Complexity, appeal and challenges of combinatorial games

Studying the precise nature of the complexity of games enables gamesters to attain a deeper understanding of the difficulties involved in certain new and old open game problems, which is a key to their solution. For algorithmicians, such studies provide new interesting algorithmic challenges. Substantiations of these assertions are illustrated on hand of many sample games, leading to a definition of the tractability, polynomiality and efficiency of subsets of games. In particular, there are tractable games that need not be polynomial, polynomial games that need not be efficient. We also define and explore the nature of the subclasses PlayGames and MathGames. (C) 2003 Elsevier B.V. All rights reserved.