Determine whether the two-person, zero-sum matrix game is strictly determined. [

Question

Determine whether the two-person, zero-sum matrix game is strictly determined. [0 2 6 3 5 4 -1 1 -4 1 6 -3] Yes, it is strictly determined. No, it is not strictly determined. If the game is strictly determined, answer the following. (If the game is not strictly determined, enter DNE for each.) (a) Find the saddle point of the game. (b) Find the optimal strategy for each player. The optimal strategy for the row player is row The optimal strategy for the column player is column (c) Find the value of the game. (d) Determine whether the game favors one player over the other. It favors the row player. It favors the column player. It is fair. It is not strictly determined. (DNE)

Explanation / Answer

If the largest of the row minima and the smallest of the column maxima occur at the same entry of the payoff matrix, then we say that the matrix has a saddle point at that location. In this case, we say the game is strictly determined and the value of the matrix entry at the saddle point is called the value of the game.

(a) Row minima is (0, 3, -4, -3)

Max of row minima is 3 which corresponds to row 2 and col 1

Col maxima is (3, 6, 6)

Min of Col maxima is 3 which corresponds to row 2 and col 1.

As, Max of row minima equals Min of Col maxima

Yes, it is strictly determined.

(a) Based on the above explanation, Saddle point of the game is (2,1)

(b)

Based on the above explanation,

optimal strategy for the row player is row 2

optimal strategy for the col player is column 1

(c)

Based on the above explanation, Value of the game is 3

(d)

As the value of the game is greater than 0, it favors the row player.

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