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)] .