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
ANswer all
1. Below is the Boeing-Airbus Game in the absence of any government policy. Suppose both governments subsidize their own producers by paying 25 if the firm enters.a. Redraw the game matrix to reflect the new payoffs.b. Find all Nash equilibria of the new game.
c. What are the welfare effects in each country, when both governments subsidize their own producer?
PRODUCE
DON’T PRODUCE
produce
-5,-5
100,0
don’t produce
0,100
0,0
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…
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