So far the games we’ve dissected have been polite enough to have exactly one Nash equilibrium — one cell where the music stops, one prediction to make. That tidiness was doing a lot of quiet work. Plenty of the most important strategic situations you’ll ever be in have several equilibria, all equally stable, and the moment that happens the equilibrium concept changes its job description. It stops telling you what will happen and starts handing you a shortlist of what could happen — the candidates, not the winner. Closing that gap between “here are the resting points” and “here’s the one we’ll actually rest on” is the entire lesson. Welcome to coordination games, where the enemy isn’t a rival trying to beat you — it’s the risk that you both guess differently about the same thing.
Pure coordination: the driving-side game
Start with the cleanest possible version, stripped of every complication. Two drivers approach each other on an empty road. Each independently picks a side — left or right. If they pick the same side, they pass safely and both are happy. If they pick different sides, they collide, and everyone has a very bad day. Crucially, there is nothing inherently better about left or right. Left-left is exactly as good as right-right. The only thing on earth that matters is that the two of them match.
Payoff matrix
The driving-side game: all that matters is matching
Both drive the same side (1, 1) and everyone passes safely. Pick different sides and it's a crash (0, 0). Neither side is 'the right answer' — the only thing that matters is agreeing. Find the two equilibria with the rings.
| Driver 2 | ||
|---|---|---|
| Drive left | Drive right | |
| Driver 1Drive left | NE11 | 00 |
| Drive right | 00 | NE11 |
A ringed payoff is that player’s best response to the rival’s choice. A cell where both are ringed is a Nash equilibrium.
What the matrix says
Driver 1 — dominant strategy: none
Driver 2 — dominant strategy: none
Nash equilibrium (pure): (Drive left, Drive left) · (Drive right, Drive right)
Look at what the matrix says. Both-left and both-right are each Nash equilibria: if the other driver is going left, your best response is left; if they’re going right, yours is right. Neither can do better by unilaterally switching, so both are genuine resting points. But they’re equally good — a perfect tie in payoff. This is called a pure coordination game: there’s no conflict of interest at all, no temptation to cheat, no better deal to hold out for. Everyone wants precisely the same thing (to match); the only problem is how do we both know which equilibrium to aim at?
The answer, in the real world, is almost never found inside the game. It’s supplied by convention — a rule everyone has learned to expect, usually crystallised by history and then frozen in place. Which side of the road a country drives on is exactly this game solved by fiat and habit: Britain settled on the left, France on the right, and now neither can switch alone even though nobody can seriously argue one side is superior. The same shape explains why the QWERTY keyboard survives despite not being optimal, why the world can’t agree on metric versus imperial, why we all count time in base-60 minutes. None of these are “the best answer.” They’re equilibria we coordinated onto and then got stuck in, because once everyone expects one, matching it is your best move.
Coordination vs. the prisoner's dilemma
These games feel nothing like the prisoner’s dilemma, and the difference is worth naming. In a dilemma, players’ interests conflict — each is individually tempted to defect, and the trouble is a bad but unique equilibrium. In a coordination game, players’ interests align — everyone wants the same outcome — and the trouble is multiple equally-good equilibria with no built-in way to pick one. One is a problem of temptation; the other is a problem of selection. They call for completely different fixes.
The equilibrium-selection problem
Here’s the awkward truth the driving game exposes. When a game has more than one Nash equilibrium, “predict the equilibrium” becomes underdetermined — the theory alone literally cannot tell you which one a pair of rational players will reach. Both drivers are perfectly rational, both want to coordinate, both know all the payoffs… and the math still shrugs. This is the equilibrium-selection problem, and for decades it was one of game theory’s most embarrassing open wounds: a beautiful theory of stable outcomes that couldn’t say which stable outcome you’d get.
The way out came from the economist Thomas Schelling, and it’s gloriously human. He noticed that real people, faced with multiple equilibria and no chance to communicate, coordinate anyway — astonishingly often — by both gravitating toward whichever option is somehow salient, obvious, or natural given their shared context. He called these focal points (now often “Schelling points”): an equilibrium that stands out from the others because of culture, convention, symmetry, or sheer conspicuousness, letting players converge on it without ever coordinating explicitly.
His classic thought experiment: you have to meet a stranger in New York City tomorrow. You were never told a time or a place, you can’t contact each other, and you win only if you both show up at the same spot at the same moment. Where do you go, and when? When Schelling posed this, a striking share of people answered the same way — Grand Central Terminal at noon. Nothing in the “payoffs” makes Grand Central better than a random street corner. It wins purely because it’s the obvious answer, the one you expect the other person to expect you to expect — a landmark so iconic it becomes the natural meeting place, and noon so naturally the “default” time. Salience, not payoff, did the selecting.
Try this one on yourself. You and a stranger must each secretly pick a positive whole number. You both win a prize only if you pick the same one — and you can’t communicate. There are infinitely many equilibria here (any number, as long as you both name it), and they’re all exactly as good as each other. So which do you write down? Overwhelmingly, people pick 1. Not because 1 pays more — it doesn’t; every match pays the same — but because 1 is unique in an obvious way: it’s the first, the smallest, the most “distinguished” positive integer, the one you’d guess a stranger would also single out. That special-ness is the entire mechanism. A focal point isn’t the highest-scoring choice; it’s the one whose salience makes it the natural common target, so both minds land on it without a word exchanged. Schelling’s insight was that this shared sense of the “obvious” is a real, usable coordinating device — often the only one available.
When equilibria are NOT equal — the standards game
The driving game was kind: both equilibria paid the same, so coordinating anywhere was a win. Reality is rarely that generous. Often the equilibria are genuinely unequal — one is better for everyone — and yet players can still get stuck on the worse one. That’s a far more painful problem, and it has its own canonical shape: the standards game.
Picture two firms (or an entire industry) choosing between two competing technical formats, A and B. As with driving, the overriding need is to match — a format nobody else uses is worthless. But here Format A is the better technology: if everyone standardises on A, each gets 3; if everyone standardises on B, each gets only 2. Both are still equilibria — but now one is plainly superior.
Payoff matrix
The standards game: two equilibria, one clearly better
Adopting the same format is what matters, but Format A is the better technology (3, 3) and Format B the worse one (2, 2). Both matches are equilibria. Nudge the payoffs and watch how being stuck on (Format B, Format B) survives even though everyone would prefer A.
| Firm 2 | ||
|---|---|---|
| Format A | Format B | |
| Firm 1Format A | NE33 | 11 |
| Format B | 00 | NE22 |
A ringed payoff is that player’s best response to the rival’s choice. A cell where both are ringed is a Nash equilibrium.
What the matrix says
Firm 1 — dominant strategy: none
Firm 2 — dominant strategy: none
Nash equilibrium (pure): (Format A, Format A) · (Format B, Format B)
Here’s the cruelty. Suppose the whole industry is sitting on Format B — the worse equilibrium. Everyone would be better off on A. Can any single firm fix it by switching to A? No. If Firm 1 jumps to A while Firm 2 stays on B, Firm 1 lands in a mismatch and drops from 2 to 1 — punished for trying to do the right thing. Neither firm can improve by moving unilaterally (that word again — the beating heart of Nash equilibrium), and so the inferior standard persists, defended not by anyone preferring it but purely by the fact that everyone else is already on it.
This is the mechanism behind lock-in and path dependence: a market, a technology, or a habit can get trapped on an inferior standard simply because it coordinated there first, and no individual has the power to defect toward the better one alone. Escaping needs something the game doesn’t supply on its own — a coordinated jump, a big player who moves first and credibly, or an announced switchover date that lets everyone leap together.
The stag hunt — coordination under risk
Now the most consequential coordination game of all, because it adds the ingredient that governs half of human cooperation: risk born of not-quite-trusting the other person.
Two hunters can team up to take down a stag — a feast, far more than either could get alone — but only if both commit; if you go for the stag and your partner wanders off, you come home with nothing. Alternatively, either can peel off and catch a hare solo — a modest, guaranteed meal that doesn’t depend on the other at all. Stag is the big cooperative prize; hare is the safe, self-sufficient fallback.
Payoff matrix
The stag hunt: the big prize needs trust
Hunting stag together pays best (4, 4) — but only if both commit. Hunting hare is safe: 2 no matter what the other does. Find the two equilibria with the rings, and notice which one you'd dare to choose.
| Hunter 2 | ||
|---|---|---|
| Hunt stag | Hunt hare | |
| Hunter 1Hunt stag | NE44 | 02 |
| Hunt hare | 20 | NE22 |
A ringed payoff is that player’s best response to the rival’s choice. A cell where both are ringed is a Nash equilibrium.
What the matrix says
Hunter 1 — dominant strategy: none
Hunter 2 — dominant strategy: none
Nash equilibrium (pure): (Hunt stag, Hunt stag) · (Hunt hare, Hunt hare)
Both-stag and both-hare are each Nash equilibria — no dominant strategy, no temptation to betray. If you’re certain your partner hunts stag, you absolutely want to hunt stag too (4 beats 2). The entire problem is uncertainty about the other player. This gives us two famous labels for the two equilibria:
- (Hunt stag, Hunt stag) = (4, 4) is payoff-dominant — the equilibrium that’s simply best for everybody. It’s what you’d choose in a heartbeat if you could trust your partner.
- (Hunt hare, Hunt hare) = (2, 2) is risk-dominant — the safe equilibrium. Hunting hare guarantees you 2 no matter what your partner does, while hunting stag exposes you to the dreaded 0 if they flake. When you’re unsure, the cautious move is hare.
The whole drama of the stag hunt is the tension between these two: the best outcome and the safe outcome are different equilibria, and which one a pair lands on comes down to trust and assurance. This makes it the model for an enormous range of situations where cooperation is best for all but requires everyone to stick their neck out together: launching a startup with co-founders, a team adopting a demanding new process, a group choosing to adopt a new standard, citizens turning out for a risky collective action — even the logic of a bank run, where keeping your money in the bank is the good equilibrium but only if you trust everyone else not to panic-withdraw first.
A stag hunt is NOT a prisoner's dilemma
This is the distinction that trips up almost everyone, so lock it in. In a prisoner’s dilemma, cooperation is not an equilibrium at all — defection is dominant, so the good outcome isn’t stable and no amount of trust can save it; you have to change the payoffs. In the stag hunt, cooperation is an equilibrium — (Stag, Stag) is a perfectly stable resting point. The problem here isn’t domination, it’s selection: two good candidates and the fear that your partner won’t pick the ambitious one. That’s why trust, communication, and credible signals — useless in a true dilemma — are exactly what unlock the stag hunt.
Practice: selection, not domination
Sort each situation. Is it a coordination problem — several equilibria, solved by a focal point or convention — or a genuine prisoner's dilemma, where defection is dominant and the trouble is temptation, not selection?
Place each item in the right group.
- Deciding which side of the road a new country will drive on
- An industry deciding which of two rival file formats to standardise on
- Two strangers picking the same landmark to meet at, with no way to talk
- Two firms each tempted to secretly cut prices below an agreed cartel price
- Two friends get cut off mid-call and each must decide whether to be the one who calls back
- Two nations each better off polluting regardless of what the other does
In a stag hunt, hunting stag together yields the best outcome for both, but hunting hare guarantees a safe payoff no matter what your partner does. You have no idea whether your partner is trustworthy. Which equilibrium is 'risk-dominant,' and why might a cautious player pick it even though it's worse for everyone?
Match each idea to its defining feature.
Pick a term, then click its definition.
Fill in the core vocabulary of coordination.
Pick the right option for each blank, then check.
A game with several equally-stable equilibria and no built-in way to choose is a game, and picking among the candidates is the problem. Players often solve it with a — an option made obvious by shared context. In a stag hunt the best-for-everyone equilibrium is , while the safe one that guards against a flaky partner is .
The strategic lever is the focal point
When a situation has multiple equilibria, the most powerful move usually isn’t outsmarting the other players — it’s creating a focal point so everyone converges on the same one. Set a default, publish a standard, announce a schedule, name a meeting place, make one option conspicuously the obvious choice. You’re not changing anyone’s incentives; you’re giving every player the shared expectation they need to coordinate. In coordination games, whoever supplies the focal point often quietly decides the outcome.
When to use it
Reach for the coordination lens whenever success depends on matching other people rather than outguessing them — adopting a shared standard or platform, agreeing on a convention, meeting up without a plan, getting a team to commit to the same risky bet. Ask first whether interests are aligned (you all want the same thing) or conflicting (someone’s tempted to defect); if aligned, you’re in a coordination game and the question is which equilibrium, not whether to trust the payoffs. Then check whether the equilibria are equal (pure coordination — any convention works) or unequal (a standards game — beware getting locked onto the inferior one), and whether risk and trust are in play (a stag hunt — the safe equilibrium may win even when it shouldn’t). In every case, the winning intervention is the same shape: manufacture the focal point that lets everyone land on the good equilibrium together.
Every game in this lesson had at least one cell where both players could happily come to rest. But some games have none — no pure combination of choices is stable, because whatever the two players settle on, at least one of them always has a reason to deviate. When there’s no equilibrium to sit still at, players are forced to become unpredictable on purpose. That’s the strange and beautiful world of the next lesson, No Pure Equilibrium: Mixed Strategies — where the only way to stop being exploited is to keep your rival guessing.