Nash equilibrium
A profile where every player is already playing a best response to the others.
Often misread asReading equilibrium as the outcome the players should want, and so rejecting mutual defection in the prisoner's dilemma as 'not really an equilibrium' on the grounds that both would prefer mutual cooperation.
How to see it
Nobody wishes they had done otherwise
A combination of choices, one per player, such that no player, told exactly what everyone else is doing, would want to change their own. It is a situation that holds still. It says nothing whatever about whether anyone is pleased with it.
The checkEquilibrium asks whether anyone can gain by moving alone, not whether everyone could gain by moving together.
Try itPoint at mutual defection in the prisoner's dilemma and ask each player separately: given that the other defects, would you rather have cooperated? Both say no, and that is the entire proof, even though both would rather be in the opposite corner.
Games that show it
- All-pay auction
- Assurance game
- Bank run game
- Battle of the sexes
- Bertrand competition with differentiated products
- Bertrand duopoly
- Braess's paradox
- Chicken
- Committee voting game
- Cournot duopoly
- Deadlock
- Driving convention
- Dutch auction
- El Farol bar problem
- English auction
- First-price sealed-bid auction
- Harmony
- Hawk-dove
- Hotelling linear city
- Investor coordination game
- Keynesian beauty contest
- Matchmaker game
- Median voter game
- Nash demand game
- Partnership effort
- Penalty kick
- Cyclic population game
- Rock paper scissors
- Second-price sealed-bid auction
- Stag hunt
- Traveller's dilemma
- War of attrition in continuous time
- A zero-sum game with a saddle point
Know these first
Leads on to
- Backward induction
- Bayesian incentive compatibility
- Bayesian Nash equilibrium
- Congestion game
- Coordination
- Coordination failure
- Correlated equilibrium
- Evolutionarily stable strategy
- Focal point
- Free rider problem
- Locally envy-free equilibrium
- Mixed strategy
- Payoff dominance
- Quantal response equilibrium
- Race to the bottom
- Risk dominance
- Selfish mining
- The shadow of the future
- Subgame perfect equilibrium
- Tragedy of the commons
- Trembling hand perfection
Easily confused with
Sources
- Nash, J. (1950). PNAS 36(1), 48-49.