Bayesian updating in a separating equilibrium implies the initially uninformed player will fully know what type he is playing when he has to make his move.

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In a separating equilibrium, each player chooses a different strategy based on his type, which fully reveals his type to the other player. Therefore, the initially uninformed player will fully know what type he is playing when he has to make his move, after Bayesian updating.

Bayesian Updating in a Separating Equilibrium Implies the Initially Uninformed