Working Papers

Communication, Timing, and Common Learning, with Jakub Steiner
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."

Nonmanipulable Bayesian Testing
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.

Efficient Dynamic Coordination with Individual Learning, with Amil Dasgupta and Jakub Steiner
We study how the presence of multiple participation opportunities coupled with private learning about payoffs affects the ability of agents to coordinate efficiently in global coordination games. Two players face the option to invest irreversibly in a project in one of many rounds. The project succeeds if some underlying state variable q is positive and both players invest, possibly asynchronously. In each round they receive informative private signals about q, and asymptotically learn the true value of q. Players choose in each period whether to invest or to wait for more precise information about q. We show that with sufficiently many rounds, both players invest with arbitrarily high probability whenever investment is socially efficient, and delays in investment disappear when signals are precise. This result stands in sharp contrast to the usual static global game outcome in which players coordinate on the risk-dominant action. We provide a foundation for these results in terms of higher order beliefs.

Robust Conventions and the Structure of Social Networks
This paper considers the equilibrium selection problem in coordination games when players interact on an arbitrary social network. We examine the impact of the network structure on the robustness of the usual risk dominance prediction as mutation rates vary. For any given network, a sufficiently large bias in mutation probabilities favoring the non-risk dominant action overturns the risk dominance prediction; bounds are obtained on the size of this bias depending on the network structure. As the size of the population grows large, the risk dominant equilibrium is highly robust in some networks. This is true in particular if the risk dominant action spreads contagiously in the network and there does not exist a sufficiently cohesive finite group of players. Examples demonstrate that robustness does not coincide with fast convergence.


Publications

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.

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.


From my previous existence as a number theorist:
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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