Failure of common knowledge of language in common-interest communication games

Abstract

This paper explores higher-order uncertainty about message availability in communication games with perfectly aligned preferences. It can be impossible to achieve ex post efficiency in equilibrium even when it is mutual knowledge that the size of the set of available messages would be sufficient to convey all payoff-relevant information. There are equilibria that achieve ex post efficiency whenever a rich language condition is satisfied: the set of available messages is large relative to the sender's assessment of the number of information sets of the sender the receiver considers possible. Weaker conditions suffice if one adopts an ex ante perspective.