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Let be a matrix with entries
. The first player sets the initial entries of
. Subsequently the second player may switch any
row or column (multiply the row or column by )
and repeat this operation any number of times.
The second player's ``score'' is the quantity
which the second
player wishes to maximize. The second player's
gain is the first player's loss (zero-sum game),
so the first player's goal is to keep the second
player's score low.
Let denote the score an optimal Player 2 can
achieve against an optimal Player 1.

Laszlo Babai
2003-06-19