Optimal design of the online auction channel: Analytical, empirical, and computational insights

Decision Sciences, Fall 2002 by Bapna, Ravi, Goes, Paulo, Gupta, Alok, Karuga, Gilbert

The Yankee auction is a special case of multi-unit English auction. Here, multiple units of the same product are sold to multiple bidders. It is well known (Rothkopf & Harstad, 1994a) that single-item results (a vast majority of auction theory studies fall under this category) do not carry over in multiple-unit settings. The multiunit and discrete nature of these mechanisms renders the traditional analytic framework of game theory intractable (Nautz & Wolfstetter, 1997).

The auction is progressive in nature; however, each new bid does not have to be strictly greater than the previous bid since there are multiple units available. The set of winning bids consists of the top N bids, where N is the number of units up for auction. A new bid either has to be equal to the minimum bid that is among the winning bids (if the set of winning bids has a cardinality of less than N), or it has to be at least equal to the minimum winning bid plus a pre-specified minimum bid increment. With multiple identical items on offer, it is possible to observe several winning bids that are equal. Once the consumers have bid for the entire lot size, a new bid will have to be greater than the smallest winning bid. When such a bid is submitted, the winner with the smallest winning bid is replaced by the new bid. If several offers are equal and at the minimum winning bid level, a time priority is applied to determine the bid to be displaced when a new and higher offer is received. The last bid at the minimum winning bid level becomes the first to leave the auction winners' list. This process continues until the auction closes. At this point the auction winners are determined. The auction terminates on or after a pre-announced closing time, and the winning bidders pay the amount they last bid to win the auction. Most auctions have a going, going, gone period such that the auction terminates after the closing time has passed and no further bids are received in the last five minutes. Note that in multiunit settings this often leads to discriminatory pricing with consumers paying different amounts for the same item. Such auctions are used on a variety of auction sites on the Internet, pioneered by Egghead.com's Surplus Auctions (now defunct) and now popularized by Ubid.com.

The key factors that auctioneers can control in Yankee auctions are: (1) the lot size; (2) the bid increment; (3) the auction duration; and (4) the opening bid.

Ignoring monitoring costs for the present, we assume that customers maximize their net value and hence always bid at the current ask price, provided that the current ask price does not exceed their valuation of the item. Rothkopf and Harstad (1994b), in their single item analysis, characterize this as the pedestrian approach to bidding. Such a strategy is consistent with the rational, net worth maximizing assumption for consumers. Easley and Tenorio (1999) extend this result to Yankee auctions, conditioning it on the absence of any cost of preparing and submitting a bid. Notably, such a strategy could involve active manual participation or could be undertaken using a programmed software agent that bids the minimum required bid at any stage during the auction. Both have been observed in practice. In adopting this strategy, bidders choose to be no more aggressive than necessary to continue competing.