Signaling game

In game theory, a signaling game is a simple type of a dynamic Bayesian game.

It is a game with two players, called the sender (S) and the receiver (R):

The game has two steps:

The two players receive payoffs dependent on the sender's type, the message chosen by the sender and the action chosen by the receiver.

The equilibrium concept that is relevant for signaling games is Perfect Bayesian equilibrium - a refinement of both Bayesian Nash equilibrium and subgame-perfect equilibrium.

A sender of type ${\displaystyle t_{j}}$ sends a message ${\displaystyle m^{*}(t_{j})}$ in the set of probability distributions over M. (${\displaystyle m(t_{j})}$ represents the probabilities that type ${\displaystyle t_{j}}$ will take any of the messages in M.) The receiver observing the message m takes an action ${\displaystyle a^{*}(m)}$ in the space of probability distributions over A.

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