Equilibrium selection
Named by 7 essays across one field — each of them below, with the objects they name alongside it.
The landscape nobody is looking at
Letting participants move one at a time to whatever is currently better can cycle forever, and on a network of congestible roads it cannot. The reason is a single number attached to each state that falls by exactly what the mover saves.
Two equilibria and no way to choose
A game can have two states nobody wants to leave, one paying more than the other, and the definition of an equilibrium has nothing to say about which happens. The two standard tie-breakers disagree, and the one that wins is usually the worse.
A mixture that is a population
A mixed equilibrium between two choosers is a knife-edge nobody has a reason to stand on. Read the same mixture as a population whose shares grow with how well they do, and it becomes a point every population is carried to — or one every population circles for ever without arriving.
Worth more for being seen first
Moving first sounds like a disadvantage, since the other side gets to see the move and answer it. When the move is a mixture that is announced and believed, it is never a disadvantage, it is worth exactly nothing in a game of pure conflict, and in other games it is worth more than any equilibrium — sometimes by announcing an action that would never be played in secret.
Patience instead of a contract
Commitment had to assume an announcement binds. Play the same game again tomorrow and the assumption is unnecessary — the future does the binding. What it costs is that nearly every outcome becomes an equilibrium, so a theory that could not choose between two now cannot choose between infinitely many.
The reading that is almost right
Every account of simultaneous choice so far has assumed the payoffs are known to both choosers and known to be known. Replace that with each chooser seeing a private reading off by a little, and a band of equilibria closes to a single point — so the assumption nobody states decides the answer.
A market too large to bargain in
Two traders swapping goods can settle anywhere along a stretch of possible deals; nothing forces a price. Bring in a second pair of the same traders and some of those deals can be refused by a group of three. With thirty of each, the only deals no group can refuse lie within a few thousandths of the one a price would produce. Edgeworth guessed in 1881 that competition shrinks bargaining to prices; Debreu and Scarf proved it, and the shrinking can be computed.
Named alongside it
The objects these essays reach for when they reach for this one.
Best replyNash equilibriumExistence proofMixed strategyCommitmentConditional probabilityCongestionConvexityDominant strategyMinimaxPotential functionZero-sum game