Matrix Games, Linear Programming, and Linear Approximation

qi = 1, pA ≥ v ≥ Aq. The number v is known as the value of game. The pair (p, q) is known as an equilibrium for the matrix game. As usual, x ≥ 0 means that every entry of the vector x is ≥ 0. We write y ≤ t for a vector y and a number t if every entry of y is ≤ t. We go even further in abusing notation, denoting by y− t the vector obtaining from y by subtracting t from every entry. Similarly we denote by M + c the matrix obtained from M by adding a number c to every entry.