Reference no: EM132617761

1. (Mechanism Design) A seller's has an item for sale. There are two risk neutral buyers whose valuations, which are private information, take on two possible values, 10 or 100. The corrsponding joint probabilities are given in the following table.

v2=10 v2=100

v1=10 1/3 1/6 v1=100 1/6 1/3

Now the seller is suggested by a HKU economist to use the following direct mechanism. Ask the two buyers to report their valuations. If the report profile is (10,10), randomly (i.e., with probability 1/2) pick one buyer and give the item together with $5 to him, and give the other buyer $15. If the report profile is (10,100) or (100,10), sell the item to the buyer with the higher report at a price of $100 and request the other buyer to pay the seller $30. If the report profile is (100,100), randomly pick one buyer and sell him the item at a price of $100.

As always, assume the seller is able to commit to the mechanism. Is truth telling an equilibrium outcome? Comment on the properties of this mechanism (in particular, comment on the expected payoff of each buyer).

1.2(voting), 1.3 (bargaining), 2.2 (reputation), and 3.2 (Nash bargaining) in Review Problems II