Department of Economics
The Ohio State University
February 10, 2004
Answer all questions, carefully label all diagrams, and show
1. (30 points)
Consider the following ±quality disclosure²game, in which a seller owns an
object that has no value to her, but is valuable to a potential buyer. The value
to the buyer is either $10, $20, or $30, each with probability one third. The
seller observes the quality of the good (i.e., the value to the buyer), but the
buyer does not observe the quality.
The game starts with nature informing the seller about the quality of the
good. Next, the seller decides whether or not to disclose the true quality to the
buyer. That is, the buyer either observes the disclosed quality (which is known
to be the truth), or else observes that quality was not disclosed. Finally, the
buyer decides whether or not to buy the good at a price of $15. If the buyer
does not buy, both players receive a payo/ of zero. If the buyer buys, the seller
receives a payo/ of $15 and the buyer receives a payo/ equal to
denotes the quality of the good.
(a) Draw and label the game tree. Be neat!
(b) This game has several weak perfect Bayesian equilibria.
WPBE in which the seller
discloses its quality. (Remember to specify
beliefs as well as strategies.)
(c) Construct a WPBE in which the seller
discloses its quality. (Re-
member to specify beliefs as well as strategies.)
For part (a), refer to the handout.
We will construct a WPBE in which the seller always discloses its quality.
The seller³s strategy is (D,D,D), meaning that the seller discloses when
, and discloses when
The buyer³s strategy is
(NB,B,B,NB), meaning that the buyer does not buy when the seller discloses
, the buyer buys when the seller discloses
, the buyer buys when
the seller discloses
, and the buyer does not buy when the seller does not
disclose. At all singleton information sets, the conditional probability of being
at that node is one.
At the buyer³s information set following no disclosure,
the beliefs assign probability one to
, probability zero to