3 Suppose You Owned A Handcrafted Antique Table It Is A Unique Item In That Is Not Available In Stores You Are Inte 1 (58.67 KiB) Viewed 61 times
3 Suppose You Owned A Handcrafted Antique Table It Is A Unique Item In That Is Not Available In Stores You Are Inte 2 (14.56 KiB) Viewed 61 times
(3) Suppose you owned a handcrafted, antique table. It is a unique item in that is not available in stores. You are interested in selling it. You know of two potential buyers labeled 1 and 2. Each buyer receives a benefit of V > 0 from owning the table. The value V is common knowledge. 1. First, suppose you use a contest to sell the table. You tell each buyer to submit an offer. Each dollar they offer gives them one ticket in a lottery. You keep all money spent on the tickets. The rules of the contest are that the person whose ticket is drawn (each ticket is equally likely to be drawn) receives the table. If no one makes an offer, you give the table to buyer 2. How much will each buyer spend on the lottery? How much will you, the seller, earn for your table? 2. Instead, suppose you use an all-pay auction to sell the table. You tell each buyer to submit a bid. You will keep all the money that was offered (regardless of who wins the table). This time, though, the buyer who submits the highest bid receives the table (with certainty). If the two submit the same bid, then the table is given to each with equal probability. If both submit a bid of zero, then the table is given to buyer 2. Is there an equilibrium where both submit a bid of V? Is there an equilibrium where both submit a bid of 0? Is there any other (pure strategy) Nash equilibria? a
3. Suppose that in the all-pay auction you had buyer 1 submit his bid first and then allowed buyer 2 to submit a bid knowing that buyer 1's bid is. What is the subgame 3 perfect Nash equilibrium of this sequential all-pay auction? Does it produce more revenue than the contest?
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