Value modification

Suppose that G is a matrix game with value v. Proof that k*G has value k * v for any positive real number k.

Give an example of a game where G has value v but ?G has a value other than ?v.

Addition

Suppose that G,H are matrix games with the same number of row and column strategies, and that they have a mixed strategy

solution in common.

Prove that if the value of G is v1 and the value of H is v2 , then the value of G + H is v1 + v2 . Give an example of G, H which only

have a common row strategy, but for which G + H has a different value than v1 + v2.