Equilibrium Analysis of Generalized Penny Auctions

The success of eBay.com has inspired a new generation of online auction websites. Quibids.com and Swoopo.com are new online retailers that sell goods using “open-outcry” auctions in which item prices go up by a fixed amount and participating bidders pay a fee for every bid they place. This format is a generalization of the “penny auction,” an auction that consists of multiple rounds in which a bidder can choose to place a bid on an item at a cost of one dollar with the effect of increasing the item's price by one and only one cent. In this paper, I present a mathematical model of penny auctions with general parameters. Using this model, I explore answers to the following questions: Can we describe how auction participants will bid in a given round of the auction? Are there unique Nash equilibria in generalized penny auctions? What can we say about the final price of an auction item, and how much revenue will the auctioneer receive in expectation?