We show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowledge relation is smooth. Conversely, for any common knowledge relation that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such...

We show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowledge relation is smooth. Conversely, for any common knowledge relation that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such...

Radner (1968) proved existence of a competitive equilibrium for differential information economies with finitely many states. We extend this result to economies with infinitely many states of nature. Each agent observes a public and a private signal. The publicly observed signal may take...

Radner (1968) proved existence of a competitive equilibrium for differential information economies with finitely many states. We extend this result to economies with infinitely many states of nature. Each agent observes a public and a private signal. The publicly observed signal may take...