Max-Min problems are two-step allocation problems in which one side
must make his move knowing that the other side will then learn what
the move is and optimally counter. They are fundamental in parti
cular to military weapons-selection problems involving large
systems such as Minuteman or Polaris, where the systems in the mix
are so large that they cannot be concealed from an opponent. One
must then expect the opponent to determine on an optlmal mixture
of, in the case men tioned above, anti-Minuteman and anti-submarine
effort. The author's first introduction to a problem of Max-Min
type occurred at The RAND Corporation about 1951. One side
allocates anti-missile defenses to various cities. The other side
observes this allocation and then allocates missiles to those
cities. If F(x, y) denotes the total residual value of the cities
after the attack, with x denoting the defender's strategy and y the
attacker's, the problem is then to find Max MinF(x, y) = Max
MinF(x, y)] ."
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