Budget Induced Strategic Bidding in Multiunit Online Auctions

The online auction has been a popular and representative model in online e-commerce over the past decade. According to a survey of National Consumers League (NCL), since eBay launched its online auction platform in 1995, nearly one-third of the online population in the U.S. have participated in an online auction. Compared with traditional auctions, the arrival process for online auctions is more random and dynamic. The stochastic arrival process, coupled with a complex decision environment for bidders that include both simultaneous and sequential auctions, engenders interesting bidding behaviors in online auctions. One of the common-observed phenomena in online ascending auctions is jump bidding, defined as submitting bids higher than required by the auctioneer (Zheng, 2012). Jump bidding is especially relevant for online auctions because of the uncertainties in both the number of bidders and their arrival process in online environments. For practitioners, jump bidding has “important revenue effects” (Avery, 1998). In some cases, jump bidding may reduce the seller’s expected revenue (e.g. when the jump bidding deters other bidders from participating), though some argue that jump bidding can potentially increase the seller’s revenue and bidders’ utility because it may improve efficiency. Regardless the direction of impact, understanding the underlying mechanisms of jump bidding is crucial for sellers and buyers in online auctions.
In academic research, several reasons for jump bidding have been identified (Avery, 1998; Easley & Tenorio, 2004; Gunderson & Wang, 1998; Isaac, Salmon, & Zillante, 2007) These include the signaling of an aggressive strategy (Avery, 1998), saving bidding cost (Easley & Tenorio, 2004), impatience (Isaac et al., 2007), and irrationality (Gunderson & Wang, 1998). Many of the existing explanations, however, do not carry over to an environment where a software agent place bids on behalf of human buyers. For example, participation costs, impatience, and irrationality may not explain the jump-bidding behavior in agent-based bidding, which is increasingly common on online auction platforms. Even when agent-based bidding is used, there are still strategic reasons for jump bidding. However, little attention has been paid to the latter kind of reasons for jump bidding. In our study, we address the aforementioned gap by proposing a novel explanation for jump bidding based on strategic behaviors under budget constraints. In real-world auctions, many bidders have budget constraints, which may force them to drop out an auction even when they have a significant positive value for an item. This means that budget-constrained bidders would strongly prefer winning than losing (which forgoes the positive value for the item). Jump bidding let such bidders enter a high bid early, thus increasing their likelihood to win. This may cause bidders to pay a higher final price, but when bidders have a strong preference for winning, they may risk a higher final price in exchange for a higher winning chance. This research has two goals. First, we hope to theoretically establish the condition under which such jump bidding behaviors occur. Second, we hope to further understand what factors play a key role in driving budget-induced jump bidding. For the first goal, we conduct a theoretical analysis. For the second, we rely on simulation. The context of this study is multi-unit ascending online auctions in which multiple bidders with unit-demand compete for multiple identical items in an ascending auction. Because budget-induced jump bidding tends to happen near the end of a bidder’s bidding cycle, we will focus on a bidder’s strategy at his margin, i.e., when the current price is one bid increment away from the maximum bid the bidder can submit within his budget constraint. In our theoretical model, we analyze two bidding strategies when the auction arrives at a bidder’s margin: a participatory strategy in which the bidder places the minimum required bid and a jump strategy in which the bidder bids one increment more than the required bid level, or his maximum bid. We derive the condition for the bidder to use the jump strategy. Based on this theoretical analysis, we characterize the optimal hybrid strategy (between participatory and jump) for an at-the-margin, budget-constrained bidder and call it strategic-at-margin (SAM) bidding. We then use the simulation method to validate our proposed SAM bidding by benchmarking it against a pure participatory strategy and a pure jump strategy. Our simulation also explores how the budget constraint and the bid increment jointly influence jump bidding at the margin.