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Chapter 15

Theory of Combinatorial Games

Aviezri S. Fraenkel* ^* Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel Robert A. Hearn† ^† H3 Labs LLC, Palo Alto, CA, USAAaron N. Siegel‡ ^‡ Twitter, San Francisco, CA, USA

Abstract

Aim: To present a systematic development of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Ascend from Nim to Chess and Go in small strides at a gradient that is not too steep. Presentation: Mostly informal; examples of combinatorial games sampled from various strategic viewing points ...

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