The Art of Staying Still: Nash Equilibrium

What your dating life, and a salary negotiation have in common and why no one dares to change their mind.

Imagine you are sitting across from a stranger at a poker table. You have a decent hand. They might too. You could bluff. They might call. In that single, suspended moment before either of you moves lies one of the most profound ideas in all of mathematics: the Nash Equilibrium.

“In any game, there comes a moment where every player, knowing what the others will do, would not wish to do anything differently. That moment is Nash Equilibrium.”

Prisoner’s Dilemma

The most famous illustration is the Prisoner’s Dilemma. Two suspects are arrested. They are placed in separate rooms and offered a deal: betray your partner, and you go free while they serve three years. Stay silent, and you both serve one year. But if both of you betray each other you each serve two years.

Rationally, each prisoner thinks: Whatever my partner does, I am better off betraying. So both betray. Both serve two years — a worse outcome than if they had both stayed silent. This mutual betrayal is the Nash Equilibrium: no player can improve their outcome by switching strategies alone.

Two rational people, thinking clearly, end up worse off than two people who simply trusted each other. The equilibrium is stable, but it is not necessarily good.

The Heart’s Own Game Theory

Love, it turns out, is full of equilibria. Consider the early stages of a relationship — that agonizing period where both people feel deeply, but neither wants to be the first to say so. Each person thinks: If I confess my feelings and they don’t reciprocate, I am exposed and hurt. Better to wait. And so both wait. Both hold back. The relationship hovers in a warm but frustrating limbo that neither truly wants.

The same logic governs long relationships too. Partners who have drifted apart but stay together out of comfort, fear of the unknown, or the sheer inertia of a shared life. Leaving feels risky. Staying feels safe even if neither person is truly happy. The relationship reaches equilibrium not because it is good, but because neither person, acting alone, sees a better move.

This is why vulnerability is so powerful. It breaks the equilibrium. Someone has to move first and in doing so, they change the entire game.

The Salary Negotiation You Were Afraid to Have

Picture a job offer. The company has a number in mind. You have a number in mind. Neither of you reveals it first. The company extends a cautious opening offer, hoping you will accept without friction. You accept, telling yourself it would be awkward to push back. And just like that — politely, professionally, with smiles on both sides — you have left money on the table that was always yours to take.

The employer fears that a high opening offer signals desperation. The candidate fears that a bold counter signals ingratitude or aggression. So both retreat behind their fear. The resulting number satisfies no one fully — but it is stable. Neither party, acting alone, feels they can safely move away from it. This is the Nash Equilibrium of the hiring room: a mutual silence that punishes honesty and rewards whoever blinks last.

The trap is not greed. It is information asymmetry. Each side is playing against a version of the other they have invented in their head and both versions are more fearsome than the reality. The employer imagines the candidate will walk. The candidate imagines the offer will be rescinded. Almost none of these fears ever come true. But they feel real enough to keep everyone frozen.

In my next post, I’ll explore how to break these equilibria and why the first move, though uncomfortable, is often the one that changes everything.