MECHANISM DESIGN BY COMPETING SELLERS

A dynamic model with many sellers and many buyers is constructed, in which buyers who fail to purchase in the current period may attempt to purchase in the future, and sellers who fail to sell may sell in the future. An equilibrium is found where sellers hold identical auctions and buyers randomize over the sellers they visit. Auctions alter the distribution of buyer types by removing high value buyers more rapidly than low value buyers, and an equilibrium distribution of buyer types is constructed. Sellers in equilibrium post an efficient reserve price equal to the sellers' value of the good, and an auction with efficient reserve is an optimal mechanism from each seller's point of view, in spite of the ability of any seller to alter the distribution of buyer types participating in the seller's mechanism by altering the mechanism.