Correlated equilibrium

A correlated equilibrium is a generalization of Nash equilibrium introduced by Robert Aumann in 1974. In a Nash equilibrium, each player independently randomizes over their actions according to a mixed strategy. In a correlated equilibrium, players receive a private signal from a common randomizing device — a 'correlation device' — and choose actions based on their signal. The distribution of signals is such that no player can gain by unilaterally deviating from the recommended action. Every Nash equilibrium is a correlated equilibrium, but the converse is false: correlated equilibria can achieve payoffs that no Nash equilibrium can reach. The correlated equilibrium concept captures situations where players can coordinate through shared information — traffic lights, social conventions, market signals — without being able to communicate directly. It is the game-theoretic formalization of coordination through common knowledge of a random event rather than through binding agreement.