When everyone acts in self-interest, where does it settle? A Nash equilibrium is the stable outcome no player can improve on alone — the heart of game theory.
Game Theory (Nash)Live
2×2 strategic games
Row player vs Column player
Cooperate
Defect
Cooperate
3
3
0
5
Defect
5
0
1
1
Nash
cyan = row payoff · green = column payoff
Controls
A Nash equilibrium is a pair of strategies where neither player can do better by unilaterally changing — the cornerstone of game theory. In the Prisoner's Dilemma both defect even though cooperating pays more; Matching Pennies has no pure equilibrium at all. Highlighted cells are the pure-strategy Nash equilibria.
Reading this result: The lone equilibrium has both players defect, even though mutual cooperation pays more — individually rational, collectively worse.
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How it works
In a Nash equilibrium, each player's strategy is a best response to the others, so no one gains by deviating. The Prisoner's Dilemma shows how individually rational choices can leave everyone worse off; Matching Pennies has no pure equilibrium at all, only a mixed one. The highlighted cells are the pure-strategy Nash equilibria of each classic game.
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