2. Consider the two-person zero-sum game with the following 2x2 pay-off matrix:
1 2
1 а11 а12
2 a21 a22
Show that if the game has no pure strategy and saddle point, player II should play
strategy 1 with the following probability;
a22-a12
(a1-a12)+(a22-az1)
91
Example: Mr. Stoneguy, a wealthy diamond dealer, decides to reward his
son by allowing him to select one of two boxes. Each box
contains three stones. In one box two of the stones are real
diamonds, and the other is a worthless imitation; and in the other
box, one is a real diamond, and the other two are worthless
imitations. If the son were to choose randomly between the two
boxes, his chance of getting two real diamonds is 0.5. Mr.
Stoneguy then suggested that he will allow his son to draw one
stone from one of the boxes and to examine it to see if it is a
real diamond and to decide which box to select. The son agreed
and decided to take the box that the stone he tested came from if
the tested stone is real and to take the other box otherwise. Will
this strategy increase the son's chance of getting two real
diamonds?
There are 2 stages in this experiment:
Stage 1- selection of box at random
Stage 2 - selection of stone at random from the selected box
in Stage 1
Let A = event of…
The following is a payoff matrix for a 4x4 game between A (column player and B
(row player). What is the expected value of this game if both players picked their
(row or column) at random?
-3 4 1 -2
-2 -3 4 1
1-2 -3 4
4 1-2 -3
Chapter 11 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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