2017•Wuhan University Journal of Natural SciencesRequires access

a-Wythoff’s game with n players

Haiyan Li, Sanyang Liu

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Abstract

Letting a = 1 in a - Wythoff’s game introduced by Fraenkel yields Wythoff’s game which is a well-known 2-player impartial combinatorial game introduced by Wythoff in 1907. A method of solving n -player impartial games was presented by Krawec in 2012. In this paper, we employ Krawec’s function to analyze n > 2 players a -Wythoff’s game and obtain game values for all a 1. The results obtained cover n -player Wythoff’s game, a special case 1-Wythoff’s game.

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What this paper is about

Letting a = 1 in a - Wythoff’s game introduced by Fraenkel yields Wythoff’s game which is a well-known 2-player impartial combinatorial game introduced by Wythoff in 1907. A method of solving n -player impartial games was presented by Krawec in 2012. In this paper, we employ Krawec’s function to analyze n > 2 players a -Wythoff’s game and obtain game values for all a 1. The results obtained cover n -player Wythoff’s game, a special case 1-Wythoff’s game.

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Available abstract

Letting a = 1 in a - Wythoff’s game introduced by Fraenkel yields Wythoff’s game which is a well-known 2-player impartial combinatorial game introduced by Wythoff in 1907. A method of solving n -player impartial games was presented by Krawec in 2012. In this paper, we employ Krawec’s function to analyze n > 2 players a -Wythoff’s game and obtain game values for all a 1. The results obtained cover n -player Wythoff’s game, a special case 1-Wythoff’s game.

Key concepts: Combinatorial game theory, Computer science, Sequential game, Repeated game, Mathematical economics, Game theory, Mathematics

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