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On the lowest-winning-bid and the highest-losing-bid auctions

By Claudio Mezzetti and Ilia Tsetlin


Theoretical models of multi-unit, uniform-price auctions assume that the price is given by\ud the highest losing bid. In practice, however, the price is usually given by the lowest winning\ud bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there\ud are k objects for sale and n bidders, and prove that it converges to the bidding function of\ud the highest-losing-bid auction if and only if the number of losers n \u100000 k gets large. When the\ud number of losers grows large, the bidding functions converge at a linear rate and the prices in\ud the two auctions converge in probability to the expected value of an object to the marginal\ud winner

Topics: Auctions, Lowest-Winning Bid, Highest-Losing Bid, k-th Price Auction, (k+1)-st Price Auction
Publisher: Dept. of Economics, University of Leicester
Year: 2006
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