单词 | maximin |
释义 | maximinadj.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. 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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