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

Question

Determine whether the two-person, zero-sum matrix game is strictly determined.(these are matrix numbers below but I entered them as a column)

1.Yes, it is strictly determined.

2.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 to play row _____

The optimal strategy for the column player is to play column _____

(c) Find the value of the game _____

(d) Determine whether the game favors one player over the other.

1.It favors the row player.

2.It favors the column player.

3.It is fair.

4.It is not strictly determined. (DNE)

Explanation / Answer

Considering what you wrote, and I quote, "these are matrix numbers below but I entered them as a column", I understand that you mean row1 consists of (4,-1,2) and the second row consists of (3,-2,1). For this matrix,

1. It is strictly determined because, in game theory, a strictly determined game has at least one Nash equilibrium with both players using pure strategies.

2. (a) Saddle point is the lowest number in its row and highest in its column. Hence, -1 is the saddle point.

(b) The optimal strategy for row player 1 would be to choose (4,-1,2) over (3,-2,1). And that of the column player will be of choosing (4,3) over (-1,-2) and (2,1).

(c) The value will be -1 as that is the saddle point. Min(row) Max(column) x = Max(row) min(column) x = v (Value)

(d) It favors the row player as he has more profit over the column player.

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