The fundamental theorem of game theory which states that every finite, zero-sum, two-person game has optimal mixed strategies. It was proved by John von Neumann in 1928. Formally, let X and Y be mixed strategies for players A and B. Let A be the payoff m
This is especially important inzero-sum games, in which the minimaxalwaysgives aNash equilibriumof the game, as the minimax and maximin are necessarily equal. Minimax theorem Theminimax theoremestablishes conditions on when the minimax and maximin of a function are equal. More precisely, the minima...
origins of game theoryjohn von neumannjean villeVon Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement ...
Twitter Google Share on Facebook minimax (redirected fromMinimax theorem) Encyclopedia min·i·max (mĭn′ə-măks′) adj. Of or relating to the strategy in game theory that minimizes the maximum risk for a player. [mini(mum)+max(imum).] ...
Elements of the KKM theory for generalized convex spaces and G -convex space versions of the von Neumann type minimax theorem and the Nash equilibrium theorem as typical examples of applications of our theory.do... S Park - 《Korean Journal of Computational & Applied Mathematics》...
It is well known that minimax theorems are important in the areas of game theory, and mathematical economical and optimization theory (see [1–5]). Within recent years, many generalizations of minimax theorems have been successfully obtained. On the one hand, the minimax theorem of two functions...
sdevel- opmentoftheminimaxtheoremfortwo-personzero-sumgamesfromhisfirstproofof thetheoremin1928until1944whenhegaveacompletelydifferentproofinthefirst coherentbookongametheory.IwillarguethatvonNeumann’sconceptionofthistheo- remasatheorembelongingtothetheoryoflinearinequalitiesaswellashisawareness ofitsconnection...
Part of the book series:Progress in Nonlinear Differential Equations and Their Applications(PNLDE, volume 24) Accesses Table of contents (9 chapters) Front Matter Pages i-viii Download chapterPDF Introduction Michel Willem Pages 1-5 Linking theorem ...
We establish the following theorems: (i) an existence theorem for weak type generalized saddle points; (ii) an existence theorem for strong type generalize... T Tanaka - 《Journal of Optimization Theory & Applications》 被引量: 262发表: 1994年 ...
Twitter Google Share on Facebook minimax criterion [′min·ə‚maks krī‚tir·ē·ən] (statistics) A concept in game theory and decision theory which requires that losses or expected losses associated with a variable that can be controlled be minimized, and thus maximizes the losses or...