Nash Equilibrium
John Nash · 1950
"In any strategic game, a stable outcome exists where no player can improve their result by changing strategy alone — everyone is already playing their best response to everyone else."
Nash proved it in one page in 1950: every game has at least one point where nobody can do better by switching strategy alone. That point isn't necessarily the best outcome for anyone — just the one nobody can unilaterally escape.
A Nash equilibrium is a set of strategies, one per player, where each is the best response to everyone else, so no single player benefits from changing course alone. Nash's 1950 PNAS paper proved such a point always exists in any finite game, which is why it became the backbone of economics and auction design. An equilibrium can be collectively terrible, as in the prisoner's dilemma, while still individually unbeatable.
What makes a Nash equilibrium 'stable,' even when the outcome is bad for everyone involved?
Read more about the topic
The explanation above is written with AI assistance. These are the originals — go to them to check it.
- Equilibrium Points in N-Person Games (1950, PNAS)PubMed Central
The Prisoner's Dilemma
"Two rational actors who cannot communicate or trust each other will often choose mutual betrayal even when mutual cooperation would leave both better off."