BIDDING PATTERNS IN SEARCH ENGINE AUCTIONS * KURSAD ASDEMIR Department of Accounting and MIS 323 Business Building University of Alberta Edmonton, AB, Canada T6G-2R6
[email protected] This study analyzes how advertisers bid for search phrases in pay-per-click search engine auctions. These auctions are fundamentally different than traditional auctions in that they have no closing times and they are continuous. We develop an infinite horizon alternative-move game of advertiser bidding behavior.
We show that bidding war cycle and static bid patterns
frequently observed in these auctions can result from Markov perfect equilibria. We consider the effect of minimum bid increment, the difference between the first and the second position, the advertisers’ patience, and the minimum bid on the advertisers’ and the search engine’s payoff.
*
Previous versions of this paper have been presented at The University Of Texas at Dallas, University of Alberta, Yahoo Research Labs, University of British Columbia, and CORS/INFORMS Joint International Meeting 2004, Alberta Industrial Organization Conference 2005. I thank all the participants. I acknowledge especially Varghese S. Jacob and Nanda Kumar of UTD and David Pennock of Yahoo Research Labs for their contribution to this paper.
1. Introduction Targeting is one of the most important success factors in an advertising campaign. Advertisers search for potential customers among the audiences of various media outlets. Since a person looking for information on a certain product or service may well be in the market for the product or the service, search engines as publishers of search listings attract highly targeted audiences. Advertisers want to attract to their Web sites as many searchers as possible. Since the audience is valuable to advertisers, competition for these listings intensifies. To exploit the competition for good positions in the search engine listings, search engines use auctions as an allocation mechanism. A separate auction is set up for each phrase that can be queried from the search engine. The following passage from Did-it.com is a good depiction of these search phrase auctions: The more you are willing to pay for a clickthru the "higher up" on the search engine results you will appear. It' s basically an endless, real-time auction between you and your competitors for the top positions (which get the majority of the traffic.) The reason being is that the traffic that positions generate drops quickly as you move down in the listings. (Pasternack 2002) We observe two kinds of bidding patterns in public bid search engine auctions: A bidding war cycle is shown in Figure 1: advertisers outbid each other until one of them drops their bid and the other one follows by dropping its bid to just 1¢ above the competitor’s bid.1 Bidding wars are known to be a competitive phenomenon in the trade press (Wegert 2003; Lee 2003). This result stems from the fact that bidding wars create continuously increasing bids. Bidding war cycle is not the only pattern in search engine auctions. Figure 2 shows another 1
This data was collected from a search engine’s public bid listings. For confidentiality reasons, the name of the search engine, the search phrase, and advertisers are concealed. Similar patterns have been reported by Kitts and Leblanc (2004) in Figure 3 of their paper and Weber and Zheng (2002) in Figure 8.
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bidding pattern where the bids and the positions of the advertisers are static. Then, a natural question is what do these different bidding patterns suggest about advertiser behavior. Date
Observe Time Position 1
Position 2
Position 3
12/30/2003 12/30/2003 12/30/2003 12/30/2003 12/30/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 12/31/2003 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/1/2004 1/2/2004 1/2/2004 1/2/2004
8:29:22 PM 8:39:14 PM 8:58:53 PM 10:27:26 PM 10:37:12 PM 12:15:33 AM 2:03:43 AM 5:30:13 AM 6:29:13 AM 9:06:34 AM 9:16:23 AM 10:44:51 AM 2:12:34 PM 5:17:02 PM 5:56:21 PM 8:43:33 PM 8:53:23 PM 12:41:33 AM 3:48:25 AM 6:06:06 AM 9:03:05 AM 12:00:08 PM 1:48:14 PM 3:06:56 PM 4:35:26 PM 5:04:54 PM 9:59:56 PM 11:48:10 PM 12:37:16 AM 2:35:16 AM 5:51:56 AM
B B B A C B A C B A B A B A B A B A B A B A B A B A B A B B B
C C C C A C C A C C C C C C C C C C C C C C C C C C C C C C C
A A A B B A B B A B A B A B A B A B A B A B A B A B A B A A A
$1.28 $1.28 $0.92 $0.93 $0.93 $0.94 $0.95 $0.95 $0.96 $0.97 $0.98 $0.99 $1.00 $1.01 $1.02 $1.03 $1.04 $1.05 $1.06 $1.07 $1.08 $1.09 $1.10 $1.11 $1.12 $1.13 $1.14 $1.15 $1.16 $1.16 $0.92
$1.27 $0.91 $0.91 $0.92 $0.93 $0.93 $0.94 $0.95 $0.95 $0.96 $0.97 $0.98 $0.99 $1.00 $1.01 $1.02 $1.03 $1.04 $1.05 $1.06 $1.07 $1.08 $1.09 $1.10 $1.11 $1.12 $1.13 $1.14 $1.15 $0.91 $0.91
$0.90 $0.90 $0.90 $0.90 $0.92 $0.93 $0.93 $0.94 $0.95 $0.95 $0.95 $0.95 $0.99 $0.99 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90 $0.90
App. Duration Hour Minute 0 0 0 0 1 1 3 0 2 0 1 3 3 0 2 0 3 3 2 2 2 1 1 1 0 4 1 0 1 3
10 19 29 10 38 48 27 59 37 10 28 28 5 39 47 10 48 7 18 57 57 48 18 29 29 55 49 59 58 16
Figure 1. Bids in bidding war cycles in search phrase auctions for a computer related phrase by advertisers A, B, and C.
Date
Observe Time Position 1
1/2/2004 8:36:24 PM 1/6/2004 2:55:50 AM 1/6/2004 9:51:02 AM
D D D
$17.25 $17.25 $17.25
Position 2
Position 3
E E E
F F G
$17.15 $17.15 $17.15
$17.05 $17.05 $17.00
App. Duration Hour Minute 85 15 -
Figure 2. Static bids in search phrase auctions for an enterprise software phrase 2
Auctions and online auctions have been studied extensively in the literature (Klemperer 1999; Lucking-Reiley 2000). Since the findings of this research stream mainly depend on the probability of winning the good (or goods) at the end of the auction, these findings are generally not applicable to the search engine auctions. The absence of a closing time and the continuous purchase of clicks at different prices make search engine auctions unique. We believe that a dynamic oligopoly is more suitable paradigm to model this setting. In this work, we first characterize the solution of the static simultaneous move game. This solution resembles the Bertrand paradox. The advertisers only make their second position payoffs. The main lesson from this model is that the difference in the value generated from the first and second position derives the competition. Then, we develop a variant of the Maskin and Tirole (1988b) dynamic oligopolistic price competition model. Most significantly, in contrast to the Maskin and Tirole (1988b) model, we introduce a war of attrition phase that does not require a “price jump” from the “price cutting” phase that are not generally observed in the empirical studies. We show that bidding wars can result from a symmetric Markov-perfect equilibrium strategy.2 One of the most important findings of our research is that we show that advertisers, on average, can bid far below their valuation. This may create large revenue losses for search engines. By calibrating our model with real data, we propose several options to search engines to alleviate the effects of cycling bids. These include introducing a reserve price for the first two positions, making the second position less desirable for advertisers, and increasing the grid size. The rest of this study is organized as follows: the next section gives a literature review. Section 3 describes the basic setup of the model. Then, Section 4 studies the one-shot simultaneous move game. We turn our attention to the dynamic version of the game in Section 5. Section 6 presents real bidding data. Finally, we conclude the paper in Section 7. 2
See Fudenberg and Tirole (1991) Chapter 13 for a discussion of Markov-perfect equilibrium.
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2. Relevant Literature Our model is similar to the Maskin and Tirole (1988b) model that studies price competition in an infinite duopoly. They develop a price war equilibrium in which firms cut prices down to a certain level and then drop their prices to the marginal cost level. Firms continue marginal cost pricing with a certain probability until one of them raises its price. Eaton and Engers (1990) extend this model to a differentiated products monopoly. Eckert (2003) studies the determinants of the existence of price wars in Canadian gasoline markets and extends Maskin and Tirole (1988b) model by changing the sharing rule when prices are equal. Wallner (1999) solves the finite version of the Maskin and Tirole (1988b) model. Maskin and Tirole (1988) model have several limitations. We note that even though our model has similar structure, there are significant differences from Maskin and Tirole (1988). Their model assume that an infinitesimally small price grid. We remove the infinitesimally small grid size assumption in our model. This allows us to study the effect of different grid sizes on the equilibrium. Another limitation of this model is that real pricing data does not show a sharp price drop to the marginal cost (see Figure 1 in Noel 2004). In real data, prices generally drop as competitors gradually undercut each other’s price and sometimes drop below marginal cost. Our bidding war cycle equilibrium has no jumps in the bids and provides a better fit to the observed bidding patterns. Yet another contribution of our model is that we do not assume that the second position payoffs equal to zero as in Maskin and Tirole (1988) do for the high price firm. Several other research streams are relevant to this study. There have been a limited number of studies on search engine auctions. Online auctions, on the other hand, received a significant attention from the research community. There is a rich literature on price competition 4
in oligopolies. We mostly derive from this literature in developing our model. We review each of these research streams in turn and highlight our contribution to each stream. Paid placement design strategies from the search engine perspective have been studied by Weber and Zheng (2002) and Feng, Barghava, and Pennock (2003). Weber and Zheng (2002) propose a two-stage model of paid placement design. They find that the search engine should rank advertisers with respect a weighted measure of quality and submitted bids. They also show that advertisers will use mixed bidding strategies. Feng, Barghava, and Pennock (2003) focus on different ranking mechanisms based on bids and relevance. They illustrate the performance of different mechanisms using a computational approach. Research on optimizing advertiser strategies focuses on building automated bidding agents. Kitts and Leblanc (2004a) develop a commercial bidding agent that has been used to manage advertiser accounts. Kitts and Leblanc (2004b) develop a simulation system that can realistically replicate search engine auctions. In addition to their contributions to automated bidding, Kitts and Leblanc (2004a, 2004b) identify typical bidding strategies adopted by advertisers. Most of the automated bidding agents use deterministic bidding rules such timed position and relative position rules. An interesting strategy – bid only one bid increment below a competitor advertiser in second price auction– is called anti-social bidding (Brandt and Weiss 2001) or gap jamming. Anti-social bidders intend to make their competitors pay the maximum amount per click and thus deplete their budgets. We contribute to this line of literature in several ways. Mainly, existing literature does not consider the dynamics of the auction. We show that the advertisers will not necessarily bid their valuation in a dynamic setting. We show that anti-social bidding may be a rational strategy in the absence of budget constraints. Understanding dynamic bidding behavior will also help
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design better automated bidding agents. For example, we find that in a bidding war cycle advertisers are better off, if they discount the future at a lower rate. An extensive literature on auctions exist in the economics literature (Klemperer 1999). Most of the theoretical predictions of this literature have not found strong empirical support (Lucking-Reiley 1999; Kagel 1995). Empirical research on auctions gained momentum with the vast availability of data on the Internet. Online auction research as well as traditional auction literature has focused on auction with closing times and discrete goods. For example, Rothkopf and Harstad (1994b) study the effect of minimum bid increment (grid size) on bidding strategies and auction design. However, the trade-off is between the auction duration (which is not an issue in this study) and grid size. Bapna, Goes, and Gupta (2003a) identify different bidding styles in multi-unit auctions and study the role of grid size. In this paper, we show that similar bidding styles can result from Markov-perfect equilibria. We also investigate the role of the grid size in a fundamentally different auction. 3. The Model 3.1. The Auction We consider an auction for a search phrase. A results page is created when a visitor submits a query to the search engine with this search phrase. Two advertisers, advertiser X and advertiser Y, bid for clicks to be listed on the paid (or sponsored) section of the results page for this search phrase. The advertiser listings are sorted in descending order according to the bids at the time of the search query. Bids are selected from a grid with an exogenous second position bid l (i.e. we assume that the third position bid is constant at l-k) and grid size k, i.e. bids can only take values l, l+k,
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l+2k,… and so forth. k is a positive integer, which determines what values the bids can take. k is the grid size or minimum bid increment (e.g. 1¢). A smaller k represents a finer grid. We define a reduced state s t = ( btX , btY ) at time t, where btY and btX are the bids of the advertisers X and Y, respectively. The full state also includes the advertiser who is about to move. In the steady state the time t does not affect the payoffs of the advertisers and the search engine, therefore we omit the time index t in several expressions. We define an indicator variable to represent the particular ordering at a given state s=(bX,bY):
(
)
I X b X , bY =
(
if b X > bY , if b X < bY .
1 0
(1)
)
This implies that I X b X , bY is equal to 1, when X is in the first position. The payment for a click at the first position depends on the advertiser’s bid at the second position. The first advertiser pays k more than the second advertiser’s bid if its bid exceeds the next advertiser’s bid; if the two bids are equal, it pays its bid. The second advertiser always pays l (l is k plus the third position bid, with a little abuse of the notation, we refer to l as the third position bid). We define the payment function at the state s=(bX,bY) as:
(
)
C X b X , bY =
bY + k
(
)
for I X b X , bY = 1, otherwise.
l
(2)
3.2. Advertisers We assume that advertiser X at the jth position gets α jX number of clicks at each time period and gets a profit of s Xj per click , for j=1,2. Therefore, given the payment function in Equation 2, X’s profit function at state s=(bX,bY) is:
7
Π
X
(b
X
,b
Y
(
)
(
(
Π1X bY + k = α1X s1X − bY + k
)=
Π =α X 2
X 2
(s
X 2
−l
)
))
(
)
for I X b X , bY = 1, otherwise.
(3)
where s1X > s2X > l . Y’s profit function is also defined similarly. We assume that X’s first position payoff when he pays l+4k for the first position is greater than her second position payoff. Formally,
Π1X ( l + 4k ) > Π 2X
(4)
Inequality 4 imposes a maximum limit on the grid size k. Note that Π1X ( l + k ) is the maximum possible payoff in this model. Advertisers discount future cash flows by the discount factor δ and maximize expected present discounted profits. Hence, X’s objective function is:
ΠX =
∞ t =0
δ t Π X ( st ) .
(5)
3.3 The Search Engine The search engine collects the payments for clicks. Therefore, the objective of the search engine is to maximize the discounted cash flow: Π SE =
∞ t =0
=
∞ t =0
( δ ) { I ( s ) (α SE t
X
t
(δ ) { I ( b SE
t
X
X t
X 1
) (
)(
C X ( st ) + α 2Y C Y ( st ) + 1 − I X ( st ) α1Y C Y ( st ) + α 2X C X ( st )
)( (
)
) (
(
, btY α1X btY + k + α 2Y l + 1 − I X btX , btY
) ) (α ( b Y 1
X t
)
)}
(6)
)}
(7)
+ k + α 2X l
Note that the search engine would like to have advertisers with high click rates. Since the payment in the first position depends on the second position bid, he wants the second advertiser’s bid to be high as well. Next, we analyze the equilibrium strategies for advertisers.
4. The One-Shot Simultaneous Move Game
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In the following sections, we assume that the advertisers are symmetric. The ordering of paid listings is indeterminate when bids are equal. Hence, without loss of generality, we assume that X occupies the first position when bids are equal. Since advertisers only obtain payoffs in one period, they would bid competitively. This is equivalent to setting the discount factor δ to zero. Proposition 1 characterizes the equilibrium in the one-shot game.
Proposition 1: In the one-shot simultaneous move game, in equilibrium both advertisers choose b*=l+n*k, where n* is a positive integer, which is defined by the following condition:
s1 −
α2 α ( s2 − l ) − k < b* ≤ s1 − 2 ( s2 − l ) . α1 α1
(8)
Proof: We solve for this equilibrium by the iterated deletion of weakly dominated strategies method. Consider the normal form of this game in Figure 3, where X is the row player and Y is the column player. X’s payoff is given on the first line while Y’s payoff is given on the second line of each cell for the corresponding bids. We drop the advertiser index for this proof. In Figure 3, b* is the bid that satisfies the following condition:
( )
(
Π 1 b* ≥ Π 2 > Π 1 b* + k
)
(9)
Condition 9 and the fact that b* belongs to the grid (i.e. b*=l+n*k) uniquely determine the value of b*. For the column player Y, it is easily seen that l+k weakly dominates l since Π1(l+k)>Π2;
l+2k weakly dominates l+k since Π1(l+2k)>Π2….b* weakly dominates b*-k since Π1(b*) Π2. b* weakly dominates b*+k since Π1(b*+k)b*), she earns less than the second position payoff when the opponent set its bid at b-k. On the other hand, if an advertiser bids too low (bY
