We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with...

We define a notion of correlated equilibrium for games with incomplete information in a general setting with finite players, finite actions, and finite states, which we call Bayes correlated equilibrium. The set of Bayes correlated equilibria of a fixed incomplete information game equals the set...

This paper analyzes the optimal provision of incentives in a sequential testing context. In every period the agent can acquire costly information that is relevant to the principal's decision. Neither the agent's effort nor the realizations of his signals are observable. First, we assume that the...

We survey the literature on multi-armed bandit models and their applications in economics. The multi-armed bandit problem is a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. This classic problem has received much...

We characterize optimal selling protocols/equilibria of a game in which an Agent first puts hidden effort to acquire information and then transacts with a Firm that uses this information to take a decision. We determine the equilibrium payoffs that maximize incentives to acquire information. Our...

An Agent who owns information that is potentially valuable to a Firm bargains for its sale, without commitment and certification possibilities, short of disclosing it. We propose a model of gradual persuasion and show how gradualism helps mitigate the hold-up problem (that the Firm would not pay...

We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with...

This paper examines moral hazard in teams over time. Agents are collectively engaged in an uncertain project, and their individual efforts are unobserved. Free-riding leads not only to a reduction in effort, but also to procrastination. The collaboration dwindles over time, but never ceases as...

We analyze the welfare consequences of a monopolist having additional information about consumers' tastes, beyond the prior distribution; the additional information can be used to charge different prices to different segments of the market, i.e., carry out "third degree price discrimination."We...

We analyze a class of games with interdependent values and linear best responses. The payoff uncertainty is described by a multivariate normal distribution that includes the pure common and pure private value environment as special cases. We characterize the set of joint distributions over...