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
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.
Dynamic Coordination with Individual Learning, with Amil Dasgupta and Jakub Steiner, Games 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
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 Steiner, Journal 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 Feinberg, Econometrica, 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.
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.