Would you please explain detailedly how to solve it Thank yo

Would you please explain detailedly how to solve it? Thank you.

In general, a sure-fire test may be stated thus: For a given m times n game, conjectured optimal strategies (p_1,...,p_m) and (q_1,..., q_n) are indeed optimal if the minimum of I\'s average payoffs using (p_1,...,p_m) is equal to the maximum of II\'s average payoffs using {q_1,...,q_n). Show that for the game with 8 times 8 matrix the mixed strategies p = q = l/117(0,0,32,60,0,16,0, 9)^T are optimal for I and II. What is the value? What about p = q= 1/87(0,0,32,36,0,16,0,3)^T?

Solution

Let the given matrix denoted by A.Then players I\'s average payoff vector using p for players II\'s 8 possible choice of coloumn in pA.And players II\'s using q of players I\'s eight possible choices of rows in Aq.The minimum of pA = maximum of Aq.