ESSAYS OF APPLIED ECONOMICS



ESSAYS ON APPLIED ECONOMICS

By

Mingli Zheng

A thesis submitted in conformity with the requirements

For the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

University of Toronto

[pic]©Copyright of Mingli Zheng (2002)

ABSTRACT

ESSAYS ON APPLIED ECONOMICS

By

Mingli Zheng

DOCTOR OF PHILOSOPHY

Department of Economics

University of Toronto

This dissertation consists of two essays on applied economics.

In the first essay, I provide an empirical assessment of competing auction theory. Specifically, it uses an extensive new data set containing detailed information about bids placed on eBay computer CPU auctions to explore bidding strategies in the presence of competing auctions. The evidence indicates that a significant proportion of bidders bid across several competing auctions at the same time and that bidders tend to submit bids on auctions with the lowest standing bid. We also find that winning bidders who bid across competing auctions pay lower prices than winning bidders who do not cross-bid. These findings jointly amount to the first evidence lending empirical support to competing auction theory.

In the second essay, I consider the convergence properties of behavior under a comparative negligence rule (CN) and under a rule of negligence with contributory negligence (NCN), assuming bilateral care with three care levels. Using an evolutionary model, we show that CN reduces the proportion of the population using low care more rapidly than does NCN. However NCN increases the proportion of the population using high (efficient) care more rapidly than does CN. As a result, the mean care level increases more rapidly and the mean social cost falls more rapidly under CN than under NCN.

ACKNOLEDGEMENTS

I am deeply indebted to my supervisor Michael Peters for his guidance. I also thank Don Dewees and Robert McMillan. Their generous help, stimulating suggestions and constant encouragements helped me in all the time of research for and writing of this thesis. My gratitude to them cannot be expressed by words.

I could not have survived the PHD study without the understanding and the support by my wife Fang Xiao. I would like to give her special thanks.

I also thank Mohr Siebeck for authorizing me to include the paper published in JITE in my dissertation.

Table of Contents

Abstract……………………………………………………………………………….ii

Acknowledgements………………………………………………………….………iv

List of Tables……………………………………………………….………………..vi

List of Figures……………………………………...………………………………..vii

Chapters

Bidding Behavior with Competing Auctions: Evidence from eBay

Abstract………………………………………………………………………1

1. Introduction………………………………………………………………..3

2. Theory of Competing Auctions………………………………………..…..7

3. Mechanism in eBay and Summary of Data………………………………11

4. Bidding Behavior with Competing Auctions in eBay……………………18

5. Do Cross Bidders Pay Lower Price?...…………………………………...26

6. Conclusion………………………………………………………………..27

References…………………………………………………………………..29

Liability Rules and Evolutionary Dynamics

Abstract……………………………………………………………………..43

1. Introduction………………………………………………………………44

2. Liability Rules and Nash Equilibrium……………………………………47

3.Evolutionary Dynamics…………………………………………………...50

4. Conclusion………………………………………………………………..68

References…………………………………………………………………..70

List of Tables

Table Page

1.1 Sample statistics for CPU auctions ……………………………………….32

1.2 Sample Statistics for Samples of Competing Auctions……………………33

1.3 Statistics of Cross Bidding in the Whole Process…………………………35

1.4 Statistics of Cross Bidders for the Last Day……………………………….37

1.5 Percentage of Cross Bidders in All bidders………………………………..38

1.6 Result on Bidding on the Auction with the Lowest Standing Bid…………39

1.7 Result on Bidding on Group with Zero Bid Auctions……………………...40

1.8 Average Number of Bids Submitted in a Group by a Bidder……………....41

1.9 Price Paid by Cross Bidders and Non-Cross Bidders………………………42

1. Payoff Under CN………………………………………………………...…49

2. Simulation Results………………………………………………………….63

List of Figures

Figure Page

1.1 A Bidding History Page From eBay………………………………….31

1.2 Histogram of Bidders’ Feedback…………………………………….34

1.3 Histogram of Bids Submission Time for Daily Sample……………..36

2.1 Proportion of Individuals Taking High care…………………………64

2.2 Proportion of Individuals Taking Medium Care……………………..64

2.3 The Composition of the Population in the Simulation……………….65

Chapter 1

Bidding Behavior with Competing Auctions:

Evidence from eBay[1]

Abstract

The existing auction literature treats on-line auctions as running independently of one another with each bidder choosing to participate in only one auction. This characterization is less than perfect: in on-line auctions, many substitutable goods are auctioned concurrently, and bidders can bid in several auctions at the same time. Recent theoretical research by Peters and Severinov (2001) is more relevant to the study of bidding behavior in on-line auctions, showing that bidders can gain from the existence of competing auctions. Specifically, a strategy in which bidders bid on the auction with the lowest standing (or prevailing) bid is a Bayesian Nash equilibrium. In the light of this work, the current paper provides the first empirical assessment of competing auction theory. Specifically, it uses an extensive new data set containing detailed information about bids placed on eBay computer CPU auctions to explore bidding strategies in the presence of competing auctions. The evidence indicates that a significant proportion of bidders bid across several competing auctions at the same time and that bidders tend to submit bids on auctions with the lowest standing bid. We find that for homogeneous items, as the difference in ending time across competing auctions becomes smaller, so more bidders bid across competing auctions and bid on the auction with the lowest standing bid. We also find that winning bidders who bid across competing auctions pay lower prices than winning bidders who do not cross-bid. These findings jointly amount to the first evidence lending empirical support to competing auction theory.

Introduction

There is a tremendous amount of interest in auctions as a means of selling items, both for vendors and theorists. The appeal of auctions is understandable: as shown in the mechanism design literature (e.g., Myerson (1981)), when a seller wants to sell an object to one of several buyers, an auction is the best way to do it.

In standard auction theory, the typical assumption is that there is a single seller and several bidders. The seller acts as a monopoly and earns rents from bidders. In practice, sellers often do not have monopoly power, but rather have to compete against other sellers. For example, in on-line auctions, many sellers sell their goods at the same time and some of the items are almost indistinguishable. Thus buyers can choose among many auctions and decide whether to buy from one among many sellers.

A few papers in the literature consider the case in which sellers compete against each other (see for instance McAfee (1993), and Peters and Severinov (1997)). But these papers assume that bidders can only choose to buy from one seller, and the only equilibrium involves buyers randomizing over available sellers. In this case, it is natural that some auctions have many bidders while other auctions have few or no bidders, and consequently that some profitable trades may not be realized.

For on-line auctions, such as those on eBay, bidders are not constrained to participate only one auction. eBay has evolved to act as a clearinghouse for a large number of homogeneous goods. At any time, there are many similar items on sale, the bidding cost for on-line auctions is very low, and bidders can easily monitor several auctions at the same time. Thus it is possible for bidders to bid across several competing auctions simultaneously.

The central question addressed in this study is: Are bidders responsive to the existence of competing auctions? If they can choose among competing auctions, how do bidders bid? Suppose that bidders bid across several competing auctions at the same time, even if they only need one item, as they search for the best deal. Doing so exposes them to the risk that they may win more than one item. But this consequence can be avoided if bidders use a specific strategy: always bid on an auction with the lowest ‘standing’ (or prevailing) bid, and bid with the minimum increment; if the bidder becomes the highest bidder in one auction, pause bidding until other bidders outbid him/her.

This strategy ensures that a bidder never wins more than one auction. Another advantage of this strategy is that bidders are never trapped in very competitive auctions. For example, suppose there are two competing auctions and four bidders, sellers’ valuations are all 0, and bidders’ valuations are 10,10, 7, and 6, respectively. If all bidders choose one auction and bid their true valuation, those two bidders with valuation 10 may end up bidding on the same auction; whoever wins the auction has to pay 10. If bidders bid across competing auctions and bid with the minimum increment, these two high valuation bidders will always end up winning two different auctions and paying a much lower price.

Most existing work on on-line auctions treats them as many independently running auctions and allows bidders to bid on only one auction. The emphasis in prior work has typically been on studying the strategic behavior of market players. For instance, Roth and Ockenfels (2000) explain the phenomenon of late bidding in eBay by the existence of a fixed auction ending time. Bidders bid late because very late bids have a positive probability of not being successfully submitted, and this provides a way for bidders to implicitly collude and avoid bidding wars. Bajari and Hortacsu (2000) study costly entry for bidders and the choice of reserve price on the part of sellers. Both models assume that bidders only bid on one auction.

A recent paper by Peters and Severinov (2001) studies the market equilibrium with competing auctions similar to those in eBay. If there is no bidding cost and no fixed ending time for auctions, the paper proves that the strategy in which bidders always submit a bid on an auction with the lowest standing bid and bid with the minimum increment is actually a (weak) perfect Bayesian equilibrium. Contrary to standard second-price auctions, in this environment bidding once and bidding one’s true valuation is not an equilibrium. Intuitively, if bidders bid their true valuation and bid only once, they may be trapped in very competitive auctions and not have opportunity to switch to other less competitive auctions. Consequently, the final price of one auction is affected by the existence of other auctions. Further, prices tend to be uniform for competing auctions, and in addition, the price is the same as the price under a double auction.

The strategy needs two assumptions: that there is no bidding cost and no fixed ending time for auctions. In eBay, these assumptions are not perfectly met. There is a bidding cost, though it is very low; and all auctions have a fixed ending time. For identical or very similar items, auctions with almost the same ending time compete against each other, while auctions with different ending times do not perfectly compete with each other. Obviously, those auctions ending early cannot compete with those ending later once they are finished, especially when many bids are clustered at the very late period, as documented by Roth and Ockenfels (2000) and Bajari and Hortacsu (2000).

Despite this discrepancy, eBay provides a valuable opportunity to see how far actual bidding behavior in the presence of competing auctions corresponds to the strategy prescribed in the theory. We have assembled data on competing auctions for CPU’s taking place in one month, the period of September 20 to October 19. Each group of competing auctions consists of auctions with the same description, the same starting price and delivery method, and with a similar ending time. We classify auctions in three ways: auctions ending in the same day, those ending within the same hour, and those ending within the same minute. Doing so allows us to identify the effect of increasing the degree of substitutability on the behavior of auction participants.

Our results provide convincing evidence that bidders bid across competing auctions (or “cross-bid”), and they tend to bid on the auction with the lowest standing bid, as the theory would predict. Further, this tendency becomes stronger as auctions become closer substitutes. Thus we find that for competing auctions that end within the same minute, bidders are more likely to cross-bid and bid on auctions with the lowest standing bid than is the case for auctions that end further apart. We also find that, on average, bidders revise their bids more often when the auctions they bid on end closer together; bidders also revise their bids more often when they cross-bid. To assess the potential gains from following the strategy outlined in the theory, we compare the winning price for winning bidders who bid across competing auctions and for winning bidders who do not, finding that bidders who bid across competing auctions pay lower prices on average than those bidders who do not. In total, these results provide the first compelling evidence in support of competing auction theory.

The paper is organized as follows: We first briefly summarize a theory with competing auctions. Then in section 3, we describe the data. Section 4 reports results of bidding behavior in eBay and in section 5, we compare the winning price for bidders who bid across competing auctions with those for bidders who do not. Section 6 concludes.

2. Theory of competing auctions

There are few papers on auctions with many sellers and many bidders. When many bidders with independent valuations simultaneously choose among many sellers, the only equilibrium (as noted above) has buyers randomizing over available sellers (see McAfee (1993) and Peters and Severinov (1997)). When there are many competing auctioneers, if bidders cannot bid across auctions, independently run auctions lead to inefficient trades, in the sense that the sum of all agents’ welfare is not maximized: some very low valuation sellers do not successfully sell their goods while some high valuation buyers cannot buy a good, because of the mismatch between buyers and sellers.

In a double auction, the outcome is much more efficient. There, potential buyers and sellers of a single good move simultaneously, with buyers submitting bids and sellers submitting asking prices. An auctioneer then chooses a price [pic]that clears the market: all sellers who ask less than [pic]sell, all buyers who bid more than [pic] buy, and the total number of units supplied at price [pic] equals the number demanded. In Wilson’s (1985) research, buyers and sellers’ valuations are drawn independently. When the number of buyers and the number of sellers are large enough, a double auction yields an efficient allocation; the sum of all agents’ welfare is maximized, and all sellers with low valuations and all buyers with high valuations successfully make trades.

The assumption that bidders have to choose one and only one auction simultaneously is critical in models with independent auctions and many buyers and many sellers. For on-line auctions, this assumption is unlikely to hold. Peters and Severinov (2001) ask the question whether independently organized auctions in a centralized exchange such as eBay can overcome the inefficiency of random matching. In their model, there are many sellers and many bidders. Each seller has a single good for sale and all goods for sale are identical. Each bidder only needs one good, so that winning more than one auction is undesirable – the additional good provides no additional utility. Auctions follow a similar pattern to eBay: the standing bid is the second highest bid and the highest bid is never revealed. However, bidders are not required to confine their attention to only one auction. Under the assumption that bidding is costless and there is no fixed ending time for auctions, the paper shows that competing auctions can overcome the inefficiency of random matching. The paper gives a symmetric strategy for bidders and proves that this strategy is a perfect Bayesian equilibrium. In equilibrium, all trades occur at the same price and the price is the same as that in a seller’s offer double auction (Satterthwaite and Williams (1989)), in which seller’s bids are equal to their reserve prices.

To help describe the bidding strategy, a bid is defined as successful if the bidder who makes it becomes high bidder, and that a bid is unsuccessful if otherwise. The main results of Peters and Severinov (2001) are repeated here:

Lemma: The symmetric equilibrium [pic] is defined as follows:

a) if the buyer is the current high bidder at any auction, or if the buyer’s valuation is less than or equal to the lowest standing bid, the buyer should pass;

b) otherwise, if there is a unique lowest standing bid, the buyer should submit a bid with the seller offering this lowest standing bid. The bid should be equal to the lowest valuation on the grid that exceeds this lowest standing bid;

c) otherwise, if more than one seller has the lowest standing bid, the buyer should submit the same bid as in (b) with equal probability at each such seller where either the seller has not received a bid, or the last bid the seller received was unsuccessful. If the last bid was successful with all sellers holding the lowest standing bid, then the buyer should bid with each of then with equal probability.

Let [pic] be the vector consisting of buyer valuations and seller reserve prices. Let [pic] be the [pic] lowest value in [pic]. Their theorem states:

Theorem: The outcome in which all buyers use the strategy [pic] is a (weak) perfect Bayesian equilibrium. Buyers trade for sure if their valuation is above [pic]. Sellers whose reserve prices are lower than [pic] trade for sure. All trades occur at the price [pic].

Bidders’ strategies can be summarized as follows: if a bidder is currently the highest bidder in any auction, he pauses until he is outbid. Otherwise, he always bids on an auction with the lowest standing bid and bids with the minimum increment. The essential idea is that with cross-bidding, bidders bid up prices with each seller as slowly as possible. They try to pick sellers where they can become the highest bidders by bidding the minimum increment. In this way, high valuation buyers are never trapped into bidding a high price by having another high valuation buyer accidentally bid against them. Cross bidding ensures that any mismatch between buyers and sellers can be solved by giving bidders the opportunity to bid on other auctions with low standing bids. As a consequence, all trade occurs at the same price. The outcome of the bidding is the same as in a seller’s offer double auction (Satterthwaite and Williams (1989)) in which seller’s bids are equal to their reserve prices.

We are interested to know whether bidders behave as the theory predicts. Economists usually seek clean theoretical results, which lie in the territory of a complete market and rational individuals. In case there is incomplete information, players are required to make probabilistic calculations and forecast future outcomes. Each player is assumed to be fully aware of the strategic value of his own private information and to know the structure of other players’ strategies. Such analysis seeks to characterize the Bayesian Nash equilibrium of the incomplete information game defined by the trading institution and the trading environment. Yet research in psychology and behavioral science is replete with examples in which individuals do not, or perhaps even cannot, perceive circumstance objectively. This raises serious questions about whether markets can achieve efficiency in practice.

There are more and more experiments in economics. Most results seem to support that the efficient outcome of the market can be achieved. One import result gaining support is the Hayek Hypothesis: markets economize on information in the sense that strict privacy together with the public information (about prices) in the market are sufficient to produce efficient competitive equilibrium outcomes.[2] How and why this is true, there is no general answer. The information flow and the contracting rule in the market may be more important than some traditional structural characteristics in determining the market outcome. However, whether players use strategies in Bayesian Nash equilibrium is dubious. In research by Forsythe et al. (1992), a market worked extremely well, yet traders in the market exhibited substantial amount of judgment bias.

3. Mechanism in eBay and Summary of Data

eBay provides a rich resource for the empirical study of auctions, and since there exists a large quantity of similar auctions at any given time, eBay also provides an excellent resource for the study of competing auctions.

eBay is a list e-commerce site. It provides a central market for buyers and sellers to meet each other by way of auctions. The income eBay earns comes from a fee charged to sellers, which varies from a fixed fee per listing, or a small proportion of the final sale price. Buyers on eBay do not pay anything to participate.

Sellers choose an auction type in which they sell their good.[3] They set a starting bid, a minimum bid increment, and the duration of the auction. Sellers also provide a detailed description of the item, which usually also includes the method of delivery and method of payment. Sellers have the option to set a secret reserve price. If they do so, during the process of the auction, eBay will indicate whether the reserve is met or not. At the end of the auction, if the reserve is not met, sellers have the right not to sell the item with the final price.

eBay uses a mechanism that resembles a second price auction. At any time, eBay shows the current standing bid of the auction, which is the current second highest bid (if there is no bid or there is only one bid, the current bid is the starting bid). When a bidder submits a bid, he knows the current standing bid, the identity of the seller (with the seller’s “feedback,” discussed below), the starting and ending time and the description of the item. He also has access to information as to how many bids have already been submitted, the identity of the bidders, and the time of the bids. However, the exact amount of each bid is not revealed until the end of the auction. The final price is the second highest bid plus a minimum increment.

At the end of an auction, eBay does not intervene in the actual transaction between the seller and the winner of the auction; the seller and the winner contact each other themselves to complete the transaction. Since bidders cannot inspect the good directly, sellers have incentives to provide false information; winners may regret the high price they have to pay and may not contact the seller to finish the purchase. To promote the faithful implementation of the transaction, eBay uses a feedback system. After each transaction (whether successful or not), the seller and the bidder can send feedback about the other party to eBay, marked as positive, neutral and negative, with values of +1, 0, -1 respectively, plus brief comments. A trader is given a feedback number, which is the sum of value of each feedback. The feedback information is public, and always associated with the trader, though eBay cannot prevent the traders from changing identity. Indeed, traders with negative feedback have a strong incentive to change their identities in subsequent trades, while traders with high feedback and good comments own an asset of good reputation. There is some evidence that the reputation associated with seller feedback has an effect on the final price of auctions (see Houser and Wooders (2001)).

When an auction has ended, eBay provides detailed information about the bid history.[4] Figure 1.1 is an example of an auction history extracted from eBay’s website. The first half page shows the basic information about the auction. It is a three-day auction, started at Oct-31-01 22:51:27 PST and ended at Nov-03-01 22:51:27 PST. The seller has feedback with value 11. The starting bid set by the seller is $10 and the minimum bid increment is $0.50. The auction received 10 bids from 4 different bidders. There was a shipping cost of $5 and optional shipping insurance $5.

The second half page shows the detailed bidding history. The bid history is sorted by the amount of each bid. The auction received its first bid of $17.50 by planetorb around 23 hours after the start of the auction. Then 4 hours before the end of the auction, bidder raheem112 started to bid. He could observe that there was already a bidder, but would not know the exact amount of bid. Since there was only one bidder at that time, the standing bid was still $10. Bidder raheem112 first bid $11, and found that the standing bid increased to $11 and he was not the highest bidder. Then he increased his bid subsequently in 2 minutes to $13, $14, $15, until at last he became the highest bidder with bid $20. The standing bid became $17.50. In the last hour of the auction, the bidder iteachcomputers submitted a bid $20, increasing the standing bid to $20. Bidder raheem increased his bid to $21, followed by another bidder who bid $23.99. Bidder planetorb finally won the auction with an unknown bid. Since the minimum increment is $0.50, the final price was $24.49, which is the second highest bid $23.99 plus the bid increment $0.50. There was no bid retraction or cancellation for this auction. eBay keeps the information of completed auctions public for one month.

Competing auctions in our sample should satisfy the following conditions: 1. they should be reasonably homogeneous in quality (including warranty) and have similar delivery method and shipping cost, 2. they should end at approximately the same time. As documented by Roth and Ockenfels (2000) and Bajari and Hortacsu (2000), bids on eBay tend to be clustered towards the end of the auction.

We use eBay CPU auctions data from a one-month period - September 20 to October 19. These are drawn for the category of “Computer, Component, CPUs” in eBay, which includes subcategories “AMD”, “Cyrix”, “Intel” and “Others”, and each subcategory includes further subcategories. At the time of writing in November 2001, there are 800 to 900 new CPU auctions every day. We choose those auctions with only one CPU for sale, and only those auctions with the method of standard auction.[5] Most of the CPUs are second hand. Table 1.1 reports the basic statistics of the sample.

In the sample, there are 7910 auctions involving a single CPU for sale. Not all items were sold. Among all auctions, 1452 of them did not receive any bids. 899 of them, which is more than 10% of the auctions, have a secret reserve price. In all 899 auctions with secret reserve price, 515 auctions had the reserve price met.

The CPUs in the sample are very different: the mean final price is $60.60, while the standard deviation is $82.34. The number of bids received is 6.66 per auction, with standard deviation of 6.91. The maximum number of bids in the sample is 49. Also the starting bids of these auctions are very different, with a mean of $29.25 and standard deviation of $61.60.

Though the conditions of properly working CPUs in the same specific category (such as Pentium III 800 retail box) are largely the same, they may be very different in many respects: some are new and never opened, others are used for several months or years; some are still under warranty, others aren’t; some are with both box and complete manual, others without. And the method of the delivery, the shipping cost and the method of payment can differ.

To overcome this complication in obtaining the competing auctions, we use a sample consisting of groups of auctions with the same product description, the same delivery method and the same shipping cost. This is done by choosing the auctions sold by the same sellers.[6] Some big second CPU sellers sell many items with the same description, the same delivery method and the same shipping cost. Without considering the different ending time, these auctions are completely indistinguishable to buyers.

Such auctions with identical items started and ended at different time. Auctions with almost the same ending time compete directly against each other, and auctions with large differences in ending time compete less directly. We get three different samples for competing auctions. Each observation in the samples is a group of auctions, which consists of 2 or more competing auctions. In the first sample (the daily sample), each group of competing auctions consists of homogenous auctions ending on the same day. In the second sample (the hourly sample), each observation is a group of competing auctions consisting of homogenous auctions with the difference of ending time being less than 1 hour. In the third sample (the minute sample), each observation is a group of competing auctions consisting of homogenous auctions with the difference of ending time being less than 1 minute.

Auctions appearing in the minute sample must appear in the hourly sample and auctions appear in the hourly sample must appear in the daily sample. The minute sample consists of groups of auctions that compete directly against each other, and the hourly and daily data consists of groups of auctions that compete against each other less directly. Table 1.2 is a sample description of the three samples.

In the daily sample, there are 550 groups of competing auctions, consisting of 1247 different auctions. Among all auctions, 305 (24%) of them do not receive any bids and 106 auctions have secret reserve price (40 of them with the reserve price not met). The hourly sample has a relatively smaller size, with 321 groups of competing auctions, consisting of 748 different auctions. Among these auctions, 196 (26%) of them do not receive any bids and 66 of them have secret reserve price (30 of them with reserve price not met). The minute sample is less than half of the size of the hourly data, with 139 groups of competing auctions, consisting of 346 different auctions. Among them 115 auctions (33% of the sample) do not receive any bids and 24 have secret reserve price (19 of them with reserve price not met).

We find that in each sample, there are bidders who are winners for more than one auction in a group of competing auctions. In the daily sample, there are 24 groups of competing auctions with bidders winning more than one auction, representing 4% of the total groups. In the hourly sample and minute sample, the number of the groups with a bidder winning more than one auctions is 18 and 10, representing 6% and 7% of the total groups.

These bidders may happen to need more than one item for themselves, or they can be professional dealers. Buyers with multiple demands can bid across more than one auction at the same time. If we consider all bidders with single unit demand, the existence of buyers with multiple demands will exaggerate the result that bidders bid across auctions. However, the proportion of such bidders is low, and the number of group in which such bidders win more than one auctions is low. In the following, we will address this problem in more detail and distinguish true cross bidders from the multiple demand bidders. Our results are not affected significantly by the existence of those multiple demand buyers.

One may be concerned that bidders, especially the novice, may not fully understand the mechanism in eBay auction. They might not use optimized strategies. We use the feedback as an indicator of traders’ experience in eBay[7]. eBay also uses feedback number in daily trade. For example, to use the “Buy It Now” feature, sellers must have a feedback greater than 10 or be ID verified[8]. Figure 1.2 is the distribution of bidders’ feedback numbers. In the daily sample, there are 2286 bidders and 21 bidders with negative feedback (1 bidder with feedback –4, 2 bidders with feedback –3, 8 bidders with feedback –2, the rest 10 with feedback –1). 60% of the bidders have feedback greater than 8. Most of the bidders have history of transactions in eBay. We can be confident that the observed behavior is not very different from the optimal one for most individuals.

4. Bidding behavior with competing auctions in eBay

Since we have very detailed bidding history for each auction, we can use it to study how bidders bid in face of competing auctions.

The most interesting result we observe is that bidders, even with single unit demand, bid across competing auctions.

In table 1.3 we report the statistics of the bidders and cross bidders in each sample. For each group of competing auctions, we use a Java program to get all different bidders and all bidders that bid on more than one auction.

We only consider the group of competing auctions with positive bid for at least one auction. In the daily sample, there are 458 such groups of competing auctions. On average, there are 2.28 auctions in each group. On average, there are 6.56 bidders for each group and 1.53 bidders bid across auctions in the group. On average, 23% of them bid across competing auctions in the group they bid.

In the hourly sample, there are 258 groups of competing auctions with positive bids for at least one auction. The number of different bidders per group is almost the same as that in the daily sample, and slightly few numbers of bidders who bid across auctions in a given group. 21% of the bidders bid across auctions in the group they bid.

In the minute sample, there are only 101 groups of competing auctions with positive bids for at least one auction. On average, there are fewer bidders in each group, with an average of 4.86[9]. And there are 1.48 bidders who bid across auctions in a given group. The data shows that a significant proportion of bidders bid across auctions in a competing group. The proportion of bidders who cross bid is higher than the other two samples, but the difference is not statistically significant. (The t-statistics for hourly sample and minute sample is 1.33 and the t-statistics for daily sample and minute sample is 1.14).

However, if we look at the bidding at the last day, we will observe significant difference in the proportion of cross bidders between the minute sample and the hourly (daily) samples. As documented at Roth and Ockenfels (2000) and Bajari and Hortacsu (2000), bids are clustered at the ending period of the auction. This is also true for our competing auction data. We have information about all the bids and the time the bids are submitted. Figure 1.3 shows the bid submission time for all auctions in the daily sample.

Bids are clustered at the ending period. Almost all auctions received their last bid in the last several hours. In addition, 28% of the samples receive their last bid within the last 60 seconds.

In Roth and Ockenfels (2000) the reason for delaying bids is that eBay auction has a fixed ending time. If the bids are submitted at the last minute, there is some probability that bids may not be submitted successfully. This can explain the very last minute bidding, but cannot explain late bidding. Roth and Ockenfels (2000) also find that even in auctions like Amazon auctions that have no fixed ending time, there is a significant amount of late biddings. Simply bidding late does not have effect that bids might not be submitted successfully. Bajari and Hortacsu (2000) argue that in a common value environment, bidders refrain from bidding earlier to avoid revealing their private information.[10]

Therefore, it is sometimes argued that early bids are not serious. We look at the data of the last day of each auction, with all different bidders in the last day and the different bidders who bid across competing auctions. We use the sample consisting of the groups with at least one auction receiving positive bids in the last day. We find that for all bidders bidding in the last day of an auction, significantly more bidders bid across competing auctions when the difference in ending time is less than 1 minute. (See Table 1.4.) For the minute sample, on average, 27% of the bidders in the last day bid across competing auctions, compared to the percentage of 0.20 in the hourly sample and 0.17 in the sample. For the hypothesis of having the same percentage of bidders who bid across competing auctions, the t-test for the minute data and the hourly data is 1.65 and the t-test for the minute data and daily data is 2.52, which is significant at the 0.01 level. And though there is slightly higher percentage of bidders who bid across competing auctions for hourly data than for daily data, the result is not statistically significant, with t-test 1.23.

We may wonder if the cross bidding observed here is only because of the existence of bidders who want more than one item at the same time. There is not a simple way to check directly if a bidder wants more than one item. We use the following methodology: bidders who need more than one item are very likely to be the high bidders on more than one competing auction. We define true cross bidders as all those bidders who bid across competing auctions but who are never the high bidder at more than one auction at the same time (type I). As an alternative, we consider true cross bidders as all those bidders who bid across competing auctions but who are not the high bidders on more than one competing auction on the last day (type II).

The first criterion for true cross bidder is stricter than the second criterion. The second criterion has already excluded all bidders who win more than one competing auctions. Some bidders excluded by the first criterion may still be true cross bidders, since at the early stage of the auctions, bidders may feel safe to be high bidders on more than auction even if they only need one item.

Table 1.5 reports the result of such considerations. When we exclude those possible bidders with more than one demand, we still observe high percentage of bidders who bid across competing auctions. For the minute data, 28 bidders are high bidders on more than one competing auction at some point of time of auction process and 21 are high bidder on more than one competing auction at some point of the last day of the auctions. The bidders who truly bid across auctions are 25% in the first criterion and 26% in the second criterion. Similarly, for the hourly data, we observe that among all bidders, 21% of them bid across competing auctions. Apart from those who need more than one item, the percentage of true cross bidder is 18% (first criterion) and 19% (second criterion). For the daily data, we observe 23% of bidders who bid across competing auctions. The percentage of true cross bidders is 21% (under the first criterion) and 22% (under the second criterion).

Another feature of bidding with competing auctions is that bidders tend to bid on the auction with the lowest standing bid. This strategy not only guarantees that a bidder never wins two auctions, it also lets bidders avoid being trapped in very competitive auctions. (This also makes the price of the auction become uniform.) We report the result on whether bidders bid on the auction with the lowest standing bid in table 1.6. [11]

When all auctions in a competing auction group are ended except the last one, bids submitted on this last auction thereafter are considered as bidding on auction with the lowest standing bid. This way of calculation tends to increase the number of bids submitted on the auction with the lowest standing bid for group of auctions with big difference in ending time, such as in the daily and hourly sample.

In the daily sample, the average number of bids a group of competing auctions received is 13.29. The average number of bids submitted on auctions with the lowest standing bid is 8.95. For the hourly sample, the average number of bid in a competing group and the average number of bids on auction with the lowest standing bid is roughly the same. The proportion of the bids submitted on the auction with the lowest standing bid is also roughly the same, representing 79% for daily sample and 77% for hourly sample (the t-test for the proportion for daily and hourly sample is 1.10).

For the minute sample, the average number of bids a group receives is relatively less, with a value of 10.89. The proportion of the bids submitted on the auction of the lowest standing bid is significant higher, with an average of 87%. The t-test for the minute data and the hourly data is 4.49 and the t-test for the minute data and the daily data is 4.33.

In all three samples, there are groups in which some auctions do not receive any bids while others receive positive number of bids. It happens usually that if there is any auction does not receive bids, then other competing auctions either receive no bids or receive only one bid. For same items, there is no reason that bidders bid on auctions with positive bids and not bid on auctions with zero bids. It is interesting to see how often it happens that in a group of competing auctions, some auctions receive no bids while other auctions receive more than one bid. Table 1.7 reports the result for three samples.

In the daily sample, there are 74 groups of competing auctions with positive bids and with zero bid auctions. 30% of them with auctions receiving more than 1 bid. In the minute sample, there are 20 groups of competing auctions with positive bids and with zero bid auctions. However, only 15% of them have auctions receiving more than 1 bid.

It is obvious from the above analysis that bidders are not following the strategy as in independent second price auction: bid once and bid the true valuation. Bidders are not following the advice form eBay to submit the true valuation and let the proxy to bid for them. The proxy bid mechanism in eBay is believed to save bidders from revising their bid. eBay’s help page about proxy bid explains the proxy bid as the following:

A proxy bid and a maximum bid are the same thing. To place a proxy bid, just enter the maximum amount you are willing to pay. eBay will then automatically bid up to your maximum amount for you. ()

In table 1.8, we report the result of the average number of bids a bidder submitted in each group. We only consider the sample consisting of groups with bidders who bid across competing auctions. With competing auctions, bidders do not bid on one auction, but rather on a group of competing auctions. We calculate the bids each bidder submitted on each competing group. There is a tendency that bidders bid more frequently when competing auctions end at almost the same time. In the minute sample, on average, each bidder submit 2.24 bids on a group of competing auctions (On average, there are 2.6 auctions in each group. Each bidder bid less than 1 bid on each auction of a group). However, for bidders bidding cross auctions, the average number of bids they submitted on a group is significantly higher. For the minute sample, each bidder who bid across auctions submits 3.97 bids on a given group of competing auctions.

Bid revising can be a consequence of the existence of competing auctions. If there is no bidding cost, bidders should bid with the minimum increment and bid many times. If bidders bid true valuation and bid only once, they may be trapped in very competitive auctions and do not have opportunity to switch to other less competitive auctions. Even if with bidding cost, bidders still revise their bids very often if the cost is not too high compared to the risk of bidding with another high bidding bidder. (They may not always bid the minimum increment, which is too costly).

5. Do cross bidders pay lower price?

Some winners of auctions bid across competing auctions, while others do not. Bidding across competing auctions gives bidders more choice in bidding. The theory predicts that bidders who bid across competing auctions can win an auction with lower price.

To test this result, we divide each group of competing auctions into two subgroups: a group consisting of auctions in which winners bid across competing auctions and with single unit demand, another group consisting of the rest of auctions. Here we define a bidder who only needs one item as in the sense that he was never the high bidder on more than one auction in any time of the auction process (criterion I). Then we compare the final price in these two sub-groups by calculating the ratio of average price paid by cross bidders and the average price paid by non-cross bidders in each group. In some groups all winners bid across competing auctions while in others none of the winners bid across competing auctions. These groups are excluded from the analysis. We keep the groups in which there are winners who bid across competing auctions and winners who do not bid across auctions. Table 1.9 reports the result.

In the minute data, there are only 17 groups of competing auctions with both winners who bid across competing auctions and those winners who do not. The ratio of the price paid by cross bidders and by non-cross bidders is 0.89, with a standard deviation of 0.19. We consider the test [pic] ratio ................
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