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Concept

Zero-sum game

A game in which one party's gain is exactly the other's loss, so the whole situation is described by a single number per cell. Mixing forces the two cautious valuations to coincide, and that common value is what each side can guarantee whatever the other does.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The value of a 2×3 zero-sum game, named from both sides. The row chooser's expected payoff against each column as a line over the mixing probability, with the lower envelope and its maximum, beside the same construction from the column chooser's side. Both give 19/15.

The value from both sides

Two choosers move at the same instant, and each asks the cautious question — how much can be guaranteed, whatever the other does. With pure choices the two answers are usually different numbers; allow a probability and they are forced to be the same one.

applied · Equilibrium A signal both can see, and neither wants to disobey. A two-by-two game with a distribution over its four cells, drawn as the weight on each. Obeying the recommendation is a best reply for both choosers, and the pair collects 21/2 between them.

A signal both can see

Two choosers who randomise privately can reach a set of outcomes that is smaller, and worse, than the set they reach when a device draws one cell and whispers each of them their half of it. Nothing is enforced and nobody is bound, and the arrangement is stable anyway.

applied · Equilibrium

Named alongside it

The objects these essays reach for when they reach for this one.

Correlated equilibriumLinear programMixed strategyNash equilibriumBest replyConditional probabilityConvexityDominant strategyDualityExhaustive searchExistence proofMinimax

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