This paper studies the effects of setting a maximal limit of the bid (price cap) in auctions, which is a new strategy that has recently emerged in the airline industry. Before a buyer participates in the auction, she is informed that her bid must lie in a range with both upper limit and lower limit specified by the auctioneer. We show that in the presence of heterogeneous participation costs, setting a price cap may be necessary to attain the maximal revenue for the seller. In such circumstances, the price cap serves as an efficient tool to attract the bidder with high valuation and nonzero participation cost, as the seller can share part of his revenue with these buyers while exploiting low valuation bidders. We also find that the presumption that the seller has full priority on his ow...[ Read more ]

This paper studies the effects of setting a maximal limit of the bid (price cap) in auctions, which is a new strategy that has recently emerged in the airline industry. Before a buyer participates in the auction, she is informed that her bid must lie in a range with both upper limit and lower limit specified by the auctioneer. We show that in the presence of heterogeneous participation costs, setting a price cap may be necessary to attain the maximal revenue for the seller. In such circumstances, the price cap serves as an efficient tool to attract the bidder with high valuation and nonzero participation cost, as the seller can share part of his revenue with these buyers while exploiting low valuation bidders. We also find that the presumption that the seller has full priority on his own profits is not critical, which extends our insight to broader scenarios when the auctioneer may pay attention to social welfare. Finally, we show that our result is robust against the assumption that there are only two buyers and one object to be sold. In the setting of the multi-object auction, the optimal auction may still entail a price cap under certain conditions.