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
©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
1.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
2.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
1.1Sample statistics for CPU auctions……………………………………….32
1.2Sample Statistics for Samples of Competing Auctions……………………33
1.3Statistics of Cross Bidding in the Whole Process…………………………35
1.4Statistics of Cross Bidders for the Last Day……………………………….37
1.5Percentage of Cross Bidders in All bidders………………………………..38
1.6Result on Bidding on the Auction with the Lowest Standing Bid…………39
1.7Result on Bidding on Group with Zero Bid Auctions……………………...40
1.8Average Number of Bids Submitted in a Group by a Bidder……………....41
1.9Price Paid by Cross Bidders and Non-Cross Bidders………………………42
2.1Payoff Under CN………………………………………………………...…49
2.2Simulation Results………………………………………………………….63
List of Figures
FigurePage
1.1 A Bidding History Page From eBay………………………………….31
1.2 Histogram of Bidders’ Feedback…………………………………….34
1.3Histogram of Bids Submission Time for Daily Sample……………..36
2.1Proportion of Individuals Taking High care…………………………64
2.2Proportion of Individuals Taking Medium Care……………………..64
2.3The Composition of the Population in the Simulation……………….65
1
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.
1.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 that clears the market: all sellers who ask less than sell, all buyers who bid more than buy, and the total number of units supplied at price 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 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 be the vector consisting of buyer valuations and seller reserve prices. Let be the lowest value in . Their theorem states: