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
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).] ...
, the minimax strategy for both players gives a Nash equilibrium of the game. This is especially important in zero-sum games, in which the minimax always gives a Nash equilibrium of the game, as the minimax and maximin are necessarily equal. Minimax theorem The minimax theorem establishes ...
The meaning of MINIMAX THEOREM is a theorem in the theory of games: the lowest maximum expected loss equals the highest minimum expected gain.
Mountain pass theorem Michel Willem Pages 7-36 Linking theorem Michel Willem Pages 37-53 Fountain theorem Michel Willem Pages 55-70 Nehari manifold Michel Willem Pages 71-80 Relative category Michel Willem Pages 81-94 Generalized linking theorem ...
be considered more frequently in game theory, too. The outcome of all these terminology is that we can very succinctly summarize our proof presented for the case of binary losses: We can simply say that our minimax theorem is an immediate consequence of Kuhn’s theorem, von Neumann’s minimax...
The applications of minimax theory are also extremely interesting. In fact, the need for the ability to "switch quantifiers" arises in a seemingly boundless range of different situations. So, the good quality of a minimax theorem can also be judged by its applicability. We hope that this ...
First, it is established in a general setting --- one not permitting invocation of minimax theory --- that Blackwell's Approachability Theorem and its generalization due to Hou are still valid. Second, minimax structure grants a result in the spirit of Blackwell's weak-approachability conjecture...
This note provides an elementary and simpler proof of the Nikaid么-Sion version of the von Neumann minimax theorem accessible to undergraduate students. The key ingredient is an alternative for quasiconvex/concave functions based on the separation of closed convex sets in finite dimension, a result...