Abstract: Matrix games can often be very large, which isn't a problem if our goal is simply to find one solution, as the simplex algorithm finds one solution quickly. If we want to find the entire solution set, however, we need to use a different algorithm, known as Shapley-Snow algorithm. This algorithm has a very large run time. The talk will present an alternative which uses the one solution given by the simplex algorithm to simplify the computations. The talk will briefly describe the definitions for matrix games and their solutions along with each algorithm involved.