Working Papers

Price Distortions in High-Frequency Markets, with Jakub Steiner
We study the effect of frequent trading opportunities and categorization on pricing of a risky asset. Frequent opportunities to trade can lead to large distortions in prices if some agents forecast future prices using a simplified model of the world that fails to distinguish between some states. In the limit as the period length vanishes, these distortions take a particular form: the price must be the same in any two states that a positive mass of agents categorize together. Price distortions therefore tend to be large when different agents categorize states in different ways, even if each individual’s categorization is not very coarse. Similar results hold if, instead of using a simplified model of the world, some agents overestimate the likelihood of small probability events, as in prospect theory.

Influential Opinion Leaders, with Antoine Loeper and Jakub Steiner
We present a two-stage coordination game in which early choices of experts with special interests are observed by followers who move in the second stage. We show that the equilibrium outcome is biased toward the experts’ interests even though followers know the distribution of expert interests and account for it when evaluating observed experts’ actions. Expert influence is fully decentralized in the sense that each individual expert has a negligible impact. The bias in favor of experts results from a social learning effect that is multiplied through a coordination motive. We show that the total effect can be large even if the direct social learning effect is small. We apply our results to the diffusion of products with network externalities and the onset of social movements.

Publications

Dynamic Coordination with Individual Learning, with Amil Dasgupta and Jakub SteinerGames and Economic Behavior, Vol. 74 (1), January 2012, 83-101
We study coordination in dynamic global games with private learning. Players choose whether and when to invest irreversibly in a project whose success depends on its quality and the timing of investment. Players gradually learn about project quality. We identify conditions on temporal incentives under which, in sufficiently long games, players coordinate on investing whenever doing so is not dominated. Roughly speaking, this outcome occurs whenever players' payoffs are sufficiently tolerant of non-simultaneous coordination. We also identify conditions under which players coordinate on the risk-dominant action. We provide foundations for these results in terms of higher order beliefs.

Nonmanipulable Bayesian Testing, Journal of Economic Theory, Vol. 146 (5), September 2011, 2029-2041
This paper considers the problem of testing an expert who makes probabilistic forecasts about the outcomes of a stochastic process. I show that, as long as uninformed experts do not learn the correct forecasts too quickly, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on some data-generating processes; however, the set of such processes is topologically small. These results contrast sharply with many negative results in the literature.

Communication, Timing, and Common Learning, with Jakub SteinerJournal of Economic Theory, Vol. 146 (1), January 2011, 230-247
We study the effects of stochastically delayed communication on common knowledge acquisition (common learning). If messages do not report dispatch times, communication prevents common learning under general conditions even if common knowledge is acquired without communication. If messages report dispatch times, communication can destroy common learning under more restrictive conditions. The failure of common learning in the two cases is based on different infection arguments. Communication can destroy common learning even if it ends in finite time, or if agents communicate all of their information. We also identify conditions under which common learning is preserved in the presence of communication.  This paper largely supercedes our earlier note, "Communication Can Destroy Common Learning."

Contagion through Learning, with Jakub Steiner, Theoretical Economics, Vol. 3 (4), December 2008, 431-458
Previously titled "Learning by Similarity in Coordination Problems."
We study learning in a large class of complete information normal form games. Players continually face new strategic situations and must form beliefs by extrapolation from similar past situations. The use of extrapolations in learning may generate contagion of actions across games even if players learn only from games with payoffs very close to the current ones. Contagion may lead to unique long-run outcomes where multiplicity would occur if players learned through repeatedly playing the same game. The process of contagion through learning is formally related to contagion in global games, although the outcomes generally differ. We characterize the long-run outcomes of learning in terms of iterated dominance in a related incomplete information game with subjective priors, which clarifies the connection to global games.

Testing Multiple Forecasters, with Yossi FeinbergEconometrica, Vol. 76 (3), May 2008, 561-582
We consider a cross-calibration test of predictions by multiple potential experts in a stochastic environment which tests whether each expert is calibrated conditional on the predictions made by other experts. We show that this test is good in the sense that a true expert – one informed of the true distribution of the process – is guaranteed to pass the test no matter what the other potential experts do, and false experts will fail the test on all but a small (category one) set of true distributions. Furthermore, even when there is no true expert present, a test similar to cross-calibration cannot be simultaneously manipulated by multiple false experts, but at the cost of failing some true experts.

Old Papers

Robust Conventions and the Structure of Social Networks

Universal Deformations, Rigidity, and Ihara's Cocycle, Communications in Algebra, Vol. 31(2), 2003, pp. 901-943.

Goldbach's Conjecture for Z[x]
(with Amarpreet Rattan), Mathematical Reports of the Academy of Science, Vol. 20(3), 1998, pp. 83-85.

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