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 study dynamic properties of the group action on the simplex that is induced by Bayesian updating. We show that generically the orbits are dense in the simplex, although one must make use of the entire group, hence departing from straightforward Bayesian updating. We demonstrate also the...

The solution concept of a Bayesian equilibrium of a Bayesian game is inherently an interim concept. The corresponding ex ante solution concept has been termed Harsányi equilibrium; examples have appeared in the literature showing that there are Bayesian games with uncountable state spaces that...

Negative results on the the existence of Bayesian equilibria when state spaces have the cardinality of the continuum have been attained in recent years. This has led to the natural question: are there conditions that characterise when Bayesian games over continuum state spaces have measurable...

A general selection theorem is presented constructing a measurable mapping from a state space to a parameter space under the assumption that the state space can be decomposed as a collection of countable equivalence classes under a smooth equivalence relation. It is then shown how this selection...