Problem First price auctions. Alice (A) owns a painting and decides to auction the work to Bob (B), Charlie (C), and David (D). All men have private iid valuations for the good 0 E [0, 1] such that VI E [0, 1], F(x) = VT. A decides to run a first price auction where she insists on a minimum bid of 0. Timing goes as follows. Nature first draws valuations and privately informs each buyer of their realization. Buyers then simultaneously submit private bids to the seller. Alice then gives the good to the highest bidder and receives the promised bid. 1. (5 points) Define the game played by the buyers (hint: I defined this in the slides). 2. (5 points) Define a symmetric buyer strategy. 3. (5 points) State a buyer's problem. 4. (10 points) Solve the Buyer's problem and characterize the symmetric strategy. 5. (5 points) Suppose that A, instead decides to run a second price auction. Explain why it is an equilibrium for each buyer to truthfully bid their valuation. 6. (5 points) Is truthfully reporting one's valuation the only equilibrium. If not, then explain why there exists alternative equilibria. 7. (5 points) In class, I established that the first price-auction is revenue equivalent to the second-price auction in spite of their distinct payment rules. Define the concept of revenue equivalence and explain its insight into markets in general. 8. (5 points) Explain why the first price auction is credible, but the second price auction is not