Backward Induction And The Game-Theoretic Analysis Of Chess Christian Ewerhart Elsevier 2002.pdf

Games and Economic Behavior 39, 206᎐214Ž. 2002
doi:, available online at http:rr
Backward Induction and the Game-Theoretic
Analysis of Chess
Christian Ewerhart1
Department of Economics, Uni¨ersity of Mannheim, Ludolfusstrasse 5,
D-60487 Frankfurt ., Germany
E-mail: @-
Received September 26, 2000; published online February 20, 2002
This 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
chessᎏwhich 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 ment on Zermelo’sŽ. 1913 nonrepetition theorem. Journal of Economic
Literature Classification Number: C72. ᮊ 2002 Elsevier ScienceŽ. USA
Key Words: chess; minmax theorem; Zermelo’s theorem.
1. INTRODUCTION
The classic paper of ZermeloŽ. 1913 has long been thought to contain a
complete statement and proof of one of the first theorems of game theory,
namely the minmax theorem for chess. This theorem asserts th