Correlated equilibrium
Players take private advice from a shared random signal and nobody wants to ignore the advice they get, which widens rather than narrows the set of Nash outcomes.
Often misread asFiling it with the refinements and so expecting it to narrow the set of equilibria, when it does the opposite: every Nash equilibrium is a correlated equilibrium, and the correlated set is generally strictly larger.
How to see it
Shared advice that nobody wants to ignore
Picture a trusted device that privately whispers a recommended action to each player. If, having heard your whisper and knowing only the odds on what the others were told, you still cannot do better than obey, the arrangement is stable. Every Nash equilibrium is one of these, with a device whose whispers happen to be independent, and many better arrangements are too.
The checkRefinements take equilibria away, generalisations add them. Correlation relaxes the assumption that players randomise independently, so the Nash set sits inside the correlated set rather than around it.
Try itWork out each player's expected payoff in the mixed equilibrium of chicken. Now add a traffic light that tells one driver to go and the other to stop, each with probability a half, with each driver seeing only their own light. Check nobody wants to disobey, then compare payoffs. Beating mixed Nash is the proof that the set is larger.
Know these first
Easily confused with
Sources
- Aumann, R. J. (1974). Journal of Mathematical Economics 1(1), 67-96.
- Aumann, R. J. (1987). Econometrica 55(1), 1-18.
- Osborne, M. & Rubinstein, A. (1994). MIT Press.