Nash Equilibrium

A Nash equilibrium is a combination of strategies (one per player) where no player can improve their payoff by unilaterally changing their choice. Everyone is best-responding to everyone else. The system is stable because no one has incentive to deviate.

John Nash proved in 1950 that every finite game has at least one such equilibrium (possibly in mixed strategies). The result earned him a share of the 1994 Nobel Prize in Economics. The concept became the central solution concept in non-cooperative game theory — the default answer to “what will happen in this game?”

Consider two cars approaching an intersection. Each can go or wait. If both go, they crash. If both wait, they waste time. The equilibria: one goes, one waits. Either configuration is stable — given what the other is doing, neither wants to change. The problem is coordinating on which equilibrium.

Nash equilibrium doesn’t predict which equilibrium will occur, only which configurations are stable. Multiple equilibria are common. Which one emerges depends on history, focal points, conventions — factors outside the formal model.

The concept has limits. Finding Nash equilibria is computationally hard. Players may not know others’ payoffs. They may not reason through the infinite regress of “I think you think I think.” They may not be rational in the way the model assumes. Real behavior often fails to match equilibrium predictions.

But deviations from Nash equilibrium are informative. If people don’t play equilibrium strategies, something explains why. Maybe they have incomplete information. Maybe they have other-regarding preferences. Maybe they’re learning. The equilibrium is a benchmark for measuring departure.

Some Nash equilibria are clearly bad. The prisoner’s dilemma has a unique equilibrium where both players defect, even though both would prefer mutual cooperation. The equilibrium is stable (neither can improve by unilaterally cooperating) but it’s collectively irrational. Stability doesn’t mean desirability.

This reveals the core insight: Nash equilibrium is about individual best-response, not collective welfare. It explains why self-interested agents end up where they end up, including places no one would choose. Solving coordination failures requires changing the game, not the players.