Auctions with a buyout price: A survey
Toshihiro Tsuchihashi∗† January 2016
Abstract
In an online auction with a buyout price placed by the seller, a bidder can purchase an item at a fixed price before the auction closes. Buyout prices are increasingly capturing the attention of economists, and numerous studies have theoretically and empirically examined the impact of a buyout price on seller revenue and the optimal decision of a bidder to exercise a buyout option. However, the analyses in the literature seem far from comprehensive. This paper reviews existing studies and their findings and then lists four issues that are not addressed in the literature. First, a buyout price is studied mainly in independent private value environments. Second, the literature ignores the signaling function of buyout prices. Third, the relation between the reserve and buyout prices is generally ambiguous although sellers on online auctions post reserve and buyout prices in various combinations. Fourth, no study investigates the effects of a buyout price in multi-unit auctions. Furthermore, we point inconsistency in the findings of empirical studies, especially results on whether a buyout price raises the final selling price.
1 Introduction
Online auctions have become popular since Onsale and eBay emerged in the market in 1995. Today, multitudes of people use the Internet to sell products. According to an eBay report, over 128 million users listed over 550 million items in auctions on eBay in 2013 (eBay Inc., 2014).
Unlike many traditional auction houses such as Sotheby’s and Christie’s, online auctions allow sellers to customize their auctions by posting a secret reserve price and a buyout price in addition to a starting price. Indeed, the notion of buyout prices is increasingly capturing the attention of economists. In an auction with a buyout price, a bidder can purchase an item at a fixed price before the auction closes. This was first introduced by Yahoo in 1999 under the name Buy Now. One year later, eBay announced its Buy It Now service. These two services provide different timings for bidders to exercise a buyout option. On the one hand, Buy Now remains throughout the auction period and allows bidders to exercise the buyout option any time before the going price reaches the buyout price. On the other hand, Buy It Now does not continue for the whole period if competitors offer a regular bid. Therefore, the literature refers to the former as permanent and to the latter as temporary.
∗Faculty of Economics, Daito Bunka University; 1-9-1 Takashimadaira, Itabashi-ku Tokyo, 175-8571 Japan; E- mail:[email protected]
†I am truly indebted to the Lunch Seminar at Daito Bunka University for their helpful comments and suggestions as well as invaluable guidance. This work was supported by JSPS KAKENHI (Grants-in-Aid for Scientific Research) Research Project Number 24730172. Any remaining errors are my own responsibility.
The buyout option appears to have been received warmly by eBay users. For the PlayStation Portable videogames category on eBay, for example, Mathews (2004) reports that sellers opted to post a buyout price in 124 (59%) of 210 auctions. Similarly, Hof (2001) demonstrates that 40% of all sellers on eBay had added a buyout option across all categories by the end of 2001.
When demand for merchandise is uncertain, auctions are superior to a fixed pricing system in terms of expected seller revenue because sellers can avoid posting an inadequate price (Wang, 1993; Kultti, 1999).1 However, a buyout price might seem to impair the benefit of auctions. From a naive perspective, a buyout price is a ceiling for a selling price and thus seller revenue; hence, a seller would rather earn more without a buyout price than by adopting it. In this case, there seems to be no rationale for a seller placing a limit on the selling price. Lucking-Reiley (2000) briefly demonstrates the benefits of a buyout price for both the seller and buyers. A buyout price not only saves the seller and buyers time, but also ensures that a buyer wins the auction. The literature, expanding in volume, explains who can benefit from a buyout price and how.
However, the analyses in the literature seem far from comprehensive. This paper surveys the literature on the use of a buyout price in online auctions, and then discusses issues that are not addressed in the literature. The remainder of the paper is organized as follows. Sections 2–4 review the theoretical research, while Section 5 includes traditional empirical and experimental research. Section 6 gives a critical analysis and indicates directions for future research on this topic.
2 Risk aversion
Budish and Takeyama (2001) is the first study to formalize an auction with a (temporary) buyout price under an independent private-value assumption. They construct a simple model with two bidders and two values, either high or low, and focus on an equilibrium in which only a high-value bidder exercises the buyout option. Their major finding is that a risk-neutral seller benefits from posting an appropriate buyout price if bidders are risk-averse. Risk-averse bidders are willing to pay a risk premium to avoid variance in selling prices. Thus, seller revenue increases from a high buyout price that a risk-neutral bidder would never accept but a risk-averse bidder would.
Since Budish and Takeyama (2001), an auction with a temporary buyout price has been modeled as a sealed-bid second-price auction where a buyout price is exogenously given. Mathews (2003) extends Budish and Takeyama (2001) to the general case where n ≥ 2 bidders have continuous valuations. In his model, bidders simultaneously decide whether to exercise a buyout option in the first stage and submit a sealed bid in the second stage. Mathews and Katzman (2006) introduce a risk-averse seller into Mathews’ (2003) model. Hidvegi, Wang, and Winston (2006) and Reynolds and Wooders
1Similarly, Bulow and Klemperer (1996) show that auctions are superior to negotiations under various conditions.
(2009) use similar models to study a temporary buyout price. In all the studies mentioned above, bidders employ a threshold strategy to exercise a buyout option in a symmetric equilibrium. A bidder exercises a buyout option if his valuation is at or above a certain threshold and does not otherwise. These studies commonly find that the threshold is an increasing function of the buyout price (i.e., a higher buyout price is less likely to be exercised) and a decreasing function of the degree of risk aversion of a bidder (i.e., a more risk-averse bidder is more likely to exercise a buyout option). More importantly, the seller is better off with a buyout price when either a seller or a bidder is risk-averse. To examine this finding, we derive a threshold strategy in a simplified version of Reynolds and Wooders’ (2009) model that analyzes a temporary buyout price. We consider an auction with a buyout price in which a seller sells an item to n ≥ 2 potential bidders. The seller values the item at zero. Each bidder’s valuation is independently and identically drawn from [0, 1] with a uniform distribution function F (v) = v ∈ [0, 1]. We assume a risk-neutral seller and risk-averse bidders. When a bidder with valuation v obtains an item and pays p, his utility is u(v − p). We assume that no reserve price is available. We denote by Fn,m the distribution function the mth highest order statistics among n bidders’ valuations follow.
The auction consists of two stages. In the buyout stage, given an exogenous buyout price p, bidders simultaneously decide whether to exercise a buyout option. If at least one bidder exercises a buyout option, the auction closes immediately and the item is sold at the buyout price. If two or more bidders try to exercise a buyout option simultaneously, the winner is randomly chosen. On the contrary, if no bidder exercises a buyout option, the bid stage then emerges. The bid stage is a sealed-bid second-price auction.
We focus on a symmetric equilibrium in which all the bidders employ a threshold strategy in the buyout stage and place a sincere bid in the bid stage. Let ¯p(v) be a threshold strategy in which a bidder with valuation v exercises a buyout option if p ≤ ¯p(v). Conditional on winning, the higher the valuation a bidder has, the higher is the final price he faces on average. Therefore, given a buyout price, a bidder with a higher valuation finds it more beneficial to exercise a buyout option because it saves him money. Consequently, a threshold strategy ¯p(v) is an increasing function of the bidder valuation.
Since a bidder with valuation v should never accept a buyout price p > v, we consider a bidder with valuation v ≥ p. First, suppose that the bidder exercises a buyout option in the buyout stage. Following the threshold strategy ¯p(v), all bidders with a valuation at or above ¯p−1(p) exercise a buyout option. If he is the only bidder to exercise, he pays p and obtains the item with certainty. On the contrary, if k other bidders also exercise, then he obtains the item with probability 1/(k+1). Therefore,
the bidder’s expected payoff is
UB(v, p) = u(v − p)
n−1
X
k=0
n − 1 k
1
k + 1(1 − F (v))kF (v)n−1−k
= u(v − p) 1 − F (v)
n
n[1 − F (v)].
Second, suppose that the bidder does not exercise a buyout option. Note that in the bid stage, regardless of the degree of risk aversion, it is a weakly dominant strategy for a bidder to submit his valuation. The bidder wins the auction in the bid stage only if the other bidders’ valuations are below his valuation and the threshold ¯p−1(p). Therefore, the bidder’s expected payoff is
UA(v, p) =
Z min{v,¯p−1(p)} 0
u(v − x)dFn−1,1(x), where Fn−1,1(x) = F (x)n= xn.
In the equilibrium, the bidder with the valuation satisfying ¯p(v) = p should be indifferent between these two decisions, i.e., UB(v, ¯p(v)) = UA(v, ¯p(v)). Therefore, we obtain
u(v − ¯p(v)) 1 − F (v)
n
n[1 − F (v)] = Z v
0
u(v − x)dFn−1,1(x), or equivalently
¯
p(v) = v − u−1n[1 − F (v)] 1 − F (v)n
Z v 0
u(v − x)dFn−1,1(x).
Given the threshold strategy, we derive seller revenue associated with buyout price p. The item is sold for the buyout price in the buyout stage if at least one bidder has a valuation at or above the threshold ¯p−1(p). Therefore, given the buyout price, expected seller revenue is
Π(p) = [1 − F (¯p−1(p))n]p +
Z p¯−1(p) 0
xdFn,2(x), where Fn,2(x) = F (x)n+ nF (x)n−1[1 − F (x)] = nF (x)n−1− (n − 1)F (x)n.
On the contrary, without a buyout price, seller revenue is ΠN B =
Z 1 0
xdFn,2(x). The buyout price yields higher seller revenue if and only if
Π(p) > ΠN B ⇔ [1 − F (¯p−1(p))n]p +
Z p¯−1(p) 0
xdFn,2(x) > Z 1
0
xdFn,2(x)
⇔ v − 1
1 − F (v)n Z 1
v
xdFn,2(x) > u−1n[1 − F (v)] 1 − F (v)n
Z v 0
u(v − x)dFn−1,1(x)
⇔ uv − 1 1 − F (v)n
Z 1
v
xdFn,2(x)> n[1 − F (v)] 1 − F (v)n
Z v 0
u(v − x)dFn−1,1(x).
Reynolds and Wooders (2009) assume bidders with constant absolute risk aversion (CARA) utility, showing that the threshold strategy indeed constructs a symmetric equilibrium and that an appropriate buyout price increases expected seller revenue. Furthermore, they show that the more risk-averse the bidder, the higher is expected seller revenue. Note that any buyout price exercised with a positive probability (i.e., p < ¯p(1)) is inefficient. The bidder with the highest valuation may not win the auction when two or more bidders exercise a buyout option.
Hidvegi, Wang, and Winston (2006) formalize an English (clock) auction with a permanent buyout price. In their model, n bidders are risk-averse and the buyout price is exogenous. The price starts at a reserve price and continuously increases. A bidder can purchase an item at the buyout price at any time but can never be active once he exits the auction. They find that bidders employ the following threshold strategy to exercise a buyout price in a symmetric equilibrium. If a bidder has a high valuation, he exercises a buyout option immediately after the auction starts. On the contrary, if a bidder’s valuation is intermediate, he remains active for a while and exercises a buyout option if a price reaches a threshold. The threshold decreases with the bidder’s valuation (i.e., a bidder with a higher valuation exercises a buyout price earlier). A bidder with a sufficiently low valuation thus never exercises his buyout option.
Reynolds and Wooders (2009) use a similar model to that of Hidvegi, Wang, and Winston (2006) and compare these two formats. They consider the three cases that bidders’ utility exhibits CARA, decreasing absolute risk aversion, and increasing absolute risk aversion. First, for a common buyout price, the set of bidders with CARA utility immediately exercising a buyout option is the same in the two formats. However, the ex post outcomes (i.e., the final selling prices) may be different because a permanent buyout price initially not accepted might be later accepted by the bidder with the highest valuation. Consequently, a permanent buyout price generates higher expected seller revenue. On the contrary, bidders are indifferent between these two formats. Second, a buyout price is exercised more often in a temporary format if bidders’ utility exhibits decreasing absolute risk aversion, whereas bidders with increasing absolute risk aversion utility accept a permanent buyout price more than a temporary one.
3 Time sensitivity
With regard to online auctions, a seller may intend to sell her item as soon as possible because she needs money or a bidder may intend to obtain an item as soon as possible because, for example, he wants to purchase a birthday present for his friend. Such a seller and bidder know the value of time and are sensitive to the passage of time. In the literature, this situation is modeled as an English
auction in which the seller and/or bidders discount their payoffs. Mathews (2004), Mathews and Katzman (2006), and Gallien and Gupta (2007) introduce a time-sensitive seller and bidder into their models. Mathews (2004) models an English auction with a temporary buyout price, whereas Mathews and Katzman (2006) and Gallien and Gupta (2007) study a permanent buyout price in an English auction. Mathews (2004) and Mathews and Katzman (2006) consider the case of fixed n bidders, whereas the number of bidders is not fixed and bidders arrive at an auction according to a Poisson process in Gallien and Gupta’s (2007) model.
Although these models are slightly different, bidders employ a threshold strategy to exercise a buyout option in a symmetric equilibrium. Similar to the previous section, a bidder with a higher valuation is more likely to exercise a buyout option. More importantly, in all the studies mentioned above, the degree of impatience and arrival time affect the threshold as well. The threshold is an increasing function of arrival time (i.e., a later-arrived bidder is unlikely to exercise his buyout option) and a decreasing function of the degree of impatience (i.e., a more impatient bidder is more likely to exercise a buyout option). The advantage of saving time by accepting a buyout price is lower for a bidder arriving late at an auction. These studies all show that a buyout price provides the advantage of early closing to impatient sellers and bidders. This result may be consistent with the following view presented by eBay that encourages early bidding:2
Why did the Buy It Now option disappear after the first bid? For auction-style listings with Buy It Now option, you have the chance to purchase an item immediately, before bidding starts. But, you have to act fast. After someone bids, the Buy It Now option disappears and bidding continues until the listing ends, with the item going to the highest bidder.
To see this finding, we derive a threshold strategy in a simplified version of Mathews’ (2004) model. A seller sells an item to n ≥ 2 bidders through an ascending auction with a temporary buyout price. The seller posts temporary buyout price p at time t = 0 and the auction ends at t = T unless a bidder exercises the buyout option. We assume that no reserve price is available. The seller values the item at zero. Each bidder’s valuation is independently and identically drawn from [0, 1] with a uniform distribution function F (v) = v ∈ [0, 1]. Both the seller and bidders are risk-neutral, but bidders are time-sensitive in that they discount their payoffs with a common discounting factor δ ∈ (0, 1]. That is, the utility function is given by u(x) = δtx for δ ∈ (0, 1]. The degree of time sensitivity increases as δ approaches zero, while δ = 1 corresponds to the case of no discounting. In the case of δ = 1, a buyout option is never exercised in the equilibrium, consistent with the literature. When a bidder appears at time t in the auction, he observes (i) arrival time, (ii) the buyout price if it remains, and (iii) the
current price if at least one bidder has already submitted. The current price equals the second-highest bid at that time.
We focus on a symmetric equilibrium in which a bidder follows an undominated threshold strategy. A threshold depends on both a buyout price and arrival time. Following a threshold strategy ¯pt(v), a bidder with valuation v exercises a buyout option immediately upon arrival if he arrives at time t and a buyout price satisfies p ≤ ¯pt(v).
Suppose that all other bidders follow the above threshold strategy and that a bidder with valuation v arrives at the auction at time t. If the buyout price has already disappeared, he would simply submit his valuation sincerely. Alternatively, we assume that the buyout price is still available. Clearly, he is the first bidder to arrive in this case. If he immediately exercises the buyout option at time t, he obtains δt(v − p). Otherwise, submitting a sincere bid leads to
δT Z v
0
(v − x)dFn−1,1(x),
where Fn−1,1(x) = F (x)n= xn. In the equilibrium, the bidder with a valuation satisfying ¯pt(v) = p, who arrived at time t, should be indifferent between these two decisions. Therefore, we obtain
δt(v − ¯pt(v)) = δT Z v
0
(v − x)dFn−1,1(x), or equivalently
¯
pt(v) = v − δT−t Z v
0
(v − x)dFn−1,1(x).
Given the threshold strategy, we derive the expected seller revenue associated with buyout price p. We assume that each bidder arrives at the auction at time t according to distribution function J(t). For the sake of simplicity, we assume that seller revenue is not discounted. Suppose that a seller chooses buyout price p. If the bidder arriving first at time t has a valuation satisfying p ≤ ¯pt(v), which occurs with probability 1 − F (¯p−1t (p)), the item is sold at buyout price p at time t immediately. Otherwise, the item is sold at the second-highest value at time t = T because the bidder submits a sincere bid. Therefore, by choosing p, the seller obtains the following expected revenue:
ΠS(p) = nhp Z T
0
[1 − F (¯p−1t (p))]dJ(t) + Z 1
0
Z v 0
xdFn−1,1(x)dF (v)i. A seller optimally chooses p∗ to maximize her expected revenue shown above.
Mathews (2004, Theorem 1) shows that if the seller as well as bidders are patient (i.e., they do not discount future expected payoffs), the seller should set the buyout price sufficiently high so that bidders do not exercise their buyout option. This result is consistent with existing studies of risk aversion. On the contrary, if the seller is impatient, she optimally chooses a low buyout price that is
exercised with a positive probability, regardless of whether bidders are patient or impatient (Mathews, 2004, Theorem 1, Theorem 2). Note that the optimal buyout price depends on the degree of time sensitivity. In addition, Mathews (2004) numerically shows that a time-sensitive seller chooses a lower buyout price that may be exercised quickly as she becomes more impatient (i.e., she discounts her payoff more) and that given this time sensitivity, an optimal buyout price increases with the number of bidders.
In the case of a permanent buyout price, a bidder observes a current price as well as a buyout price when arriving. Because a permanent buyout price does not disappear even if some bidders submit bids, the current price may depart from zero. Therefore, the threshold depends on the buyout price as well as arrival time and the current price. Moreover, it may be optimal for the bidder to wait for a while and then exercise the buyout option. In other words, he remains active until the current price rises to his threshold and then exercises the buyout option. However, Gallien and Gupta (2007) show that this is not the case. In a symmetric equilibrium, a bidder immediately exercises a buyout option on arrival if the buyout price is at or below his threshold. On the contrary, the bidder submits a sincere bid at the end of the auction if the buyout price is above his threshold. Gallien and Gupta (2007) note that multiple equilibria yield the same outcome.
Moreover, they compare these two formats and numerically obtain the following findings. First, for a common buyout price, given the arrival time, the threshold is lower in the permanent format (i.e., a bidder more likely exercises a buyout option when facing a permanent buyout price). Consequently, a permanent buyout price generates higher expected seller revenue. This finding is counterintuitive at first glance, because a bidder appears to be under strong pressure when facing a temporary buyout price: a temporary buyout price disappears immediately if someone bids. Gallien and Gupta (2007) explain that there are more potential bidders in the permanent format, intensifying bidding compe- tition because some competitors may have already arrived by the time a new bidder arrives at the auction. Thus, for a bidder, exercising the buyout option is more attractive in the permanent format. The uncertain number of bidders plays an important role in Gallien and Gupta’s (2007) model. Sec- ond, if bidders are extremely impatient (δ → 0), the seller optimally sets a permanent buyout price higher than the temporary one. The second result is intuitive. From the first result, a bidder less likely exercises a buyout option in the temporary format. Thus, to prevent her from discounting expected utility, the seller should optimally choose a temporary buyout price below the permanent one.
4 Other explanations
Economists have proposed other theoretical models to explain the rational usage of buyout prices. This section considers three frameworks: seller competition and multi-unit demand, participation cost, and reference point. All the studies below assume that the seller and bidders are risk-neutral and patient. 4.1 Seller competition and multi-unit demand
The works mentioned above consider a monopolistic seller; however, we often observe that similar (or identical) items are sold on online auctions. Kirkegaard and Overgaard (2008) extend Black and de Meza’s (1992) model to formalize this situation and study a temporary buyout price.
We first examine Black and de Meza’s (1992) finding regarding sequential second-price auctions. In their model, two sellers sequentially intend to sell identical items to n ≥ 2 bidders demanding two units of the item with diminishing utility. Each seller owns one item. A bidder with valuation v obtains utility v from the first unit and kv (< v) from the second unit with k ∈ (0, 1). Clearly, in the second auction, bidders have a weakly dominant strategy to submit the marginal valuation, that is, v for the first unit and kv for the second unit. Black and de Meza (1992) show that in the first auction, bidders optimally submit a bid below their valuations (b(v) < v) in a symmetric equilibrium. Specifically, in the first auction, a bidder with valuation v submits
b(v) = E(max{ky1, y2}|y1= v)
= 1
Fn−2,1(v)[kvFn−2,1(kv) + Z v
kv
xdFn−2,1(x)],
where y1 and y2represent the highest and second-highest valuations among n − 1 bidders, respectively. Intuitively, competition in bidding is not severe in the first auction because every bidder has a chance to obtain one unit later even if he loses the first auction. Moreover, he may win the bid in the second auction even if his valuation is only the second highest among all bidders. Because of bid shading (i.e., placing a bid below the actual valuation), the first seller gains less than the second seller. There are only two equilibrium outcomes. The bidder with the highest valuation wins two units (v1 > kv1 > v2) and the bidder with the highest valuation and the one with the second-highest valuation obtain one unit each (v1 > v2> kv1).
Kirkegaard and Overgaard (2008) allow only the first seller to post a temporary buyout price in their model. As usual, bidders employ the threshold strategy to decide whether to accept or reject the buyout price. Kirkegaard and Overgaard (2008, Proposition 2) show that the threshold is non- monotonic regarding a buyout price. This result implies that multiple equilibria may arise, given the buyout price.
The first seller can increase her expected revenue by choosing an appropriate buyout price in cases where the buyout price is between the second-highest valuation and second-highest bidder’s bid (v2 > p > b(v2)). By exercising the buyout option, the second-highest bidder can obtain one unit and gain a positive payoff, yielding a higher selling price to the first seller. Note that in this case the bidder with the second-highest valuation would obtain nothing without a buyout price. In other words, the additional revenue by posting a buyout price stems from changing the winner in the first auction. However, a seller may fail to post a buyout price within the appropriate range stated above because of uncertainty about bidder valuations. Such an inappropriate buyout price lowers expected seller revenue. Kirkegaard and Overgaard (2008, Proposition 3) show that the advantage dominates the disadvantage and thus the first seller’s expected revenue increases with a buyout price. The optimal buyout price is accepted with a positive probability (Kirkegaard and Overgaard, 2009, Theorem 1), and hence a buyout price results in inefficiency. Moreover, a buyout price reduces the second seller’s revenue as well as the sum of the revenue of the first and second sellers.
4.2 Participation cost
Empirical evidence shows that bidders incur positive costs for participating in auctions and bidding. A participation cost is often discussed in the context of choosing selling formats, that is, a posted price, pure auctions, and auctions with a buyout price. The literature interprets a participation cost in (at least) two ways. A participation cost emerges from bidding behavior (Wang, Montgomery, and Srinivasan, 2008; Sun, Li, and Hayya, 2010). Usually, it is difficult for bidders to determine a bid price from information such as the potential number of competitors and current price. This type of cost, a cognitive cost, might discourage bidders from placing a bid and encourage them to exercise a buyout option. Alternatively, bidders may find it unsatisfactory to search for particular objects from excessive items on online auctions and hence hesitate to participate in auctions (Che, 2011). This type of cost reduces the chance of a buyout price being accepted as well as a bid being placed because bidders may leave auctions owing to the cost.
Wang, Montgomery, and Srinivasan (2008) model a sealed-bid second-price auction with a tem- porary buyout price in which a seller sells an item to n ≥ 2 potential bidders. Both the seller and bidders are risk-neutral. The seller values the item at zero, whereas each bidder’s valuation is inde- pendently and uniformly distributed on [0, 1]. Wang, Montgomery, and Srinivasan (2008) introduce separately the costs bidders incur to submit a bid (participation cost) and to exercise a buyout option (completion cost). They assume that each bidder’s participation cost is exogenously given from [0, 1] and common among the bidders. The auction is modeled as a two-stage game. In the first stage, the bidders simultaneously decide whether to exercise a buyout option and whether to submit a bid.
Two thresholds characterize a bidder’s optimal decision. A bidder does not enter the auction (i.e., he neither submits a bid nor exercises a buyout option) if his valuation is below a participation threshold. On the contrary, a bidder exercises a buyout option if his valuation is at or above a buy threshold, and submits a sincere bid if his valuation is intermediate (i.e., between the participation and buy thresholds).
By using the model mentioned above, Wang, Montgomery, and Srinivasan (2008) discover the following results. First, the participation threshold increases with the participation cost and number of bidders. In other words, bidders are more likely to participate in an auction and submit a bid as the participation cost lowers and number of bidders falls. The participation cost clearly discourages bidder entry. The impact of the number of bidders is also intuitive. A bidder with fewer competitors has a larger chance of winning and a stronger incentive to enter an auction.
Second, the buy threshold increases with the buyout price and decreases with the participation cost and number of bidders. In other words, bidders are more likely to exercise a buyout option if the buyout price is set lower, the participation cost is higher, and there are more bidders. A relatively high participation cost increases the advantage of a buyout price for bidders because bidders can save on the participation cost by exercising the buyout option. Similarly, bidders find it more beneficial to exercise the buyout option if they face more competitors, because an increase in the number of bidders intensifies bidding competition and reduces the chance of winning the auction. Third, an optimal buyout price is unique, increasing with the number of bidders but indeterministic with the participation cost. A positive correlation between the optimal buyout price and number of bidders is consistent with Gallien and Gupta’s (2007) finding. Finally, a numerical analysis shows that a buyout price generates an increase in expected seller revenue with a wide range of parameters for the number of bidders and participation cost.
Sun, Li, and Hayya (2010) consider a seller’s optimal choice of selling format. A seller intends to sell an item to n ≥ 2 bidders and selects a format from posted price, pure auction, and auction with a buyout price. The auction is a sealed-bid second-price auction. Both the seller and bidders are risk-neutral. A seller incurs an operation cost when an item remains unsold in any format. The seller values the item at zero, whereas each bidder’s valuation is independently and identically distributed on [v, ¯v]. Observing their own valuation and the selling format, bidders simultaneously decide whether to enter the auction to submit a bid or exercise a buyout option (if available). A bidder incurs an entry cost to enter the auction.
Similar to Wang, Montgomery, and Srinivasan (2008), two thresholds characterize a bidder’s opti- mal decision. A bidder does not enter the auction if his valuation is below a participation threshold. A
bidder exercises a buyout option if his valuation is at or above a buyout threshold and submits a sincere bid otherwise. The seller’s optimal choice is complicated to derive; thus, Sun, Li, and Hayya (2010) numerically show that under a broader range of parameters (number of bidders and participation and operational costs), a seller prefers an auction with a buyout price to a pure auction.3
Che (2011) introduces the entry cost bidders incur into a two-bidder two-valuation model and constructs a two-period model. In period 1, a seller initially chooses a temporary buyout price and a reserve price, and then one bidder arrives at a sealed-bid second-price auction. The bidder decides whether to enter the auction with a positive entry cost and then chooses a bid or a purchase at the buyout price. In period 2, another bidder appears and makes the decision that the early-arrived bidder similarly faced in period 1. Note that in period 2, the later-arrived bidder gathers additional information about whether the early-arrived bidder actually submitted a bid or left the auction. In cases of a tie, the item is randomly assigned to the bidders.
If a buyout price is not available, the seller simply sets a reserve price at the expected bidder surplus, which is either high or low, relating to the bidder valuation. A high reserve price prevents a low-valuation bidder from entry; thus, the seller can sell her item at the high reserve price if at least one bidder has a high valuation. Alternatively, a low reserve price encourages the early-arrived bidder to enter in period 1 irrespective of his valuation. In period 2, however, a low-valuation bidder never enters because he ends in a tie at best and his expected payoff is negative due to the entry cost. A high-valuation bidder enters whenever the early-arrived bidder has a high valuation with sufficiently low probabilities. This implies that a low reserve price deters even a high-valuation bidder from entering in period 2 if the early-arrived bidder tends to have a high valuation.
A buyout price encourages a high-valuation bidder to enter in period 2 and improves expected seller revenue. Che (2011) derives two equilibria when a high-valuation bidder solely exercises a buyout option, similar to the equilibrium in Budish and Takeyama (2001). In one equilibrium, a seller posts a low reserve price with an appropriate buyout price. In period 1, a high-valuation bidder enters an auction and immediately accepts the buyout price, but a low-valuation bidder does not enter the auction. In period 2, however, both types of bidders enter the auction and submit sincere bids. In another equilibrium, a seller posts a low reserve price with an appropriate buyout price (these prices are different from those mentioned above). In period 1, both types of bidders enter an auction and a high-valuation bidder solely accepts a buyout price. In period 2, however, a high-valuation bidder
3They report that a posted price can outperform an auction with a buyout price when the number of bidders is large and participation cost high (Sun, Li, and Hayya, 2010, Observation 3). In other words, a seller’s optimal choice of format depends on the number of bidders and participation and operational costs, which explains why these formats co-exist on online auctions.
enters the auction and submits a sincere bid, whereas a low-valuation bidder does not enter. These two equilibria lead to efficient outcomes.
4.3 Buyout price as a reference point
Shunda (2009) adopts a behavioral economics framework to examine the rationality of using a buyout price and constructs a model similar to Rosenkrantz and Schmit’s (2007) model, where bidders have reference-dependent utility. The seller values her item at zero. Each bidder observes his valuation independently and identically drawn from [v, ¯v] according to distribution function F . Bidders can incur disutility if the winning price is far from a certain reference price. The only difference between the models is that in Rosenkrantz and Schmit (2007), bidders use a reserve price (r) to form the reference price, whereas in Shunda (2009), the reference price (ρ) is given as a convex combination of the buyout and reserve prices; that is, ρ = λr + (1 − λ)p with λ ∈ (0, 1). Conditional on winning with payment x, a bidder with valuation v and reference price ρ obtains v − x − ε(x − ρ). The positive impact of a reference price is featured by ε, where ε = 0 corresponds to a standard reference-free preference.
An auction consists of two stages. In the first stage, the seller chooses the temporary buyout and reserve prices and bidders simultaneously decide whether to accept or reject the buyout price. If all bidders reject the buyout price, the second stage, that is, a sealed-bid second-price auction, emerges. Shunda (2009) shows that two thresholds characterize a unique symmetric equilibrium (Proposition 1 and Proposition 2). As usual, a bidder exercises a buyout option if his valuation is at or above a buyout threshold. One important point is that the buyout threshold decreases with the reserve price (i.e., a buyout price is exercised more often for a higher reserve price). Unlike reference-free cases, the bidder does not submit a bid in the second stage if his valuation is below a participation threshold. Importantly, the participation threshold increases with the buyout price, i.e., a higher price less likely encourages the bidder to submit a bid, even after the buyout price was rejected in the first stage. Moreover, the bidder submits a bid β(v) = (v + ερ)/(1 + ε) in a weakly dominant strategy when participating in the second stage. Shunda (2009) emphasizes the importance of the impact of a buyout price on bidding behavior. No other theoretical works assuming reference-free utility can explain the effect of a buyout price on bidding behavior, although the empirical evidence indicates that the buyout price itself raises the winning bid.4 Moreover, Shunda (2009, Theorem 1) shows that a seller optimally chooses the cutoff v∗< ¯v, implying that the buyout price is accepted with a positive probability. Further, in this model, an appropriate buyout price leads to inefficiency.
4For example, Dodonova and Khoroshilov (2004) empirically show that bidders place higher bids in auctions with a higher buyout price. They suggest that bidders use a buyout price to form the reference price. Popkowski Leszczyc, Qiu, and He (2009) also show that a buyout price serves as a reference price; however, they find that uncertainty about a product value softens the reference-price effect.
5 Empirical studies
Field studies are usually motivated with questions such as who uses a buyout option and when, and they focus on the relation between observable seller characteristics and the buyout price. On the contrary, experimental studies can control for the environment to examine bidder behavior. In this section, we examine some empirical studies. Section 5.1 introduces three field studies, section 5.2 introduces two field experiments, and section 5.3 introduces three laboratory experiments.
5.1 Field studies
Anderson, Friedman, Milam, and Singh (2008) investigate the effects of product and seller character- istics on seller choice on the starting and buyout prices and other predicted auction outcomes. They collect data from the Palm Vx PDA (a personal digital assistant) auctions on eBay from August 6 to September 11, 2001, and focus on 722 samples from a successful sale: 212 auctions with a buyout price and 510 pure auctions. The average selling price in the samples is $201.5 in the former and
$198.0 in the latter. Each sample includes product characteristics (new or damaged product) and seller characteristics (frequency of listing items during the periods above, number of listings at the same time, and positive and negative feedback scores).
The empirical analysis is carried out as follows. First, they estimate the effects of product and seller characteristics on seller choices. They use ordinary least squares (OLS) estimation for continuous choices such as the starting and buyout prices and logit estimation for binary choices such as sellers’ decision on whether to offer a buyout option. Second, they estimate the contribution to the transaction price using two-stage least squares (2SLS) estimation. To control for potential endogeneity, they employ four instrumental variables: duration, number of bids, number of unique bidders, and whether the buyout price is accepted. As noted above, the dataset is restricted to auctions resulting in a successful sale; thus, the result is conditional on a successful sale.
Their findings are as follows. First, with regard to product characteristics, sellers appear to post a buyout price more often on new items and damaged ones. The share of auctions with a buyout price of new items (31.8%) and items mentioning significant damage (33.3%) exceeds the average share of all auctions with a buyout price (29.4%). However, the buyout prices of new and damaged items are different. Indeed, the ordinary least squares regressions suggest that sellers increase the buyout price by $20 for a new item but reduce it by $32 for a damaged one. Second, the frequencies of listing items and posting a buyout price are positively correlated. The statistics indicate that 34.7% of frequent sellers post a buyout price, whereas the ratio of infrequent sellers using a buyout price is 25.2%. This result, suggesting a positive relation between experience in trading on eBay and the usage of a buyout
price, has been confirmed by other empirical studies (Durham, Roelofs, and Standifird, 2004).5 Third, providing a buyout price modestly raises the selling price, whether the buyout price is accepted or rejected, but this effect is not statistically significant.6 However, conditional on a buyout price being posted, a $1 increase in the buyout price statistically significantly raises the selling price by $0.29.
Wang, Montgomery, and Srinivasan (2008) theoretically obtain three testable predictions: the optimal buyout price posted by a seller is positively correlated with the number of potential bidders; the participation cost bidders incur negatively affects the optimal buyout price; and a seller is likely to choose a pure auction when the participation cost, reserve price, and number of bidders are high. To test these predictions, they correct the data of four categories of electrical product auctions on eBay from April 1 to May 20, 2003.7 The dataset consists of 1418 samples, where approximately 30% of auctions have a buyout price, while the share of auctions with a buyout price is diverse among the four categories.
The analysis is twofold. First, by using the log-normal regression model, they test their prediction. For the analysis, they restrict their attention to auctions with a buyout price. The proxy variables are employed as follows. Since an auction with a longer duration tends to attract more bidders, duration can work as a proxy variable for the number of potential bidders. On the contrary, a bidder with a higher feedback score incurs a smaller participation cost because more experienced bidders are more familiar with the auction rules and transactions. Therefore, the bidder’s feedback score works as a proxy variable for the participation cost. Second, by using the multinomial logit model, they estimate the effects of the variables on endogenous entry in an auction. They find that the logit analysis supports all the predictions mentioned above in all four categories.
Chen, Chen, Chou, and Huang (2013) empirically investigate the impact of a buyout price on a selling price. There are two important differences between this study and other empirical ones. First, they choose (Taiwan) Yahoo Auction, which provides a buyout price in the permanent format,
5Durham, Roelofs, and Standifird (2004) collect 138 samples of US Silver Dollar (American Eagle coins) auctions from eBay and study the functions of a temporary buyout price. In their experimental field study, all auctions have the same starting price of $1.00, but the buyout prices are diverse. They find a positive correlation between feedback number and the frequency of posting a buyout price. Moreover, they find that buyout prices are accepted more often in auctions listed by a seller with a better reputation and less likely accepted in auctions listed by new sellers (i.e., sellers with limited feedback scores). A buyout price statistically and significantly raises the selling price. The average price for 41 auctions with a buyout price is $10.27 and the remaining auctions have an average selling price of $9.56.
6Grebe, Ivanova-Stenzel, and Kroger (2006) report a different observation from 668 auction samples in arts, antiques, and collectibles on eBay in March and April 2002. They observe that selling prices do not reach the buyout prices in 92% of auctions after the buyout prices were rejected, implying that bidders can make a “correct” decision. Moreover, they note that time preferences might not explain the benefits of a buyout price, because buyout prices can save only 2.9 days, while the duration is on average 7 days.
7The categories are an Apple iPod MP3 player 10 GB, Lexar memory stick 128 MB, KitchenAid 525 W mixer, and KitchenAid KSM103 professional mixers.
rather than eBay. They point out the advantage of empirically studying a permanent buyout price in that the record of a buyout price remains until the auction closes. Second, they exclude from their main analysis auctions with a buyout price equal to the starting price. This usage of buyout prices represents selling at a fixed price. This is an important point because offering a buyout price and selling at a fixed price are completely different strategies to a seller.
Chen, Chen, Chou, and Huang (2013) collect data from digital camera auctions (several types of Nikon Coolpix digital compact cameras) on Taiwan Yahoo Auction from April 3 to August 2, 2008. The empirical analysis focuses on 785 samples: 131 auctions with a buyout price and 654 pure auctions. The average selling price is NT$6,977 in the former and NT$3,758 in the latter.
The analysis is twofold. First, they consider the selection problem, observing the transaction price only in auctions resulting in a successful sale. For the selection problem, they adopt a probit selection model. The variables explain a successful sale and include the seller’s feedback rating score, number of bidders, and starting price. Second, they estimate the contribution to the transaction price using the 2SLS method. For the estimation, they employ two instrumental variables (number of days since the seller joined Yahoo Auction as a member and number of listings by the seller) to consider the potential endogeneity on posting a buyout price.
They make the following findings. First, a probit regression shows the negative effect of a starting price on a successful sale. On the contrary, the seller’s feedback score and number of bidders positively contribute to a successful sale. Second, the 2SLS analysis results with the instruments suggest that a buyout price significantly increases a selling price. The seller’s feedback rating and number of bidders have positive impacts on the selling price as well. Finally, the auction of new items tends to end with higher selling prices, but this finding is not statistically significant.
5.2 Field experiments
Standifird, Roelofs, and Durham (2005) conduct a field experiment using the eBay platform and consider the impacts of a buyout price on bidding behavior. They prepare new eBay accounts for 84 auctions of the US Silver Dollar (American Eagle coins) on eBay between October and December 2001. They choose the silver coin auction because it is easy to obtain and evaluate the coins and the auction participants do not buy the coins for resale. The auctions are controlled for in that they have identical starting prices ($1.00), shipping costs ($2.00), and descriptions, although the buyout prices are diverse. The auctions are classified into four groups, each consisting of 21 auctions. The silver coins in the first group are sold in pure auctions to obtain the market price of the coin. From the market price obtained in the first group ($6.82), the rest of the auctions offer different buyout prices: a high price ($8.05) for 21 coins in the second group, an intermediate price close to the market price
($6.80) for the third group, and a low price ($5.60) for the last group. All the coins are successfully sold. The high buyout price is never accepted; however, of the 21 auctions, two and five auctions (9.5% and 23.8%, respectively) in the third and fourth groups respectively end with the buyout price. Standifird, Roelofs, and Durham (2005) discover the following findings. First, a chi-square test confirms no statistically significant difference between the selling prices in all four treatments. This finding suggests that a buyout price does not affect a selling price and hence expected seller revenue. Second, experienced bidders are more likely to accept a buyout price. As the authors note, however, the small sample of bidders exercising the buyout price (7 of 62 or 11.1%) limits the scope of the analysis. Finally, few bidders accept a buyout price set below the market price. In fact, only 23.8% of the low buyout prices are accepted. Moreover, the average selling price exceeds the low buyout price. This finding contradicts the theory suggesting the risk aversion or impatience of bidders. Alternatively, Standifird, Roelofs, and Durham (2005) explain this phenomenon by hedonic benefits; that is, bidders enjoy participating in auctions and beating their competitors.8
Grebe, Ivanova-Stenzel, and Kroger (2006) conduct a framed field experiment and analyze the impact of a buyout price on seller revenue and auction efficiency. They perform seven experimental sessions, each consisting of six eBay auctions. In total, 84 subjects are assigned to a group consisting of a seller and two bidders. The experimenters prepare valid eBay accounts with similar transaction histories and feedback scores to control for the effect of reputation. A seller uses the prepared account to log into eBay, but bidders use their existing accounts. In the experiment, a seller first accesses eBay and lists a used book. She posts a buyout price but the starting price is set by the experimenters. Second, two bidders are separately informed of their “valuations” of the auctioned item, which are independently drawn from V = {1, 1.5, 2, · · · , 49.5, 50} with equal probability, while a seller values the item at zero. Bidders have asymmetric roles. Bidder 1 has to decide whether to exercise a buyout option within two minutes. If bidder 1 rejects the offered price, both bidder 1 and bidder 2 compete in bids. Since the bidders are given five minutes for bidding, they can make multiple bids. In addition, they conduct a follow-up experiment where the experiments offer 10 pairs of lotteries to assess the risk attitudes of subjects.
With the normalization of V to [0, 1] and a uniform distribution, theory predicts as follows. If both the seller and bidders are risk-neutral, the seller optimally sets the buyout price sufficiently high (p ≥ 0.50) for the bidders not to accept in the equilibrium. According to the equilibrium threshold strategy, bidders accept p ≤ 0.50 but reject p > 0.50.
8This concept is commonly used in the marketing and psychology literature. Hedonic benefits emerge as a significant factor, where the transaction itself provides value to the individual consumer independent of the actual procurement of a particular item (Standifird, Roelofs, and Durham, 2005).
The following results are obtained. First, the average buyout price is 0.50, which falls within the range of theoretically optimal prices (p ≥ 0.50). In fact, a price of p = 0.50 is most frequently observed (13.3%). However, 47% of buyout prices are chosen below the optimal level. Grebe, Ivanova- Stenzel, and Kroger (2006) state that this observation implies that half of the sellers are risk-averse. Second, 36% of buyout prices are accepted. High buyout prices (p > 0.50) are often accepted, whereas low buyout prices (p < 0.50) are sometimes rejected. In fact, 31% of bidders accept high buyout prices (p > 0.50) and 14% reject low prices (B < 0.50). The authors state that this result indicates the diverse risk attitudes among bidders. Third, a buyout price does not significantly impact seller revenue and bidder payoff, although it yields a small reduction (6%) in bidder payoff. Fourth, bidders often exhibit underbidding after rejecting a buyout price. In fact, bidders reduce their bids by 13.5% on average, and 65% of bids are set below the bidder’s actual valuation. That is, they do not follow a weakly dominant strategy. Note that experienced bidders tend to weaken underbidding but this impact is not significant. Moreover, experience in trading on eBay has no significant impact on the decision on buyout prices. Finally, the ratio of efficient outcomes remains at the level of 87%.
5.3 Laboratory experiments
By employing a similar environment to the framed field experiment in Grebe, Ivanova-Stenzel, and Kroger (2006), Ivanova-Stenzel and Kroger (2008) conduct a laboratory experiment with 90 subjects (students of various departments at Humboldt University). They consider the impacts of a buyout price on seller revenue, bidder payoff, and auction efficiency. They perform four experimental sessions, each comprising eight auctions. Subjects are randomly assigned to a group consisting of a seller and two bidders. The bidder valuation is independently drawn from V = {0, 1, 2, · · · , 99, 100} with equal probability, while a seller values the item at zero. The auction consists of two stages. In the first stage, one bidder is randomly selected. A seller chooses an integer between 0 and 100 as the buyout price. The selected bidder then decides whether to accept or reject the buyout price. If he rejects it, the second stage emerges. In the second stage, both the bidders enter an ascending auction. Note that the second bidder is not informed of the rejected buyout price. This random selection of a bidder represents online auctions in which bidders randomly arrive at an auction and, in many cases, early-arrived bidders can solely exercise the buyout option.
Ivanova-Stenzel and Kroger (2008) obtain results consistent with those in Grebe, Ivanova-Stenzel, and Kroger (2006), except one factor. Underbidding is observed in the latter but not in the former study. In fact, regression analysis shows that bidders submit bids according to a dominant strategy regardless of whether they face a buyout price, implying that the introduction of a buyout price does not change bidding behavior. The common results are (i) more than half of buyout prices (51.6%)
are chosen below the optimal level, (ii) high buyout prices are frequently accepted (57%), whereas low ones are sometimes rejected (18%), and (iii) a buyout price does not significantly impact seller revenue and bidder payoff, although bidders slightly reduce their payoffs with a buyout price (11% reduction in bidder payoff). A buyout option gives the advantage to neither seller nor bidder. Moreover, they find that 85% of outcomes are ex post efficient. As Ivanova-Stenzel and Kroger (2008) point out, it is unclear whether the introduction of a buyout price induced ex post inefficient outcomes in the experiment, because other experimental studies of a sealed-bid second-price auction without a buyout price report that the ratio of efficient outcomes is approximately 90% (Guth, Ivanova-Stenzel, and Wolfstetter, 2005; Pezanis-Christou, 2002).
Shahriar and Wooders (2011) conduct a laboratory experiment to explore the impact of a tem- porary buyout price on seller revenue and auction efficiency under both private and common values. They perform six experimental sessions, each comprising 30 auctions. All 96 subjects are randomly assigned to a group consisting of four bidders. The subjects in each group participate in any of the four auctions: private value auctions with and without a buyout price and common value auctions with and without a buyout price. In this section, we focus on private values. A bidder is given a private value independently and uniformly drawn from [0, 10] in dollars, and the buyout price is set at $8.10 by the experimenters. From the answers to the questionnaire aimed to measure the risk attitudes of subjects, any buyout price above $7.50 theoretically raises expected seller revenue. Following the theoretical frames of previous studies (Mathews and Katzman, 2006; Reynolds and Wooders, 2009; Shahriar, 2008), a two-stage game features an auction with a temporary buyout price. In the first stage, bidders simultaneously decide whether to accept or reject the buyout price. If all bidders reject the buyout price, bidders enter the second stage, which is an ascending auction.
Shahriar and Wooders (2011) make the following findings. First, a buyout price is accepted in 45% of auctions. Since this acceptance rate implies risk-averse bidders, they estimate a degree of risk aversion, assuming that bidders have CARA utility in the shape of u(x) = (1 − eαx)/α, where α ≥ 0 represents the degree of risk aversion. The estimation significantly indicates risk aversion (α = 1.092). Moreover, as theory predicts, the bidder valuation positively affects the acceptance rate. A probit regression shows that among bidders with a valuation above the buyout price, a $1 increase in the bidder valuation significantly increases the probability of acceptance by 26.6%. Second, the introduction of a buyout price yields a 6.8% increase in seller revenue from $6.06 to $6.47. This increase is statistically significant. A pairwise comparison also shows that bidders exercising a buyout option would submit a bid below the buyout price if they participated in pure auctions. Moreover, the data show that a buyout price reduces the variance in seller revenue, suggesting that a risk-averse
seller also prefers a buyout option. Third, the introduction of a buyout price does not influence bidding behavior. After rejecting a buyout price, bidders submit a bid in the subsequent auction as if they are participating in a pure auction. However, note that bidders do not follow a dominant strategy; rather, they lower the bid in auctions with or without a buyout price. The regressions show that bids are approximately 95% of bidders’ valuations. Finally, as theory predicts, auction efficiency reduces with the buyout price. The bidder with the highest valuation obtains an item in 93.3% of pure auctions, whereas the ratio is only 89.4% in auctions with a buyout price. That is, introducing a buyout price reduces ex post efficiency by 3.8%. However, the difference is not statistically significant. Shahriar and Wooders (2011) discuss that the overall results appear to be consistent with the theoretical predictions assuming risk-averse bidders.
Durham, Roelofs, Sorensen, and Standifird (2013) conduct a laboratory experiment to consider the impacts of a buyout price on acceptance rate, seller revenue, bid timing, and auction efficiency. Their study is especially motivated by the question of why eBay and Yahoo adopt different buyout systems. They recruit 48 subjects (students of economics courses at Western Washington University) and perform eight experimental sessions between May 2005 and October 2009. Each session consists of four blocks of 10 auctions; thus, each subject engages in 40 auctions. Subjects are randomly assigned to a group consisting of two bidders. Two bidders first enter into a series of ascending auctions without a buyout price in the first block and then a series of ascending auctions with temporary/permanent buyout prices in the subsequent blocks.9 The bidder valuation is a uniform draw from [1, 100] and buyout prices are high (75), middle (50), or low (25), as chosen by the experimenters. Bidders are given 60 seconds for each auction. After the experiments, subjects answer a risk questionnaire aimed at measuring their risk attitudes.
Since a low buyout price (25) is suboptimal, in the sense of lowering seller revenue, we focus on the results relating to the middle and high buyout prices (50, 75). First, the acceptance rates of permanent and temporary buyout prices are almost the same (55.8% vs. 52.6%). In fact, the probit regressions show that the difference is not statistically significant. Naturally, in both formats, the probabilities are greater when the valuations of both bidders exceed the buyout price than when a single bidder has a valuation above it. Moreover, low buyout prices are accepted more often than high ones. Second, both temporary and permanent buyout prices weakly improve seller revenue. The statistics show that permanent buyout prices yield 12.8% higher revenue than temporary ones, but the difference is not statistically significant. Third, both temporary and permanent buyout prices facilitate early bidding, defined as bids occurring in the first four seconds in their study. The data
9Durham, Roelofs, Sorensen, and Standifird (2013) distinguish two bidding systems. Bidders are allowed or not
show that bids are concentrated on the ending time in pure auctions; the timing is separated into early and late in auctions with a buyout price. In particular, to restrict the proxy bidding case, 44% of bids are early bids when bidders faced a temporary buyout price, whereas only 18% are early bids in auctions with a permanent buyout price. The difference is statistically significant. The result seems consistent with Gallien and Gupta’s (2007) findings, indicating that a bidder submits a bid at the closing when facing a permanent buyout price. Finally, buyout prices, regardless of whether they are temporary or permanent, improve auction efficiency. An item is allocated to a bidder with a higher valuation in 69.6% of pure auctions. On the contrary, the shares are 77.4% in the temporary format and 73.3% in the permanent one. The final finding contradicts the theoretical prediction and hence is interesting. All theoretical works state that the introduction of a buyout price reduces auction efficiency; that is, the bidder with the highest valuation does not always obtain the item. As stated above, late bidding is observed in all auctions regardless of whether a buyout price existed. Durham, Roelofs, Sorensen, and Standifird (2013) argue that late bidding (known as sniping) reduces auction efficiency and that early bidding induced by a buyout price improves efficiency. This point can be empirically tested by conducting an experiment that employs a soft-close rule as an ending auction, because late bidding occurs less in soft-close auctions (Roth and Ockenfels, 2002; Ariely, Ockenfels, and Roth, 2005; Ockenfels and Roth, 2006). In summary, the two formats affect seller and bidder behavior in similar ways, except with regard to the timing of bids.
6 Concluding remarks
Yahoo made its first move to introduce a buyout price in online auctions, and its model was followed by eBay shortly after. Although a buyout option is preferred by many sellers and bidders, at first glance it seems irrational to use this technique. In fact, an auction is superior for sellers to a posted price under a variety of conditions, and the upper bound of a selling price can depress expected seller revenue. In such situations, economists have attempted to rationally explain what leads users to employ the buyout price. This paper marshals some of the existing studies of applying a buyout price, a frequently used method in online auctions.
The literature suggests theoretical explanations for the rational usage of buyout prices. The first is risk aversion. If a seller and bidders are risk-averse in the sense that they avoid variance in the selling price, they benefit by applying a buyout price. A buyout price functions as insurance; its advantage lies in the risk premium that risk-averse users are willing to pay. Time sensitivity is another explanation. A seller saves time by offering items at a lower buyout price, whereas bidders willingly pay a premium to obtain the items they want quickly. Behavioral economics presents another aspect of buyout prices.
Along with a reserve price, a buyout price forms a reference price for bidders. Other theoretical works suggest that a buyout price increases seller revenue in cases where bidders incur an entry cost and only one seller uses a buyout option among multiple competitors.
These explanations are appealing, but the analyses seem far from comprehensive compared with, for instance, studies of a reserve price being accumulated. In the following, we list four issues that are not addressed in the literature.
First, all studies, except Shahriar (2008) and Shahriar and Wooders (2011), focus on auctions with private value and we do not know if a buyout price raises expected seller revenue in interdependent environments as well. As mentioned previously, sellers on eBay auctions indicate a buyout price prevalently in various categories, some of which are considered to be auctions with an interdependent value. We may draw an affirmative answer from this observation, but Shahriar (2008) obtains a negative result in a common-value environment. He studies a temporary buyout price in an auction with a common value in which a seller sells an item to n ≥ 2 potential bidders. The bidders are risk-averse with CARA utility in the form of u(x) = (1 − e−αx)/α, where α ≥ 0 represents the degree of risk aversion. Bidders each receive a payoff-relevant signal, which is an independent draw from [v, ¯v], and a common value is given by an average of all bidders’ signals.
Shahriar (2008) constructs a two-stage model. In the buyout stage, by observing the individual signal, bidders simultaneously decide whether to accept or reject the buyout price given exogenously. If all bidders reject the buyout price, a bid stage emerges, which is a sealed-bid second-price auction. In a symmetric equilibrium, similar to independent private-value environments, the bidder employs a threshold strategy in the buyout stage. More importantly, in a specific case with two bidders, the author shows that any buyout price reduces expected seller revenue whenever a buyout option is exercised with a positive probability. The outcome implies that a common value may change the impact of a buyout price dramatically. However, experimental observations do not support this result. Following Shahriar’s (2008) model, Shahriar and Wooders (2011) conduct a common-value auction experiment with a temporary buyout price. From the report, a buyout price increases seller revenue, but not to a statistically significant extent. Further, after turning down a buyout price, bidders submit a relatively low bid compared with an auction without a buyout price, leading to a decline in seller revenue.10 The results obtained in these two studies imply that a buyout price must be studied in interdependent value environments.
Second, the literature ignores the signaling function of buyout prices. In fact, a number of second-
10A buyout price can lower expected seller revenue if bidder valuations are discrete as well. Inami (2011) extends Budish and Takeyama’s (2001) model to n ≥ 2 bidders with m ≥ 2 types. The author focuses on the equilibria where a bidder exercises a buyout price if his value is at or above a certain threshold and otherwise submits his value truthfully. Inami (2011) shows that a buyout price increases seller revenue in two-type cases, but not necessarily in three-or-more-type cases. Moreover, discrete types may cause the optimal choice of the buyout price to be more complicated.
hand items are listed on online auctions, and bidders are naturally interested in the quality or condition of used goods. From a seller’s perspective, she wishes to reveal more information if her item is of high quality or is in good condition. A buyout price may contribute to satisfy this situation. In fact, Anderson, Friedman, Milam, and Singh (2008) note that the signaling function of a buyout price may explain the phenomenon of a selling price ending extremely high with a large buyout price. To the best of my knowledge, no theoretical paper so far has considered a buyout price as a signal.11 Although a buyout price signal may be practical at a glance, it is difficult to show the rational use of buyout prices as quality signals theoretically. A buyout price serves as a signal only if a seller has to face a trade-off when posting higher buyout prices. However, this is not the case for a buyout price. To see this, suppose that a higher buyout price implies an item of higher quality. In this case, a higher buyout price is accepted with a higher likelihood by bidders because they more willingly pay for an item of higher quality. Thus, posting a high buyout price generates benefits to a seller of a high selling price and a high acceptance probability, instead of a trade-off. We thus need to solve the difficulty in modeling a buyout price signal.
Third, sellers on online auctions post reserve and buyout prices in various combinations. A natural question that arises is what is the optimal combination of reserve and buyout prices. Since the pair jointly provides the lower and upper bounds of a bid price, deciding their optimal combination is equivalent to determining the optimal interval of a bid price.12 Despite the introduction of both reserve and buyout prices in the model, a reserve price is exogenous in most studies.13 The important exceptions are Shunda (2009) and Che (2011). Shunda (2009) introduces a reference price formed jointly by the reserve and buyout prices. The optimal buyout price exceeds the optimal reserve price, and Shunda’s model delivers a higher optimal reserve price relative to that where a reference price is solely formed by a reserve price. In the model where bidders incur a participation cost, Che (2011) characterizes the optimal combination of reserve and buyout prices. However, only two values appear in Che’s model and the relation between the reserve and buyout prices (i.e., complement or substitute) is generally ambiguous.
Fourth, although multi-unit auctions hold a prominent position in the recent literature on auctions, a buyout price is not studied in this context. Sellers on online auctions frequently indicate a buyout
11The signaling function of a reserve price is well investigated theoretically and empirically. Cai, Riley, and Ye (2007) consider a sealed-bid second-price auction with interdependent value where each bidder’s valuation depends upon a seller’s and all the bidders’ private signals in a general environment. Anderson, Friedman, Milam, and Singh (2008) provide empirical evidence showing the slightly positive impact of a starting price (i.e., public reserve price) on a selling price.
12Chen, Chen, Chou, and Huang (2013) report the positive relation between the starting and buyout prices in Taiwan Yahoo Auction. The average starting price reaches NT$5,978 in auctions with a buyout price, whereas it remains at only NT$4,991 in pure auctions.
13For example, a reserve price is not a strategic variable in Gallien and Gupta (2007) and Reynolds and Wooders (2009).
