlike the usual theoretical explanations, which rely on imperfect knowledge of prices, we found that a "loss leader" strategy may account for price dispersion even when prices are perfectly known. We also found that this example requires very specific conditions, and that a reasonable set of assumptions actually excludes the possibility of "loss leader" strategies unless search costs are present.

In (10), I contribute to the theory of the classic "Blotto" game, a popular model of electoral and military competition. Some of my novel results involve the case of asymmetric competition, where one side has more resources than the other.

Papers | (Back to Overview)

WORKING PAPERS

1. “Reputation without Commitment,” with Muhamet Yildiz.

2. “A Bayesian Model of Risk and Uncertainty,” with Nabil Al-Najjar

3. “A Bayesian Foundation for Classical Hypothesis Testing”

4. “Robust Predictions in Infinite-horizon Games--An Unrefinable Folk Theorem,” with Muhamet Yildiz (forthcoming, Review of Economic Studies)

5. “Sensitivity of Equilibrium Behavior to Higher-Order Beliefs in Nice Games,” with Muhamet Yildiz (Games and Economic Behavior, April 2011)

6. “Testing Theories with Learnable and Predictive Representations,” with Nabil Al-Najjar, Alvaro Sandroni, Rann Smorodinsky (Journal of Economic Theory, November 2010)

7. “Price Dispersion and Loss Leaders,” with Attila Ambrus (Theoretical Economics, December 2008)

8. “Comparative Testing of Experts,” with Nabil Al-Najjar (Econometrica, May 2008)

9. “A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements,” with Muhamet Yildiz (Econometrica, March 2007)

10. “Impact of Higher-Order Uncertainty,” with Muhamet Yildiz (Games and Economic Behavior, January 2007)

11. “Two Notes on the Blotto Game” (B.E. Journal of Theoretical Economics -- Contributions, forthcoming)

12. “Fairness and Tax Policy: a response to Mankiw's proposed ‘Just Deserts’” (Eastern Economic Journal, Summer 2011)

13,14. “The Subjective Approach to Ambiguity: A Critical Assessment,” and “Rejoinder” to same, with Nabil Al-Najjar (Economics and Philosophy, November 2009)

15. “A result on Zig-zag Permutations: A Combinatorial Proof,” (The Mathematical Gazette, forthcoming, July 2012)
16. “Lattice Walks in Z^d and Permutations with No Long Ascending Subsequences,” with Ira Gessel and Herbert Wilf (The Electronic Journal of Combinatorics, 1998)