Combinatorial game theory

Combinatorial game theory (CGT) is a branch of applied mathematics and theoretical computer science that typically studies sequential games with perfect information. Study is largely confined to two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning condition. CGT has not traditionally studied games randomness and imperfect or incomplete information (sometimes called games of chance, like poker), favoring games whose position is public to both players, and in which the set of available moves is also public (perfect information). Combinatorial games include well-known games like chess, checkers, Go, Arimaa, Hex, and Connect6. They also include one-player combinatorial puzzles, and even no-player automata, like Conway's Game of Life. In CGT, the moves in these games are represented as a game tree.

Game theory in general includes games of chance, games of imperfect knowledge, and games in which players can move simultaneously, and they tend to represent real-life decision making situations.

Game theory

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, biology and poker. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

Game theory (disambiguation)

Game theory is the study of participants' behaviour in strategic situations.

Game theory may also refer to:

See also

Game Theory (album)

Game Theory is the seventh studio album by American hip hop band The Roots, released August 29, 2006, on Def Jam Recordings. The group's first release for the label after leaving Geffen Records, the album was recorded by the Roots mostly using the Apple-developed software application GarageBand. A darker, grittier album with minimal emphasis on hooks in comparison to their previous work,Game Theory features a stripped-down sound similar to the work of Public Enemy, with lyrics that concern sociological themes and the late hip hop producer J Dilla.

The album debuted at number nine on the U.S. Billboard 200 chart, selling 61,000 copies in its first week. It produced two singles and achieved moderate sales success. Upon its release, Game Theory received acclaim from most music critics and earned a Grammy Award nomination for Best Rap Album. To date, the album has sold over 200,000 copies in the United States.

Music

In an interview for Rolling Stone magazine, Questlove expressed his view on contemporary black music and described the concept of Game Theory, comparing it to previous works: