Axioms for Correlated Equilibrium

We characterize correlated equilibrium in finite normal-form games.

Interpreting correlated strategies as action recommendations, we show that correlated equilibrium is the unique solution concept that never recommends a pure-strategy dominated action, treats payoff-equivalent actions interchangeably, and respects the sure-thing principle under uncertainty about payoffs and the correlation device.

A parallel characterization identifies coarse correlated equilibrium among solution concepts that recommend dominant actions whenever they exist and treat payoff-equivalent actions as strongly interchangeable.