Question: Consider a situation in which two major companies are in the process of devising a plan to compete for securing a very lucrative business contract. Let us assume that each company has three alternatives (low bid, medium bid, and high bid). These alternatives and their respective payoffs can be reflected in the form of a 2-person, zero-sum game, as shown in the table. Our problem is to identify the optimal strategy for each of the two companies.

B₁ B₂ B₃

A₁ 2 5 7

A₂ -1 2 4

A₃ 6 1 9

a. Show that the game does not have a saddlepoint.

b. Reduce the game matrix using the rule of dominance.

c. Solve the reduced game using the analytic method.

d. Check your solution by using the linear programming method on the original game matrix.