Von Neumann's minimax theorem
Statement
In a two-player zero-sum game with finite strategy sets, the minimax value equals the maximin value. There exists a value v and optimal (possibly mixed) strategies for both players such that the first player can guarantee at least v and the second can guarantee at most v. This founded the mathematical theory of games.
Formula
minimax = maximin
Equation
max_x min_y u(x,y) = min_y max_x u(x,y) = v
Source
von Neumann, Zur Theorie der Gesellschaftsspiele, 1928.
Domains
mathematics, economics, game-theory