An object is auctioned to bidders in a first price sealed-bid auction. The valuation of bidder is denoted by ( = 1,2, … , ), and is drawn independently from the uniform distribution on [0,1]. Each bidder has a utility function () = m ( = 1,2, … , ), where ≥ 0 is the net payoff for the bidder from the auction and m ≥ 2 is an integer. Thus the bidders are risk-loving, with higher values of m representing greater willingness to take risks.
a) Derive each bidder’s optimal bidding strategy in a symmetric equilibrium of the auction, and derive the seller’s expected revenue from this auction. Briefly comment on these results.