An extensive form representation of a signaling game
In game theory, a signaling game is a simple type of a dynamic Bayesian game.[1]
The essence of a signalling game is that one player takes an action, the signal, to convey information to another player, where sending the signal is more costly if they are conveying false information. A manufacturer, for example, might provide a warranty for its product in order to signal to consumers that its product is unlikely to break down. The classic example is of a worker who acquires a college degree not because it increases their skill, but because it conveys their ability to employers.
A simple signalling game would have two players, the sender and the receiver. The sender has one of two types that might be called "desirable" and "undesirable" with different payoff functions, where the receiver knows the probability of each type but not which one this particular sender has. The receiver has just one possible type.
The sender moves first, choosing an action called the "signal" or "message" (though the term "message" is more often used in non-signalling "cheap talk" games where sending messages is costless). The receiver moves second, after observing the signal.
The two players receive payoffs dependent on the sender's type, the message chosen by the sender and the action chosen by the receiver.[2][3]
The tension in the game is that the sender wants to persuade the receiver that they have the desirable type, and they will try to choose a signal to do that. Whether this succeeds depends on whether the undesirable type would send the same signal, and how the receiver interprets the signal.
^Subsection 8.2.2 in Fudenberg Trole 1991, pp. 326–331
^Gibbons, Robert (1992). A Primer in Game Theory. New York: Harvester Wheatsheaf. ISBN 978-0-7450-1159-2.
^Osborne, M. J. & Rubinstein, A. (1994). A Course in Game Theory. Cambridge: MIT Press. ISBN 978-0-262-65040-3.
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