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Article Excerpt
I. INTRODUCTION
Standard auction theory predicts that in a private-value English oral auction, the winner will be the bidder with the highest valuation for the object and the selling price will be the second-highest valuation. In those auctions, a reasonable strategy for a bidder would be to increase each bid by the minimum bid increment. This solution is referred to as the "ratchet solution," "straightforward bidding," or as "pedestrian bidding." Jump bidding occurs when a new offer is submitted that is above the old offer plus the minimum bid increment permitted.
In this paper, I study the sequence of bidding in an open-outcry English auction to examine how strategic bidding affects price determination. I do this by examining the nature of jump bidding in data I have collected from a series of public auctions of used cars in New Jersey. The auction literature has not fully addressed and characterized jump bidding in English auctions.
The theoretical literature on the conditions under which jump bidding will emerge (e.g., Avery 1998; Daniel and Hirshleifer 1998; Easley and Tenorio 2004; Isaac, Salmon, and Zillante 2007; Macskasi 2000; Rothkopf and Harstad 1994) does not include any models of English auctions with affiliated values and discrete bid levels. Table 1 summarizes the different models' predictions. The empirical and experimental literature on jump bidding is also quite narrow. Plott and Salmon (2004), Isaac, Salmon, and Zillante (2005, 2007), and Isaac and Schnier (2005) found support for jump bidding in their studies. Borgers and Dustmann (2005), in analyzing the United Kingdom's sale of licenses for third-generation mobile telephone services, found that, although the majority of bids in the auction were the lowest admissible bids, there were a significant number of jump bids. Haile and Tamer (2003) also documented jump bidding in a regular English auction and reported that the gap between first-and second-highest bids is usually above the minimum bid increment allowed. Section II provides a detailed literature survey.
In order to characterize jump bidding, and because the auctions I study have no seller's reserve price, I define the "First Jump" as the first offer submitted by any bidder. The "Second Jump" is the difference between the second offer submitted by a bidder and the first offer. The "Last Jump" is the difference between the winning bid and the previous offer. (1) I further define the "Average Jump" (2) across all jumps excluding the First and Last Jumps. Figure 1 describes these variables graphically.
I find that jump bidding is a widespread empirical regularity in the sale of all items. The jumps depend on the presale estimate of the item's price and are not affected by the selling order. For almost all items, bidders use jump bidding to increase the current offer. Furthermore, on average, the First Jump is greater than the Second Jump, which is greater than the Average Jump, which in turn is greater than the Last Jump. I offer several explanations for the existence of jump bidding.
These findings suggest that there is some strategic bidding behavior in the way bidders advance their bids. Bidders consider the way the auction progresses, which implies that a bidder's strategy includes not only the stopping point along the bidding path but also the precise nature of the path that led there. Consideration of jump bidding strategy sheds light on whether an open-outcry auction is best interpreted with models that assume private- or common-item valuations. Under the assumption of independent private values, bidding history should not affect the point at which a bidder drops out. This is not the case in a common-value auction, in which each stage of the auction is used as a device for signaling. The selling price in an English auction with common values will be path dependent. Hence, a simple test of the effect of the First Jump on the selling price determines the type of the auction.
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II. LITERATURE SURVEY
The theoretical literature on bidding patterns in ascending auctions demonstrates the conditions under which straightforward bidding arises in equilibrium and when we expect jump bidding. The lack of any model of an English auction with affiliated values and discrete bid levels is noticeable. The experimental literature demonstrates the existence of jump bidding, sometimes with a model that supports jump bidding. The empirical literature demonstrates the existence of jumps as well. This paper fills the gap by reporting and then analyzing jump bidding in a regular sequential open-outcry English auction.
Rothkopf and Harstad (1994) explored the role of discrete bid levels in oral auctions. They addressed the question of when it is optimal to skip a bid level. They demonstrated that in a two-bidder game with private valuations drawn from nonincreasing distributions, pedestrian bidding by both bidders is an equilibrium as long as the interval between allowed bids is not too big.
Daniel and Hirshleifer (1998) (DH hereafter) demonstrated that, when a single good is auctioned to two bidders with private values, if there is a cost to submit a bid, such a cost can lead to a jump bidding equilibrium. They demonstrated also that the jump between the first and the second bid is increasing in the first bid. The set-up in the model is different from the usual English auction because there is no auctioneer in takeover contests.
Macskasi (2000) extended the model of DH to three players. Again, the motivation for the jump is a positive bidding cost, and the game is over after, at most, three positive bids. Under the suggested equilibrium, jump bids favor the bidders.
Easley and Tenorio (2004) argued that the cost associated with entering online bids and uncertainty about future entry can explain jump bidding in an ascending-price Internet auction. The model is similar to that of DH, with the difference that even if bidders pass, they will suffer the cost. The motivation for the jumps is bidding costs and the use of the jumps as signals. The model involves two identical risk-neutral bidders with private valuations who will potentially compete over one unit. There is demand uncertainty, and with probability q, the opponent will not find the auction. They find that when costs are zero, the ratchet solution is equilibrium. When costs are positive, the item can either be sold after one or two stages or else remains unsold. They examined their model's assumptions using Yankee-type Internet auctions (3) and found that jump bidding is more likely earlier in the auction and that the incentive for jump bidding increases as competition becomes stronger. They also found that jump bidders place fewer bids and that increased early jump bidding in auctions reduces the total bids placed.
Avery (1998) has shown that a jump bid may be used to intimidate one's opponents and serves as a correlating device among bidders. The choice of bids allows bidders to communicate within the auction, and the jump can signal aggressive behavior. The implied aggressiveness discourages competition because it suggests that the bidder values the good more than everybody else and that if the opponent wins, he probably overbid. The model involves two risk-neutral bidders competing in a single English auction with affiliated valuation and signals and describes a public auction as a two-stage game. In the first stage, bidders can use their initial bid, 0, or a cutoff point, K, to communicate through jump. This communication has a cost because the initial bid may win the auction. In the second stage, the players proceed as in an ordinary open-exit auction, in which their initial bids serve to select their subsequent bidding strategies. Adding signaling stages to the game will reduce the average price, and the equilibrium produces an exact set of expected prices between the first-price and the second-price auction.
Isaac, Salmon, and Zillante (2007) provided a dynamic model of bidding in ascending auctions. They solved the model using backward induction and dynamic programming to obtain the solution for two risk-neutral bidders with private valuations that draw their values from a uniform or normal distribution. They found that jump bidding occurs in equilibrium, is of moderate size, and is motivated by impatience and a combination of distribution and discreteness factors. In addition, there is a convergence to straightforward bidding, and the expected revenue in the straightforward bidding is slightly higher. The authors provided evidence from FCC (Federal Communications Commission) auctions on the existence of jump bidding. Table 1 summarizes the different models' predictions and assumptions.
The empirical and experimental literature on jump bidding is quite narrow. Plott and Salmon (2004) developed a model of the behavior of bidders in simultaneous ascending auctions, in each round, based on surplus maximization and bid minimization. The purpose is to give the auctioneer an idea of the bidders' valuation during the auction process. They demonstrated that the model is valid in an...
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