Gourt > Science > Math > Combinatorics > Combinatorial Game Theory (1)
Combinatorial game theory (CGT) is a mathematical theory that only studies two-player games which have a position which the players take turns changing in defined ways or moves to achieve a defined winning condition. CGT does not study games of chance (like poker), but restricts itself to games whose position is public to both players, and in which the set of available moves is also public. CGT principles can be applied to games like chess, checkers, Go, Hex, Connect6 but these games are mostly too complicated to allow complete analysis (although the theory has had some recent successes in analyzing Go endgames).
Applying CGT to a position attempts to determine the optimum sequence of moves for both players until the game ends, and by doing so discover the optimum move in any position. In practice, this process is tortuously difficult unless the game is very simple.
CGT should not be confused with another mathematical theory, traditionally called game theory, used in the theory of economic competition and cooperation. Game theory includes games of chance, games of imperfect knowledge and games in which players move simultaneously.
More on [ Combinatorial game theory ]
Dots and Boxes :: Paper and Pencil
Sprouts :: Paper and Pencil
Game Theory :: Economics
StackExchange: Just starting with [combinatorial] game theory - http://stackexchangesites.com/hXk
stackexchange (stackexchange) Wed, 09 Dec 2009 02:49:37 -0000
StackExchange: Just starting with [combinatorial] game theory - http://stackexchangesites.com/hXk
Aviezri Fraenkel - A comprehensive bibliography on combinatorial games; several papers about combinatorial games; and information about where to publish such results.
David Eppstein - Combinatorial Game Theory - Many up-to-date links, and a short introduction.
Dice Theorem - How many ways are there of throwing n indistinguishable dice each with m faces?
Elwyn Berlekamp - Combinatorial Game Theory - Elwyn's research in the field, including several papers.
Erik Demaine's Combinatorial Games - Research on pushing blocks, Clickomania, Phutball, and sliding coins. Survey paper on algorithmic combinatorial game theory.
404
Games that interest John Conway - Clever Games for Clever People, from the book On Numbers and Games.
Jeff Erickson - Mathematical Games, Toys, and Puzzles - Links to several game theorists and actual games, plus a brief introduction. Also a couple of papers on game theory, about Toads and Frogs and Sowing Games.
| Nash Bargaining via Flexible Budget Markets | |
| Next Video | |
