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A parent stands in the grocery store aisle. Their child is having a meltdown over a candy bar. “If you don’t stop screaming,” the parent says through gritted teeth, “we’re leaving this store right now and going straight home.”
The child keeps screaming.
Why? Because the child, perhaps unconsciously, has run a game theory calculation. Mom still has a cart full of groceries. She needs milk for tomorrow morning. She’s already invested twenty minutes selecting items. The threat isn’t credible.
This simple scene captures one of game theory’s most powerful insights: threats only work when they’re believable. And believability has nothing to do with how loud you say something or how angry you look. It has everything to do with whether following through serves your interests.
The Problem Every Threat Maker Faces
Think about the last time someone made a threat. Maybe a company threatened to take legal action if you didn’t pay a disputed bill. Maybe a coworker threatened to quit if they didn’t get a raise. Maybe a country threatened sanctions if another country didn’t change its behavior.
Now ask yourself: did they follow through? More importantly, should they have followed through?
This is where things get interesting. Making threats is easy. Following through is costly. And everyone knows it.
Consider a landlord threatening to evict a tenant for being three days late on rent. The eviction process takes months, costs thousands in legal fees, and leaves the unit empty during the proceedings. The tenant knows this. So does the landlord know that the tenant knows this? And does the tenant know that the landlord knows that the tenant knows?
Welcome to game theory.
When Backing Down Makes Sense
Here’s something that feels wrong but is mathematically correct: sometimes the best move after making a threat is to not follow through.
A software company threatens to sue everyone using pirated copies of their product. Sounds tough. But litigation costs millions. The company would spend more money on lawyers than they’d ever recover. Every user doing mental math realizes the threat is hollow.
The company faces a dilemma. Following through proves they’re serious but bankrupts them. Backing down proves they’re bluffing but saves money. Either way, they lose.
This is the threat maker’s trap. You want the other party to believe you’ll do something that, when the moment comes, you’d rather not do. The threat only works if they believe you. But if they think it through, they’ll realize you won’t follow through. So they won’t comply. Which means you either have to follow through anyway and hurt yourself, or back down and lose credibility forever.
The Backward Induction Test
Game theorists have a simple method for testing threat credibility. They call it backward induction, though the concept is straightforward enough that a child in a candy aisle intuitively grasps it.
Start at the end. Imagine the moment has arrived and you must decide whether to execute your threat. What happens if you do? What happens if you don’t? Which outcome do you prefer?
If you’d prefer to back down when the moment comes, your threat isn’t credible right now.
A country threatens to start a trade war if another country doesn’t lower tariffs. Both countries would lose billions in a trade war. When decision day arrives, starting that war would hurt the threatening country more than swallowing its pride. Everyone can see this from the beginning. The threat lacks bite.
But here’s where it gets counterintuitive. Sometimes making yourself worse off is the key to making your threat work.
The Power of Burning Bridges
Imagine two armies facing each other across a river. One army crosses the river and then, bizarrely, burns the bridge behind them. This seems insane. They’ve eliminated their own escape route.
But that’s exactly the point.
Now the opposing army knows: these soldiers will fight to the death because they have no choice. Retreat is impossible. What looked like a crazy move suddenly becomes terrifying. The opposing army might just decide to retreat instead of fighting an enemy with nothing to lose.
This is a commitment device. You remove your ability to back down, which makes your threat to stand and fight completely credible.
Consider a company locked in price negotiations with a supplier. The company’s CEO announces publicly in the press that they will never pay more than a certain amount. Now backing down means public humiliation and shareholder fury. The CEO has tied their own hands. The supplier knows that continuing to demand more won’t work because the CEO genuinely cannot agree, regardless of whether it makes business sense.
Commitment devices show up everywhere once you start looking. Union leaders who would lose face with members if they accepted certain terms. Politicians who make campaign promises that lock them into positions. Dating someone who announces you’re moving in together to all their friends before asking you, making it awkward to say no.
The strategy sounds paradoxical: reduce your own options to increase your power. But the math works out. When you can’t back down, others take your threats seriously.
The Madman Theory
This leads to an even stranger insight. Sometimes being seen as irrational helps.
If everyone believes you’re a cold, calculating decision maker, they can predict your moves. They know you won’t follow through on threats that hurt you. But if they think you’re a little crazy, that you might actually do something that harms your own interests just out of spite or principle or unpredictability?
Now your threats carry weight.
Richard Nixon allegedly wanted the Soviet Union to believe he was unstable enough to use nuclear weapons irrationally. Whether this was genuine or performance art doesn’t matter. The possibility that he might not behave according to standard rational actor models made his threats more credible, not less.
Parents sometimes understand this instinctively. The parent who occasionally does follow through on seemingly irrational threats, even when it’s inconvenient, builds a reputation. Their future threats become credible because their children genuinely aren’t sure whether they’ll follow through.
The lesson isn’t to become erratic. It’s that complete predictability can sometimes work against you in strategic situations.
How to Test Any Threat
You can evaluate any threat, whether you’re making it or receiving it, with three questions:
First, would following through benefit the threat maker after the fact? Not before, when they’re hoping you’ll comply. After, when you haven’t complied and they must decide what to do. If the answer is no, the threat is probably empty.
Second, has the threat maker created any commitment devices? Have they staked their reputation publicly? Signed contracts with penalties? Made moves that eliminate their ability to back down? Real commitment devices cost something to create and can’t be easily undone.
Third, does the threat maker have a reputation to maintain? This one’s tricky. If this is a one time interaction, reputation doesn’t matter much. But if they make threats regularly and need people to take future threats seriously, they might follow through even at a cost, to preserve credibility.
A debt collector threatening legal action over a small debt probably won’t sue. The cost exceeds the benefit in that single case. But if word spread that they never follow through, their entire business model collapses. So maybe they do sue occasionally, at a loss, to keep other debtors compliant.
When Threats Backfire
Sometimes making a threat damages your position even if it’s credible.
You’re negotiating a business deal. The other side is reasonable and working toward a mutually beneficial outcome. Then you issue an ultimatum: accept these terms by Friday or we walk away.
Even if you’d genuinely walk away, even if this threat is credible, what have you accomplished? You’ve turned a cooperative negotiation into a confrontational standoff. You’ve signaled distrust. You’ve made the other side angry or defensive. They might accept worse terms just to spite you, or walk away from a deal they would have made, simply because they don’t want to be bullied.
Credible threats aren’t always smart threats.
This matters in relationships, business, diplomacy, and everyday life. Just because you can make a believable threat doesn’t mean you should. The act of threatening changes the dynamic, often for the worse.
The Coordination Problem
Here’s a scenario that stumps people: Two companies are competing fiercely for market share. Company A threatens that if Company B lowers prices, Company A will match them and both companies will lose profits.
This seems like a credible threat. If Company B lowers prices, Company A really would match them because not matching means losing all their customers. And both companies would indeed be worse off.
So why doesn’t this threat work? Why do price wars happen constantly?
The answer lies in coordination failures. Company A’s threat only helps if Company B believes that by keeping prices high, both companies benefit. But Company B might think that if they lower prices first, they’ll capture market share before Company A reacts. Or Company A might think Company B is about to lower prices, so they’d better lower prices first as a preemptive move.
Even mutually harmful outcomes happen when neither side trusts the other to act cooperatively. The threat becomes credible but ineffective because both sides end up in the scenario they wanted to avoid.
This explains why countries sometimes stumble into wars nobody wanted, why environmental degradation continues even though it harms everyone, and why traffic jams persist even though all drivers would benefit from orderly merging.
What This Means for You
The next time someone threatens you, run backward induction. What would actually happen if you didn’t comply? Would they follow through? What would that cost them? Do they have a reputation to maintain? Have they built commitment devices?
Often you’ll find the threat is more bark than bite. Other times you’ll realize it’s genuine and you should take it seriously. Either way, you’ll make better decisions than just reacting emotionally.
And when you’re making threats, be honest with yourself. Can you actually follow through? Will you want to when the moment comes? If not, you’re probably better off not making the threat at all and finding another approach.
The most successful strategic actors aren’t the ones who make the most threats. They’re the ones who make threats rarely, follow through consistently, and understand that sometimes the best move is the one you never have to make because everyone knows you would.
The Grocery Store Revisited
Back to that parent in the grocery store. The child is still screaming. The cart is still full. But suppose the parent does something unexpected. They calmly abandon the cart, take the child’s hand, and walk out of the store.
It costs them time. They’ll need to come back later. They’ve made their day harder. But they’ve sent a signal. Next time, when they make a threat, their child will do backward induction and reach a different conclusion.
Sometimes following through on a threat that hurts you in the moment builds credibility that serves you for years. That’s the counterintuitive magic of game theory. The best strategic moves often look irrational until you zoom out and see the whole game.
The question isn’t whether your threat sounds convincing. It’s whether, when the moment comes, you’d genuinely rather follow through than back down. If the answer is yes, your threat is credible. If the answer is no, everyone who thinks it through will eventually figure that out.
