  We provide a syntactic construction of correlated equilibrium. For any finite
game, we study how players coordinate their play on a signal by means of a
public strategy whose instructions are expressed in some natural language.
Language can be ambiguous in that different players may assign different truth
values to the very same formula in the same state of the world. We model
ambiguity using the player-dependent logic of Halpern and Kets (2015). We show
that, absent any ambiguity, self-enforcing coordination always induces a
correlated equilibrium of the underlying game. When language ambiguity is
allowed, self-enforcing coordination strategies induce subjective correlated
equilibria.
