Backward induction and the game-theoretic analysis of chess

Ewerhart, Christian (2002). Backward induction and the game-theoretic analysis of chess. Games and Economic Behavior, 39(2):206-214.

Abstract

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.

Abstract

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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