An equilibrium is not an optimum

14 September 2026 · The Law of the Board

In 1950 a young mathematician described a situation in which no player can improve their position by changing strategy alone, given what everyone else is doing. Such a situation is stable. It will hold.

And — this is the whole point, and the part that gets lost every time the idea is popularised — it does not have to be good.

Stable and bad at the same time

The everyday use of "equilibrium" carries a suggestion of balance, of things having settled where they belong. Discard that. An equilibrium is a resting point, nothing more. It is where a system stops moving because nobody has a unilateral reason to move it.

A system can settle into an outcome that every single participant dislikes and remain there indefinitely. Not because anyone approves, not because anyone is trapped by force, and not because anyone lacks information. Simply because the first person to deviate would make their own position worse, and everyone can see that.

Nobody plans the traffic jam. Nobody wants it. Everybody builds it, every morning, each by making a decision that is individually correct.

The diagnostic

You are looking at an equilibrium rather than a failure when three things are true.

Everyone can see the problem. Nothing hinges on hidden information. Ask any participant and they will describe the bad outcome accurately and often bitterly.

No individual can fix it. The person who stops working the punishing hours does not reform the industry; they lose the promotion. The company that raises prices alone does not end the price war; it loses the customers. Deviation is punished individually and the benefit, if it came, would be shared.

It persists across personnel. Replace everyone involved with different, better people facing the same rewards and the outcome reproduces. This is the strongest signal and the easiest to check historically.

Where all three hold, the search for someone at fault is misdirected. The search is satisfying, it is what almost all commentary consists of, and it is usually wrong.

Why this changes what you do about it

If a bad outcome is a failure of will or competence, the response is pressure: better people, clearer expectations, stronger enforcement. Against an equilibrium, that response fails predictably, and its failure is then read as evidence that the pressure was insufficient. This is how organisations spend a decade escalating an intervention that could not have worked at any magnitude.

Against an equilibrium there are only a few real moves, and they all change the structure rather than the people.

Change the payoffs. Make deviation cheaper or conformity more expensive. A penalty on the punishing-hours firm, a subsidy for the first mover, a cost imposed on the behaviour everyone dislikes.

Add or remove a player. A regulator, an entrant, a party who can absorb the first-mover cost because they are not competing on the same axis.

Make commitments binding. If everyone can simultaneously commit to the better outcome and be held to it, the first-mover problem dissolves. Collective agreements exist for exactly this reason, and they fail exactly where enforcement fails.

Remove your own options. The counterintuitive one. Being unable to do something can strengthen your position, because it removes the choice the other side was counting on you making. This is why binding constraints are sometimes sought rather than resisted.

Change who moves first, or how often. Repeating a game changes what is rational inside it, because future rounds put a price on today's defection. Many stuck situations are stuck only because they are being played once.

Where it shows up

A price war both companies wanted to avoid and neither can end. An arms race where each state arms for safety and both become less safe. An industry where everyone overworks because the first to stop loses. A school system that exhausts its children and cannot reform itself. A meeting where nobody says the obvious thing.

These situations look nothing alike. The machinery underneath them is identical, and once you can see it, you cannot stop seeing it.

The uncomfortable part

The framework is amoral by construction. It describes what the incentives push toward, not what anyone ought to do, and it will tell you that a bad arrangement is stable without telling you that it is acceptable.

That distinction has to be held deliberately. Explaining why something persists is not the same as endorsing it, and the explanation is what any serious attempt to change it has to start from. An intervention designed against a fault, when the thing is an equilibrium, does not fail slowly. It fails completely, and takes the credibility of the next attempt with it.

Common questions

What is a Nash equilibrium in simple terms?

A situation in which no player can improve their own position by changing strategy alone, given what everyone else is doing. It is stable and it will hold — but stable does not mean good. A system can settle into an outcome that every participant dislikes and stay there indefinitely.

How do you know you are looking at an equilibrium rather than a failure?

Three signs. Everyone involved can describe the problem accurately. No individual can fix it alone without making their own position worse. And it reproduces when you replace the people with different, better people facing the same rewards. Where all three hold, looking for someone at fault is misdirected.

How do you break a bad equilibrium?

Change the payoffs so deviating is cheaper. Add or remove a player. Make commitments binding so everyone can move at once. Remove your own options, which can increase your power. Or repeat the game, because future rounds put a price on today's defection. See the Law of the Board.