16/12/04 13:18:43.16 gDf64zAj.net
>>64 付録
便宜のためgame1の部分を抜粋する （原文PDFの方が見やすいだろうが）
URLﾘﾝｸ(www.ma.huji.ac.il) PUZZLES ”Choice Games”Sergiu Hart November 4, 2013
Choice Games November 4, 2013
Consider the following two-person game game1:
・ Player 1 chooses a countably in?nite sequence x = (xn)n∈N of real numbers, and puts them in boxes labeled 1,2, ...
・ Player 2 opens all the boxes except one, in some order, and reads the numbers there; then he writes down a real number ξ.
・ The unopened box, say box number i, is opened; if xi = ξ then Player 2 wins, and if xi not = ξ then Player 1 wins.
Theorem 1
For every ε > 0 Player 2 has a mixed strategy in game1 guaranteeing him a win with probability at least 1 - ε.
Remark. The proof uses the Axiom of Choice.
つづく