Myerson-Satterthwaite Theorem and Asymmetric FPA Auctions

In this paper Myerson-Satterthwaite theorem with asymmetric First price auction (FPA) has been subject of investigation. Bilateral inefficiency trade theorem versus the efficiency of the FPA auctions in which there is supposedly no dominant strategy, where bids are private information, and are made simultaneously, where highest bid wins and winning bidder pays the winning bid. This type of auction may not be Pareto efficient (this condition requires that the item is allocated to the bidder with highest valuation). But in the sealed FPA auctions highest bidder does not know other bidders' valuations and may lose to another bidder. In the auction setting we set reserve price that causes efficiency loss and decreases probability of trade. The results are ambiguous dependent on the type of the solution method used. Three methods of solution were used: Fixed point finite difference iterations, Backward shooting method, and Constrained strategic equilibrium (C.S.E). The reserve price set was 0.5 since θ_s∈(0,1)and θ_b∈(0,1), so the buyers' value is likely to be [0.1,1] and the sellers' value is likely to be [0,0.9],so in such case reserve price would eliminate low bidder types. The results are ambiguous in a sense that under Backward shooting method convergence is not true, so the Myerson-Satterthwaite theorem does hold which is not case under Fixed finite difference point iterations, and Constrained strategic equilibrium (C.S.E).Phenomenon known as winner's curse occurs in a case of incomplete information