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Signaling Games

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Signaling games refer narrowly to a class of two-player games of incomplete information in which one player is informed and the other is not. The informed player’s strategy set consists of signals contingent on information, and the uninformed player’s strategy set consists of actions contingent on signals. More generally, a signaling game includes any strategic setting in which players can use the actions of their opponents to make inferences about hidden information. The earliest work on signaling games was Spence’s (1974) model of educational signaling and Zahari’s (1975) model of signaling by animals. During the 1980s researchers developed the formal model and identified conditions that permitted the selection of unique equilibrium outcomes in leading models.

Introduction

The framed degree in your doctor’s office, the celebrity endorsement of a popular cosmetic, and the telephone message from an old friend are all signals. The signals are potentially...

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Notes

  1. 1.

    Chakraborty and Rick Harbaugh (2010) construct informative equilibria in a game in which the sender’s preferences are independent of type.

Abbreviations

Babbling equilibrium:

An equilibrium in which the sender’s strategy is independent of type and the receiver’s strategy is independent of signal.

Behavior strategy:

A strategy for an extensive-form game that specifies the probability of taking each action at each information set.

Behavioral type:

A player in a game who is constrained to follow a given strategy.

Cheap-talk game:

A signaling game in which players’ preferences do not depend directly on signals.

Condition D1:

An equilibrium refinement that requires out-of-equilibrium beliefs to be supported on types that have the most to gain from deviating from a fixed equilibrium.

Divinity:

An equilibrium refinement that requires out-of-equilibrium beliefs to place relatively more weight on types that gain more from deviating from a fixed equilibrium.

Equilibrium outcome:

The probability distribution over terminal nodes determined by an equilibrium strategy in a game.

Handicap principle:

The idea that animals communicate fitness through observable characteristics that reduce fitness.

Incomplete information game:

A game in which players lack information about the strategy sets or payoff functions of their opponents.

Intuitive criterion:

An equilibrium refinement that requires out-of-equilibrium beliefs to place zero weight on types that can never gain from deviating from a fixed equilibrium outcome.

Nash equilibrium:

A strategy profile in a game in which each player’s strategy is a best response to the equilibrium strategies of the other players.

Neologism-proof equilibrium:

An equilibrium that admits no self-signaling set.

Pooling equilibrium:

A signaling-game equilibrium in which each all sender types send the same signal with probability one.

Receiver:

In a signaling game, the uninformed player.

Self-signaling set:

A set of types C with the property that precisely types in the set C gain from inducing the best response to C relative to a fixed equilibrium.

Sender:

In a signaling game, the informed agent.

Separating equilibrium:

A signaling-game equilibrium in which sender types send signals from disjoint subsets of the set of available signals.

Signaling game:

A two-player game of incomplete information in which one player is informed and the other in not. The informed player’s strategy is a type-contingent message and the uninformed player’s strategy is a message-continent action.

Single-crossing condition:

A condition that guarantees that indifference curves from a given family of preferences cross at most once.

Spence-Mirrlees condition:

A differential condition that orders the slopes of level sets of a function.

Standard signaling game:

A signaling game in which strategy sets and payoff functions satisfy monotonicity properties.

Type:

In an incomplete information game, a variable that summarizes private information.

Verifiable information game:

A signaling game with the property that each type has a signal that can only be sent by that type.

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Acknowledgments

I thank the Guggenheim Foundation, NSF, and the Secretaría de Estado de Universidades e Investigación del Ministerio de Educación y Ciencia (Spain) for financial support and Richard Brady, Kanako Goulding Hotta, and Jose Penalva for their comments. I am grateful to the Departament d’Economia i d’Història Econòmica and Institut d’Anàlisi Econòmica of the Universitat Autònoma de Barcelona for hospitality and administrative support.

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  1. Department of Economics, University of California, San Diego, CA, USA

    Joel Sobel

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Correspondence to Joel Sobel .

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    Robert A. Meyers

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Sobel, J. (2015). Signaling Games. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_481-4

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