Competition among auctioneers in large markets

We analyse a multistage game of competition among auctioneers. First, the auctioneers commit to some reserve prices; second, the bidders enter one auction, if any; and finally, the auctions take place. We show that for any finite set of feasible reserve prices, each auctioneer announces a reserve price equal to his production cost if the numbers of auctioneers and bidders are sufficiently large, though finite. Our result supports the idea that optimal auctions may be quite simple. Our model also confirms previous results for some “limit” versions of the model by McAfee (Econometrica 61 (1993) 1281-1312), Peters (Rev. Econ. Stud. 64 (1997) 97-123), and Peters and Severinov (J. Econ. Theory 75 (1997) 141-179).