Backward Induction and the Game-Theoretic Analysis of Chess
The paper scrutinizes various stylized facts related to the minmax theorem for chess. We first point out that, in contrast to the prevalent understanding, chess is actually an infinite game, so that backward induction does not apply in the strict sense. Second, we recall the original argument for the minmax theorem of chess - which is forward rather than backward looking. Then it is shown that, alternatively, the minmax theorem for the infinite version of chess can be reduced to the minmax theorem of the usually employed finite version. The paper concludes with a comment on Zermelo's (1913) non-repetition theorem.
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- Mycielski, Jan, 1992. "Games with perfect information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 3, pages 41-70 Elsevier.
- Ewerhart, Christian, 2000.
"Chess-like Games Are Dominance Solvable in at Most Two Steps,"
Games and Economic Behavior,
Elsevier, vol. 33(1), pages 41-47, October.
- Ewerhart, Christian, 2000. "Chess-like games are dominancesolvable in at most two steps," Sonderforschungsbereich 504 Publications 00-24, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- Schwalbe, Ulrich & Walker, Paul, 2001. "Zermelo and the Early History of Game Theory," Games and Economic Behavior, Elsevier, vol. 34(1), pages 123-137, January.
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