What is Combinatorial Game Theory?
Q: What is Combinatorial Game Theory?
A: Combinatorial Game Theory (CGT) is a branch of applied mathematics and theoretical computer science that studies combinatorial games, and is distinct from "traditional" or "economic" game theory.
Q: What conditions must a game meet to be considered a combinatorial game?
A: For a game to be considered a combinatorial game, it must have at least two players, it must be sequential (i.e. Players alternate turns), it must have perfect information (i.e. no information is hidden), it must be deterministic (i.e. non-chance), luck cannot be part of the game, there must be a defined amount of possible moves, the game must eventually end, and the game must end when one player can no longer move.
Q: What type of games does Combinatorial Game Theory focus on?
A: Combinatorial Game Theory focuses largely on two-player finite games which have winners and losers (i.e., do not end in draws).
Q: How are these types of games represented?
A: These types of games can be represented by trees with each vertex representing the resulting game from particular move from the directly below it on the tree.
Q: What are some goals for CG theorists?
A: Some goals for CG theorists include finding values for these types of games as well as understanding the concept of “game addition” which involves each player making only one move in two different games leaving the other unchanged during their turn.
Q: Who founded CGT?
A: Elwyn Berlekamp, John Conway and Richard Guy are credited with founding CGT in their published work called Winning Ways for Your Mathematical Plays in the 1960s.
