Correlated Equilibrium, explained.
A correlated equilibrium is a joint recommendation distribution under which no player benefits by deviating from their recommendation given the information it supplies.
Why it happens
A device equally recommends Go/Wait or Wait/Go in a declared two-action game. Against an obedient partner, following yields expected payoff 1.5; always Go yields −1 and always Wait 0.5. Conditional obedience inequalities are shown.
A correlated equilibrium is a joint recommendation distribution under which no player benefits by deviating from their recommendation given the information it supplies.
Read the result
Use conditional incentives after each recommendation, not only the unconditional average payoff. The partner’s obedience is a supplied part of this game.
A worked example
Compare following a device with ignoring it
Play recommendations while following the device and inspect the Go/Wait histories.
Compare expected payoff 1.5 with always-Go payoff minus one and always-Wait payoff one-half.
Check that deviating after either recommendation lowers payoff against the implied partner action.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A device equally recommends Go/Wait or Wait/Go in a declared two-action game. Against an obedient partner, following yields expected payoff 1.5; always Go yields −1 and always Wait 0.5. Conditional obedience inequalities are shown.
Where this idea is useful
A practical use
Ask how a shared coordination device changes conditional incentives rather than simply adding another independent random choice.
A common misconception
“Correlated equilibrium is just independent random play by both players.”
The device supplies a joint distribution and information through recommendations. Here opposite recommendations avoid the collisions caused by independent half-probability Go choices.
What this explanation leaves out
- The partner obeys and all payoffs are stipulated. This distribution need not improve another game, and the activity is not traffic-control guidance.
Does this device solve every coordination problem?
No. The incentive inequalities depend on the declared game and information; another payoff matrix can invalidate obedience.
What does your recommendation reveal about the other participant’s likely action?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.