We concern a sender-receiver game of common interests having
infinite types, e.g the set [0,1]<sup>2</sup>, but with finite signals. In our paper,
we extend the game by introducing multiple priors over the type space
and use incomplete preferences in Bewley’s way. We characterize the
equilibria under incomplete preferences by E-admissibility. Besides,
it has the equivalence between the equilibria and Voronoi languages.
Further, we demonstrates the existence of the indeterminacy of the
game. At last, we present that vague words, e.g. cheap, big, red,
etc., exist in the Knightian worlds but not in the Bayesian worlds,
which means that vagueness comes from the way we view the world
in Knightian method.