What is a Nash equilibrium?
In a Nash equilibrium, each player’s strategy is a best response to the others’, so nobody gains by deviating unilaterally. John Nash proved in 1950 that every finite game has at least one equilibrium in mixed strategies; he shared the 1994 Nobel Prize in economics.
📌 At a glance
- Proposed by
- John Nash (1950)
- Condition
- Mutual best responses
- Existence
- Guaranteed in mixed strategies for finite games
- Classic example
- Prisoner’s dilemma
Example
In the prisoner’s dilemma, confessing is better whatever the other does, so (confess, confess) is the equilibrium, even though mutual silence would leave both better off. Equilibria need not be Pareto optimal, may be multiple, or may exist only in mixed strategies (rock-paper-scissors).
Frequently asked questions
- What is a Nash equilibrium?
- A strategy profile where no player benefits from changing strategy alone.
- Is a Nash equilibrium always efficient?
- No; the prisoner’s dilemma shows it can be worse for everyone.
References
- Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1), 48–49.
- Nash, J. (1951). Non-cooperative games. Annals of Mathematics, 54(2), 286–295.