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Theory of Combinatorial Games

Author

Listed:
  • Fraenkel, Aviezri S.
  • Hearn, Robert A.
  • Siegel, Aaron N.

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.

Suggested Citation

  • Fraenkel, Aviezri S. & Hearn, Robert A. & Siegel, Aaron N., 2015. "Theory of Combinatorial Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    • Handle: 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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    More about this item

    Keywords

    Combinatorial game theory; Partizan games; Misère play; Nim; Chess; Go; Impartial games; Sprague-grundy theory; Computational complexity; Constraint logic;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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