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单词 maximin
释义

maximinadj.n.

Brit. /ˈmaksɪmɪn/, /ˌmaksɪˈmɪn/, U.S. /ˈmæksiˌmɪn/
Forms: 1900s– maxi-min, 1900s– maximin.
Origin: Formed within English, by compounding. Etymons: maximum n., minimum n.
Etymology: < maxi- (in maximum n.) + min- (in minimum n.), after minimax adj. Compare max-min adj. and n.
Originally Economics.
A. adj.
Of, relating to, or designating a strategy that maximizes the smallest gain that can be relied on by a participant in a game or other situation of conflict. Cf. minimax adj.
ΘΚΠ
society > leisure > sport > types of play, actions, or postures > [adjective] > strategy
game1840
maximin1949
multiflex1977
the world > action or operation > prosperity > success > mastery or superiority > [adjective] > specific advantage
minimax1947
maximin1949
zero-sum1965
1949 Econometrica 17 184 The policy of ‘minimax regret’..may..be a plausible description of the actual behaviour of some individuals. But individuals of different temperaments might follow different policies: e.g. ‘maximin complacency’.
1954 D. Blackwell & M. A. Girshick Theory Games & Statist. Decisions i. 27 ξ0 is called a maximin strategy for player I.
1957 R. D. Luce & H. Raiffa Games & Decisions iv. 81 A strategy which dictates choices c and g on moves 2 and 4, respectively, cannot be maximin for this game.
1972 J. Rawls Theory of Justice §26. 152 The maximin rule tells us to rank alternatives by their worst possible outcomes.
1999 Nature 8 July 129/1 In a way, von Neumann was right. On the other hand, his own celebrated maximin theorem reduces to a corollary of Nash's existence proof.
B. n.
= max-min n.
ΘΚΠ
the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem
pons asinorum1718
Fermat's theorem1845
Bernoulli's theorem1865
Fermat's last theorem1865
Fourier's theorem1880
remainder theorem1886
Stokes' theorem1893
Jordan('s) (curve) theorem1900
Waring's theorem1920
Gödel's theorem1933
maximin1953
incompleteness theorem1955
Schwarz inequality1955
1953 Amer. Econ. Rev. 43 399 The player is maximizing the minimum pay off, or ‘playing the maximin’.
1958 Engineering 21 Mar. 369/2 Player A will thus determine the smallest value in each row and choose the largest of these minima, the ‘maximin’.
1970 G. S. G. Beveridge & R. S. Schechter Optimization xii. 656 This result represents the mini-max theorem of von Neumann and Morgenstein [sic] (1953), which states that A's expected gain is at least P, and B's expected loss is at worst L, where P = L... The value of P (and L) lies between the row maxi-min and the column mini-max.
This entry has been updated (OED Third Edition, March 2001; most recently modified version published online March 2022).

maximinv.

Brit. /ˈmaksɪmɪn/, U.S. /ˈmæksiˌmɪn/
Origin: Formed within English, by conversion. Etymon: maximin adj.
Etymology: < maximin adj. Compare maximining n.
rare. Chiefly Economics.
1. transitive. To make equal to a maximin value.
ΚΠ
1949 Amer. Econ. Rev. 39 205 Minimaxing the loss or, as I would prefer to put it, maximining profits.
2. intransitive. To adopt or employ a maximin strategy.
ΚΠ
1953 Amer. Econ. Rev. 43 402 The Nash definition yields the same saddle-point solution that is implied by the von Neumann-Morgenstern solution concept (i.e., it corresponds to both players maximining).
1973 Philos. Q. 23 248 He thinks that POPs would, in choosing their principles, ‘maximin’—that is to say, choose which has the best worst outcome.
This is a new entry (OED Third Edition, March 2001; most recently modified version published online March 2022).
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adj.n.1949v.1949
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