Construct · 1 fields · 1 citations

saddle: a standalone construct

One name. One construct. A landmark on the map.

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saddle1 CONSTRUCTSaddle pointVON NEUMANN · MINIMAX

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Game theory and optimization

A minimax equilibrium of a payoff function

Von Neumann's 1928 Zur Theorie der Gesellschaftsspiele proved that a two-person zero-sum game has a saddle point: a pair of strategies where one player's smallest guaranteed gain equals the other's smallest guaranteed loss, so neither can do better by changing alone. At such a point the payoff function is a lowest value along one player's choices and a highest value along the other's, the shape that gives the point its name. The referent is an equilibrium of an abstract payoff function, proven and computed, not a dip in the ground or a joint in the hand.[1]

Unit
One pair of strategies that is a minimum along one axis and a maximum along the other
Recovery means
Not applicable
Measured by
Found by solving the minimax problem, for example by linear programming for a finite zero-sum game

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Nearby constructs

equilibrium4 fields · 4 citationsjingle · one word, four constructsgame2 fields · 3 citationsjingle · one word, two constructszero-sum2 fields · 3 citationsjingle · one word, two constructs

References

  1. von Neumann, J. (1928). Zur Theorie der Gesellschaftsspiele. Mathematische Annalen, 100(1), 295–320. https://doi.org/10.1007/BF01448847

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