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Computational Complexity pp 2830–2844Cite as

Signaling Games

  • Reference work entry

Article Outline

Glossary

Definition of the Subject

Introduction

The Model

Equilibrium

The Basic Model

Cheap Talk

Verifiable Information

Communication About Intentions

Applications

Future Directions

Acknowledgments

Bibliography

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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 in a game determined by equilibrium strategy.

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 sent 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 indifferent curves from a given family of preferences cross at most one.

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 delMinisterio de Educación y Ciencia (Spain) for financial support and Jose Penalva for his comments. I am grateful to the Departament d'Economiai d'Història Econòmica and Institut d'Anàlisi Econòmica of the Universitat Autònoma de Barcelona for hospitality and administrativesupport.

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Authors and Affiliations

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

    Joel Sobel

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Sobel, J. (2012). Signaling Games. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_174

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