Department of Economics
Principles of Microeconomics, Honors
Static Games with Incomplete Information
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?
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
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
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
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 <Withholdprofitable,
Offerunprofitable> 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?