Common Knowledge of Language and Iterative Admissibility in a Sender-Receiver Game

This paper investigates the implications of common knowledge of language on cheap talk games. A general framework is proposed where language is modeled as a direct restriction on players’strategies, and the predictions under iterative admissibility (IA) are characterized. We apply this framework to sender-receiver games a la Crawford and Sobel (1982) (CS), where the Receiver takes a one-dimensional action. We incorporate two observations about natural language into the language assumption: 1) there always exists a natural expression to induce a certain action, if that action is indeed inducible by some message, 2) messages that are more dif