John Nash: When No One Gains by Switching

Why it attracts me

Some patterns last even though nobody would choose them from scratch. A team keeps a process everyone complains about. Two people keep an argument going because neither wants to be the first to soften. John Nash gave me a precise way to think about why. His idea, now called the Nash equilibrium, describes a situation where no player can do better by changing their own choice alone, as long as the others keep theirs. In 1994 he shared the Nobel prize in economics for this work.

The idea

A game here means players, the choices open to each, and how each player values the possible results (Choices That Depend on Other People). A Nash equilibrium is a set of choices, one per player, where each choice is already the best reply to the others. Nobody has a reason to switch alone. Nash showed in 1950 that every game with a limited number of players and choices has at least one such point, if players are allowed to mix their choices at random.

Two things often get lost. First, an equilibrium is not the best outcome. It is only a point where no one gains by moving alone. Second, it belongs to a game that has been spelled out. Without stated players, choices and values, calling a life pattern an equilibrium is only a loose comparison.

What I think (and don't know)

I think the idea explains why change is often hard. If a better pattern needs everyone to move together, no single person can get there by acting alone. That is why building trust over many rounds (Trust Built Over Many Rounds) or changing the rules (Cooperation by Changing the Game) can matter more than trying harder.

I am less sure how far the idea stretches. Real people do not always choose their best reply. They learn, misread each other, and care about more than the payoff. I use the idea as a sharp question, not a full explanation of anyone's life.

Where it connects

Nash is one of two thinkers, with Hugh Everett (Hugh Everett: Quantum Measurement Without Collapse), who inspire a family name and a personal picture of choice and possibility (A Family Name Inspired by Everett and Nash). They worked in different fields on different problems. Stable life patterns can resemble equilibria, but Nash's mathematics says nothing about branching worlds or a journey through realities (Life as a Journey Shaped by Choices).

An example

Imagine two coworkers, Ana and Ben, who each decide whether to share their notes before a joint review. These are made-up teaching numbers, and higher is better:

• Both share: each gets 3.
• Only one shares: the sharer gets 0 and the other gets 4.
• Neither shares: each gets 1.

If Ben shares, Ana does better keeping her notes (4 instead of 3). If Ben keeps his, Ana still does better keeping hers (1 instead of 0). The same holds for Ben. So "neither shares" is the only Nash equilibrium, even though both sharing would give each of them 3 instead of 1. This is the prisoner's dilemma: stable, but not ideal.

Questions I am still carrying

• Which patterns in my life hold because no one gains by changing alone, and which are just habit?
• What does it take for a group to move together to a better pattern?
• Where am I calling something stable when I really mean stuck?

Questions I'm still exploring

• Which patterns in my life hold because no one gains by changing alone, and which are just habit?
• What does it take for a group to move together to a better pattern?
• Where am I calling something stable when I really mean stuck?

Sources and further reading

• NobelPrize.org, "John F. Nash Jr. – Facts" — 1994 prize, shared, "for their pioneering analysis of equilibria in the theory of non-cooperative games".
• John F. Nash Jr., "Equilibrium Points in n-Person Games," Proceedings of the National Academy of Sciences 36(1): 48–49 (1950)