Game Theory · GT-07
A shared signal — a traffic light, a coin flip both sides can see — can coordinate players onto outcomes no independent mixing ever reaches.
A generalization of Nash equilibrium where players condition their strategies on a shared public signal, allowing coordination and higher average payoffs than any combination of independent (even mixed) strategies could achieve.
Introduced by Robert Aumann in 1974 ('Subjectivity and Correlation in Randomized Strategies'), work that contributed to his 2005 Nobel Memorial Prize in Economic Sciences.
The Mechanism
Traffic light as correlating device — a real-world correlated equilibrium
Neither driver needs to guess the other's move — the shared signal removes the coordination problem entirely, achieving what independent randomization (each driver privately flipping a coin) could never reliably deliver: zero collisions, by construction.
01 · CORRELATION CAN BEAT INDEPENDENT MIXING
A strictly larger solution set
Every Nash equilibrium is a correlated equilibrium, but not the reverse — a correlating device can achieve joint outcomes (in expectation) that lie outside what any combination of independent Nash strategies can reach, simply because it lets players' actions depend on the same information rather than each guessing separately.
02 · THE SIGNAL NEEDS NO ENFORCEMENT POWER, ONLY CREDIBILITY
Coordination without a contract
A traffic light has no ability to physically stop anyone — it works purely because following it is each driver's own best response once they trust everyone else will follow it too. The device coordinates beliefs, not behavior directly; the incentive to comply still has to hold on its own.
03 · MARKETS AND INSTITUTIONS AS CORRELATING DEVICES
A broader lens than traffic
Aumann's framework reframes many social institutions — opening bells on stock exchanges, published weather forecasts, publicly announced interest-rate decisions — as correlating devices that let independent actors coordinate on an equilibrium none of them could reach alone through private reasoning.
Where It Fails / Inversion
Where it fails / inversion
A correlating signal only produces good coordination if the underlying incentives actually make following it a best response for everyone — a corrupt or manipulable 'shared signal' (rigged information, a biased referee) can just as easily correlate players onto a worse, exploitative outcome. The device amplifies whatever incentives are already in place; it doesn't fix bad ones.
How To Use It
Worked example · industry-wide reference pricing
When multiple businesses independently reference the same public benchmark (a published commodity index, a central bank rate) to set their own prices, they achieve a kind of tacit coordination — without ever communicating directly — purely because they're all conditioning on the same public signal. This is why regulators watch shared reference points closely: the same mechanism that resolves traffic can also quietly resolve into price coordination.
How to use it
When two parties keep failing to coordinate through negotiation alone, look for (or propose) a neutral public signal both can condition on — a published index, a scheduled announcement, a visible traffic-light-style status. It often resolves what direct back-and-forth cannot, because it changes the coordination problem, not just the incentives.
See Also