If a pooling equilibrium is played in a signaling game, beliefs about the sender type can take on any form along the branch of the game tree that is not played in equilibrium, but on the branch that is played, beliefs are identical to the probability distribution with which "nature" assigned types to the sender.

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In a pooling equilibrium of a signaling game, beliefs about the sender type can take on any form along the branch of the game tree that is not played in equilibrium. However, on the branch that is played in equilibrium, beliefs are based on the probability distribution with which "nature" assigned types to the sender. This is a key feature of the signaling game and the basis for the information conveyed by the sender to the receiver.

If a Pooling Equilibrium Is Played in a Signaling Game