With cheap talk, more can be achieved by long conversations than by a single message - even when one side is strictly better informed than the other.

This paper undertakes a careful examination of the concept of conditional probability and its use. The ideas are then applied to resolve a conceptual puzzle related to Savage's "Sure-Thing Principle."

With cheap talk, more can be achieved by long conversations than by a single message-even when one side is strictly better informed than the other. ("Cheap talk" means plain conversation-unmediated, nonbinding, and payoff-irrelevant.) This work characterizes the equilibrium payoffs for all...