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Von Neumann's work in game theory culminated in his 1944 book Theory of Games and Economic Behavior, co-authored with Oskar Morgenstern. [12] The second edition of this book provided an axiomatic theory of utility, which reincarnated Daniel Bernoulli's old theory of utility (of money) as an independent discipline. This foundational work ...
Example game of Dots and Boxes on a 2×2 square board. The second player ("B") plays a rotated mirror image of the first player's moves, hoping to divide the board into two pieces and tie the game. But the first player ("A") makes a sacrifice at move 7 and B accepts the sacrifice, getting one box.
Sequential game: A game is sequential if one player performs their actions after another player; otherwise, the game is a simultaneous move game. Perfect information : A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them.
The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and ...
In game theory, "guess 2 / 3 of the average" is a game where players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player(s) who select a number closest to 2 / 3 of the average of numbers chosen by all players.
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...
The core sections of the Companion are aimed primarily at readers who are already familiar with mathematics at the undergraduate level. [2] [5] Much of the rest of the book, such as its collection of biographies, would be accessible to a mathematically inclined high school student, [2] [3] [6] and there is enough depth of coverage in the book ...
In game theory, normal form is a description of a game. Unlike extensive form , normal-form representations are not graphical per se , but rather represent the game by way of a matrix . While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria , some information is lost as compared to extensive ...