Bidding strategies in online auctions with different ending rules and value assumptions

• We divide the auction process into two stages and then use backward induction to study various online auctions.
• In second-price online auctions it is dominant to report true value for all customers.
• That when to bid is independent of hard-close and soft-close for first-price online auctions under PV.
• Late bidding is dominant under CV, but only in first-price online auctions with hard-close under PV.

Compared with traditional auctions, online auctions (used by, e.g., eBay and Yahoo) have several distinguishing features, including different ending rules (hard-close and soft-close), sequential arrival of customers, and random numbers of customers, all of which make bidding behavior more complex. The phenomenon of late bidding has been reported in the literature and, although the origin of this behavior has been analyzed theoretically, it is still not clear. Here, we study both first- and second-price online auctions with either hard- or soft-close ending rules and assume either private value (PV) or common value (CV). By dividing the auction process into two stages and then using backward induction, we find that late bidding is dominant under CV, but under PV late bidding dominates only in first-price online auctions with hard-close. Moreover, for second-price online auctions the dominant strategy for customers is to report their true value immediately upon arrival under PV but near the end of the auction under CV, irrespective of ending rules. Finally, we find that the timing of customer bidding is the same for hard- and soft-close except for first-price online auctions under PV.