5 A two-person zero-sum game with an n n reward matrix A is a symmetric game if A  AT.

a Explain why a game having A  AT is called a symmetric game.

b Show that a symmetric game must have a value of zero.

c Show that if (x1, x2, . . . ,xn) is an optimal strategy for the row player, then (x1, x2, . . . ,xn) is also an optimal strategy for the column player.

d What examples discussed in this chapter are symmetric games? How could the results of this problem make it easier to solve for the value and optimal strategies of a symmetric game?