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Two-player turn-based perfect-information games, surreal numbers, impartial games and Sprague-Grundy theory, partizan games
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Two-player item picking game
Two players $A$ and $B$ play this game: There are $n$ items, where the $i$th item is of value $a_i$ to player $A$ and is of value $b_i$ to player $B$. Two players take turns picking items, and each pl …