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Abstract

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.