There are a single item for sale and two bidders, i = 1,2. Each bidder i's...

 

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There are a single item for sale and two bidders, i = 1,2. Each bidder i's private type is given by t = x + y, where x1, x2 and y are all distributed independently and uniformly ti on [0, 1]. The value of the item is the same for both bidders, and it is given by v = = 1 (t1+t2). (i) Consider first the first-price sealed-bid auction. Show that it is a Bayesian Nash equilibrium (BNE) that each bidder uses the strategy s* (t) {ti. Verify that in this equilibrium, the expected revenue raised by the auction is ( ). = (ii) Next, consider the second-price sealed-bid auction. Show that it is a BNE that each bidder uses the strategy s*(t) = ti. Verify that in this equilibrium, the expected revenue raised by the auction is (iii) Consider again the second-price sealed-bid auction. Now suppose that t and t are common knowledge among the bidders (but they are not known to the seller). Show that it is a BNE that each bidder uses the strategy s* (ti, tj) = (ti+tj)/2. What is the expected revenue in this equilibrium? Why is it different from revenue raised in (i) and (ii)? There are a single item for sale and two bidders, i = 1,2. Each bidder i's private type is given by t = x + y, where x1, x2 and y are all distributed independently and uniformly ti on [0, 1]. The value of the item is the same for both bidders, and it is given by v = = 1 (t1+t2). (i) Consider first the first-price sealed-bid auction. Show that it is a Bayesian Nash equilibrium (BNE) that each bidder uses the strategy s* (t) {ti. Verify that in this equilibrium, the expected revenue raised by the auction is ( ). = (ii) Next, consider the second-price sealed-bid auction. Show that it is a BNE that each bidder uses the strategy s*(t) = ti. Verify that in this equilibrium, the expected revenue raised by the auction is (iii) Consider again the second-price sealed-bid auction. Now suppose that t and t are common knowledge among the bidders (but they are not known to the seller). Show that it is a BNE that each bidder uses the strategy s* (ti, tj) = (ti+tj)/2. What is the expected revenue in this equilibrium? Why is it different from revenue raised in (i) and (ii)?

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i FirstPrice SealedBid Auction In a firstprice sealedbid auction each bidder bids their private type ... View the full answer