Question

briefly explain the 3 elements that form a perfect bayes-nash equilibrium for a signaling game

Answer 1

The perfect Bayesian equilibria in such a game can be divided in three different categories or elements pooling equilibria, separating equilibria and semi-separating

• A pooling equilibrium is an equilibrium where senders with different types all choose the same message. This means that the sender's message does not give any information to the receiver, so the receiver's beliefs are not updated after seeing the message.
• A separating equilibrium is an equilibrium where senders with different types always choose different messages. This means that the sender's message always reveals the sender's type, so the receiver's beliefs become deterministic after seeing the message.
• A semi-separating equilibrium is also called partial-pooling equilibriumi, it is an equilibrium where some types of senders choose the same message and other types choose different messages.

If there are more types of senders than there are messages, the equilibrium can never be a separating equilibrium (but may be semi-separating equilibria). There are also hybrid equilibria, in which the sender randomizes between pooling and separating

Perfect Bayesian equilibrium is not a subset of Nash equilibrium. Perfect Bayesian equilibrium requires players to have beliefs that are consistent with the equilibrium strategies of other players. Nash equilibrium does not explicitly specify the beliefs of the players.

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