For the 2 x 2 game find the optimal strategy for each player

For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas.

500    -200

000     300

For row player R:

r1=_________

r2=_________

For column player C:

c1=_________

c2=_________

Find the value v of the game for row player R.

v=__________

Solution

By definition, a saddle point is a pay off that is simultaneously a row minimum and a column maximum. In this case the row minima are 0 and -200 and the column minima are 500 and 300. So there is no saddle point.

For row player

R₁ = Min (Row 1) = -200

R₂ = Min (Row 2) = 0

For Column player

C₁ = Max (Column 1) = 500

C₂ = Max (Column 2) = 300

Value v of the game for the row player

      v= Min (Max(C₁ ,C₂ )) = Min (500,300) = 300