Question

In a one-shot game, if you advertise and your rival advertises, you will each earn $5 million in profits. If neither of you advertises, your rival will make $4 million and you will make $2 million. If you advertise and your rival does not, you will make $10 million and your rival will make $3 million. If your rival advertises and you do not, you will make $1 million and your rival will make $3 million.

1. Write the above game in normal form.
2. Do you have a dominant strategy?
3. Does your rival have a dominant strategy?
4. How much would you be willing to bribe your rival not to advertise?

Answer 1

Normal form of the game:

	A	NA
A	(5, 5)*#	(10, 3)#
NA	(1, 3)	(2, 4) *

A stands for Advertise

NA stands for Not Advertise

Row strategies belong to me

Column strategies belong to the rival.

For me, A is the dominant strategy since, payoff received from A is (5,10) and payoff received from NA is (1,2)

5>1 and 10 > 2

So, Advertise is the dominant strategy of me.

For the rival, we look at column strategies:

Rival does not have any dominant strategy. Becuase, 5 > 3 but 3 is not greater than 4.

The Nash equilibrium of the game is (A, A) = (5, 5)

Rival will not advertise if I decide to Advertise. I get 10 and rival get 3

When both advertise, then rival gets 5. So, there is a need to compensate rival for the utility loss.

Maximum Willingness to Pay (WTP) = 10 - 5 = 5

**if you liked the answer, then please upvote. Would be motivating for me. Thanks.