The TwoPersonZeroSumGame class represents a data type for computing optimal row and column strategies to two-person zero-sum games.

This implementation solves an M-by-N two-person zero-sum game by reducing it to a linear programming problem. Assuming the payoff matrix A is strictly positive, the optimal row and column player strategies x* and y* are obtained by solving the following primal and dual pair of linear programs, scaling the results to be probability distributions.

(P)  max  y^T 1         (D)  min   1^T x
     s.t  A^T y <= 1         s.t   A x >= 1
              y >= 0                 x >= 0

If the payoff matrix A has any negative entries, we add the same constant to every entry so that every entry is positive. This increases the value of the game by that constant, but does not change solutions to the two-person zero-sum game.

This implementation is not suitable for large inputs, as it calls a bare-bones linear programming solver that is neither fast nor robust with respect to floating-point roundoff error.