Definition of the Subject
The correlated equilibrium is a game theoretic solution concept. It was proposed by Aumann (1974, 1987) in order to capture the strategic correlation opportunities that the players face when they take into account the extraneous environment in which they interact. The notion is illustrated in section “Introduction.” A formal definition is given in section “Correlated Equilibrium: Definition and Basic Properties.” The correlated equilibrium also appears as the appropriate solution concept if preplay communication is allowed between the players. As shown in section “Correlated Equilibrium and Communication,” this property can be given several precise statements according to the constraints imposed on the players’ communication, which can go from plain conversation to exchange of messages through noisy channels. Originally designed for static games with complete information, the correlated equilibrium applies to any strategic form game. It is geometrically and...
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Abbreviations
- Bayesian game :
-
An interactive decision problem consisting of a set of n players, a set of types for every player, a probability distribution which accounts for the players’ beliefs over each other’s types, a set of actions for every player, and a von Neumann-Morgenstern utility function defined over n-tuples of types and actions for every player.
- Nash equilibrium :
-
In an n-person strategic form game, a strategy n-tuple from which unilateral deviations are not profitable.
- Pure strategy (or simply strategy) :
-
A mapping which, in an interactive decision problem, associates an action with the information of a player whenever this player can make a choice.
- Sequential equilibrium :
-
A refinement of the Nash equilibrium for n-person multistage interactive decision problems, which can be loosely defined as a strategy n-tuple together with beliefs over past information for every player, such that every player maximizes his expected utility given his beliefs and the others’ strategies, with the additional condition that the beliefs satisfy (possibly sophisticated) Bayes updating given the strategies.
- Strategic (or normal) form game :
-
An interactive decision problem consisting of a set of n players, a set of strategies for every player, and a (typically, von Neumann-Morgenstern) utility function defined over n-tuples of strategies for every player.
- Utility function :
-
A real valued mapping over a set of outcomes which reflects the preferences of an individual by associating a utility level (a “payoff”) with every outcome.
- von Neumann-Morgenstern utility function :
-
A utility function which reflects the individual’s preferences over lotteries. Such a utility function is defined over outcomes and can be extended to any lottery λ by taking expectation with respect to λ.
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Forges, F. (2015). Correlated Equilibria and Communication in Games. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_103-3
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