Correlated equilibrium

Correlated equilibrium
A solution concept in game theory
Relationship
Superset of	Nash equilibrium
Significance
Proposed by	Robert Aumann
Example	Chicken

In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann (1974). The idea is that each player chooses their action according to their observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from the recommended strategy (assuming the others don't deviate), the distribution is called a correlated equilibrium.

An ${\displaystyle N}$-player strategic game ${\displaystyle \displaystyle (N,A_{i},u_{i})}$ is characterized by an action set ${\displaystyle A_{i}}$ and utility function ${\displaystyle u_{i}}$ for each player ${\displaystyle i}$. When player ${\displaystyle i}$ chooses strategy ${\displaystyle a_{i}\in A_{i}}$ and the remaining players choose a strategy profile described by the ${\displaystyle N-1}$-tuple ${\displaystyle a_{-i}}$, then player ${\displaystyle i}$'s utility is ${\displaystyle \displaystyle u_{i}(a_{i},a_{-i})}$.

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