Theory of Combinatorial Games

Aviezri S. Fraenkel, Robert A. Hearn and Aaron N. Siegel

Chapter 15 in Handbook of Game Theory with Economic Applications, 2015, vol. 4, pp 811-859 from Elsevier

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 along scenic mountain trails illustrate the theory. Add-on:Atasteof constraint logic, a new tool to prove intractabilities of games.

Keywords: Combinatorial game theory; Partizan games; Misère play; Nim; Chess; Go; Impartial games; Sprague-grundy theory; Computational complexity; Constraint logic (search for similar items in EconPapers)
JEL-codes: C72 C79 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamchp:v:4:y:2015:i:c:p:811-859

DOI: 10.1016/B978-0-444-53766-9.00015-X

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