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, under general conditions on the tester's prior, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on data-generating processes where the tester quickly learns the true probabilities by updating her prior. However, the set of processes on which informed experts are rejected is topologically small. These results contrast sharply with many negative results in the literature.Probability forecasts, testing, experts

Influential Opinion Leaders

We present a simple model of elections in which experts with special interests endorse candidates and endorsements are observed by the voters. We show that the equilibrium election outcome is biased towards the experts' interests even though voters know the distribution of expert interests and account for it when evaluating endorsements. Expert influence is fully decentralized in the sense that individual experts have no incentive to exert influence. The effect arises when some agents prefer, ceteris paribus, to support the winning candidate and when experts are much better informed about the state of the world than are voters.Voting, coordination, experts

Communication Can Destroy Common Learning

We show by example that communication can generate a failure of common knowledge acquisition. In the absence of communication, agents acquire approximate common knowledge of some parameter, but with communication they do not.Common knowledge, communication

Communication, Timing, and Common Learning

We study the effect 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 divgerent 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.communication, common learning, approximate common knowledge

Communication, Timing, and Common Learning

We study the effect 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.Common knowledge, communication, learning

Influential Opinion Leaders

We present a simple model of elections in which experts with special interests endorse candidates and endorsements are observed by the voters. We show that the equilibrium election outcome is biased towards the experts' interests even though voters know the distribution of expert interests and account for it when evaluating endorsements. Expert influence is fully decentralized in the sense that individual experts have no incentive to exert influence. The effect arises when some agents prefer, ceteris paribus, to support the winning candidate and when experts are much better informed about the state of the world than are voters.election, manipulation, global game

Communication Can Destroy Common Learning

We show by example that communication can cause common knowledge acquisition to fail. In the absence of communication, agents acquire approximate common knowledge of some parameter, but with communication they do not.

Contagion through learning

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. We characterize the long-run outcomes of learning in terms of iterated dominance in a related incomplete information game with subjective priors. 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.Similarity, learning, contagion, case-based reasoning, global games

Contagion through Learning

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. We characterize the long-run outcomes of learning in terms of iterated dominance in a related incomplete information game with subjective priors. 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.Similarity, learning, contagion, case-based reasoning, global games, coordination, subjective priors.

Efficient Dynamic Coordination with Individual Learning

We study how the presence of multiple participation opportunities coupled with individual learning about payoff 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 theta is positive and both players invest, possibly asynchronously. In each round they receive informative private signals about theta, and asymptotically learn the true value of theta. Players choose in each period whether to invest or to wait for more precise information about theta. 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.