Name

A. Incomplete Information: In this two person - two action game player 2 comes in two flavors: green and red.  He knows his own type.  Player 1 does not know player 2's flavor/type, but believes that Player 1 is green with probability 0.60 .  The payoff matrices for the two types of player 2 are

1. Does a Green type Player 2 have a dominant strategy?  If so, what is it?

2. Does a Red type Player 2 have dominant strategy? If so, what is it?

3. Does Player 1 have a dominant strategy when playing against a Green type Player 2? If so, what is it?

4. Does Player 1 have a dominant strategy when playing against a Red type Player 2? If so, what is it?

5. Does Player 1's belief about Player 2's type matter in finding the solution to the game? Yes  No

6. What is the strategic profile for the solution to the game?  You need a strategy for Player 1 and a strategy for Player 2 that consists of an action to be taken by a red player and an action to be taken by a Green player.

B. Caveat Emptor: This is a parable that bears a remarkable resemblance to events on Wall Street during 2001 and 2002.  Rob R. Baron has a company for sale.  He has been operating his firm for some years.   It can be one of two types, either profitable or a loser.  Bea Wear is contemplating the purchase of the firm.  The problem is that Bea does not know whether or not the firm is truly profitable.  It is possible for Rob to make the firm look profitable by hiring the 'right' sort of accountants to dress up the books.  The problem is that Rob would hire accountants to audit the books in any case.  Neither the offer price nor inspection of the books will reveal to Bea what type of firm Rob is offering to the market place.

If the firm is profitable then it has value of V to Bea.  If it is a loser then it is only worth W to her.  In the event that the firm is a loser Rob always hires auditors to dress up the firm at an incremental cost of c. Let the price of the firm be p.  A table that summarizes the situation is

		Rob R. Baron
		Profitable			Unprofitable
		Offer	Withhold		Offer	Withhold
Bea Wear	Buy	V-p, p	0, 0		W-p, p-c	0, 0
	Refuse	0, 0	0, 0		0, -c	0, 0

There are only two possible actions from which Bea may choose.  As she looks at Rob she sees that he must have an action to be taken when his firm is profitable and an action to be taken when his firm is unprofitable.  Hence, from Bea's perspective, a strategy for Rob is a doublet.

7. In the following normal form table fill in the cells with Rob's strategies:

8. Suppose that V = $100, W = $60, p = $70 and c = $20. What will be Rob's payoff if he offers an unprofitable firm and Bea refuses to buy?

9. Using the values assigned in 8., what will be Rob's payoff if he offers an unprofitable firm and Bea unwittingly agrees to buy?

10. On a separate piece of paper, for your own use, write out the normal form of the game. Use the values for V, W, p and c of problem 8 to compute the payoffs. Does Rob have any dominated strategies?  Fill in the blanks:

11. Let g represent Bea's belief about the probability that Rob has a profitable firm for sale.  Consequently Bea's belief that Rob is trying to unload an unprofitable firm is 1-g. When Rob plays the strategy <Offer, Offer> and Bea plays the strategy Buy, what is Bea's expected payoff (expressed in terms of g and using the values for V, W, p and c assigned in problem 8)?

12. Continuing with the notation in the previous parts., when Rob plays <Withhold_profitable, Offer_unprofitable> and Bea plays Buy what is Bea's expected payoff (expressed in terms of g)? Again use the same values for V, W, p and c.

13. Using the same values for V, W p and c, how large must g be in order for Buy to be a dominant strategy for Bea?