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1、A Simple Model of Search Engine Pricing Kfi r Eliazand Ran Spiegler December 5, 2009 Abstract We present a simple model of how a monopolistic search engine optimally determines the average quality of fi rms in its search pool. In our model, there is a continuum of consumers, who use the search engin
2、es pool, and there is a continuum of fi rms, whose entry to the pool is restricted by a price set by the search engine. We show that a monopolistic search engine may have an incentive to set a relatively low price that encouarges low-relevance advertisers to enter the search pool. This conclusion is
3、 independent of whether the search engine charges a price per click or a fi xed access fee. KEYWORDS: search engines, internet, two-sided markets, sequential search 1Introduction A search engine is a platform that serves a two-sided market. It is based on a tech- nology that potentially improves the
4、 quality of consumer search. Before the advent of internet search engines, yellow pages were the closest example of a search engine. Firms pay in order to be included in the yellow pages, with various degrees of prominence. The yellow pages organize the set of fi rms according to some categorization
5、 system. In internet environments, consumers use search engines by submitting a query in a lan- guage dictated by the search engine. The objects that the query elicits depend on the search engines method. In particular, a “sponsored links” system assigns objects to queries according to a mechanism i
6、n which fi rms pay the search engine for (prominent) appearance on the list of query results. Financial support from ERC grant no. 230251, NSF grant SES #0802789, ESRC (UK) and the Sapir Center is gratefully acknowledged. We thank Mark Armstrong for helpful comments. Brown University.E-mail: Kfi r_E
7、liazBrown.edu.URL: http:/www.econ.brown.edu/fac/Kfi r_Eliaz. Tel Aviv University and University College London. E-mail:r.spieglerucl.ac.uk.URL: http:/www.homepages.ucl.ac.uk/uctprsp/ 1 In the current age of Google, there is a near-monopoly in the industry of internet search engines. Our objective in
8、 this short paper is to present a simple, tractable model of sponsored-link pricing by a monopolistic search engine. Our model builds on a model of sequential consumer search due to Wolinsky (1986). We enrich Wolinskys model by allowing for heterogeneity in the fi rms degree of “relevance” for consu
9、mers, and by introducing a search engine that controls the search pool via its pricing decision. Our main result is that the search engine may fi nd it optimal to degrade the quality of the search pool by setting a low price-per-click that encourages low-relevance fi rms to enter. This leads to high
10、er search costs and higher prices in the search pool. While it may come as no surprise that monopoly can generate an ineffi cient outcome, the dis- torting eff ects of monopoly in the case of search engine pricing are novel and therefore, worthy of separate enquiry. Here, a better pool of fi rms has
11、 a negative eff ect on the monopolists profi ts because it leads to more competition among the fi rms, which, in turn, leads to lower prices and shorter searches (i.e., fewer “clicks”). Because we assume a large population of fi rms, our model allows us to abstract from auction-theoretic aspects and
12、 considerations of prominence (see our discussion in Section 5), in order to focus in the simplest manner possible on implications of search engine pricing for consumer search costs and product prices. As such, our paper complements existing theoretical work on search engines. The closest paper to o
13、urs is Chen and He (2006), which develops a model of price competition with sequential consumer search, in which a fi nite number fi rms with diff erent degrees of relevance bid for prominence. They show that the search engine may sometimes be better off with a lower quality pool in the sense that i
14、ts revenue from the position auction has an inverted U-shape with respect to the highest level of relevance. However, unlike our model, the search engine in their framework cannot control the average quality (relevance) in its search pool. In addition, we assume a large population of fi rms, which e
15、nables us to get more mileage in the analysis of the search engines problem. Ellison and Athey (2008) combine a model of sequential consumer search with a position auction design by the search engine, without incorporating price setting by fi rms in the search pool. Armstrong, Vickers and Zhou (2009
16、) analyze price competition with sequential consumer search, where one fi rm appears fi rst in the consumers search list. Finally, the main result in this paper is also reminiscent of Hagiu and Jullien (2009), who make a similar point - namely, that platforms in two-sided markets may have an incenti
17、ve to put obstacles on consumer search - in the context of a very diff erent two-sided-market model. 2 2A Model Let us begin with a market search model without a search engine, which extends a model due to Wolinsky (1986) by introducing heterogeneity among fi rms in a way that broadly follows Chen a
18、nd He (2006). The market consists of a continuum of consumers and a continuum of fi rms. A fi rms type is a number q, which is distributed over 0,1. When a consumer is matched with a fi rm of type q, the match has positive value for the consumer with probability q. Conditional on a positive-value ma
19、tch, the consumers willingness to pay for the fi rms product is randomly drawn (independently across all matches) from U0,1. The fi rms cost of providing their products is normalized to zero. We interpret q as a measure of the fi rms “relevance” for the consumers.For example, think of fi rms as webs
20、ites providing holiday packages. A fi rm with a higher q corresponds to a website with a wider range of destinations and hotel types, such that the consumers need is more likely to be met. Note that all the heterogeneity among fi rms is summarized by the probability of a positive-value match, but th
21、ere is no heterogeneity conditional on this event. This modelling strategy greatly simplifi es the analysis. The market interaction proceeds as follows. Each fi rm simultaneously chooses a price for its product.Consumers form a belief of the distribution of prices in the market, and follow a convent
22、ional sequential-search process with a search cost of s per round. When a consumer samples a fi rm, he learns the value of the match and the fi rms price, and optimally decides whether or not to continue searching (i.e., drawing a new sample from the population of fi rms). A stopping rule is a funct
23、ion that specifi es the realized match values and prices for which the consumer stops searching. For analytical convenience, we focus on market outcomes in which all fi rms charge the same price. A uniform-price market equilibrium is a price pand a stopping rule for consumers, which satisfy the foll
24、owing properties: (i) given that all fi rms charge p, the consumers stopping rule is optimal; (ii) given the consumers stopping rule and the belief that all fi rms charge p , no fi rm has an incentive to deviate to a diff erent price. Let us now introduce a monopolistic search engine into the model.
25、 Before the above market interaction takes place, the search engine limits fi rms entry into the search pool. Specifi cally, the search engine posts a “price-per-click” r. This is a payment from the fi rm to the search engine each time a consumer visits the fi rm. Note that the payment is independen
26、t of whether the fi rm eventually transacts with the consumer. Only fi rms 3 that accept the posted price-per-click are admitted into the search pool. In the ensuing market equilibrium, consumers base their behavior on a correct expectation of the set of fi rms that entered the search pool. The sear
27、ch engine chooses r to maximize its revenue, which is r multiplied by the expected number of “clicks” - i.e., the expected number of samples that consumers draw in the market equilibrium induced by r. Our assumption that fi rms are charged per click is motivated by the observation that this is how r
28、eal-life search engines operate. We will depart from this assumption later in this paper. Following the same motivation, we assume that consumers are not charged for accessing the search engines pool of fi rms. However, this assumption is also partly justifi ed if there exists a “universal” pool whe
29、re all fi rms belong (including those that are left outside the search engines pool), where consumers can search for free. This pool can be interpreted as offl ine search. Since fi rms in the search engines pool are on average more relevant than fi rms in the universal pool, consumers will tend to p
30、refer searching in the former. However, if the search engine employs an access fee to extract consumers surplus with access fee, this may impel them to switch to the universal pool. 3Analysis Our analysis proceeds in two steps. First, we take the set of fi rms that enter the search pool as given and
31、 characterize uniform-price equilibrium. Second, we incorporate this characterization into the search engines problem and determine the optimal price-per- click. 3.1Equilibrium Characterization for a Given Search Pool Let us begin with a characterization of uniform-price market equilibria, taking th
32、e set of fi rms that entered the search pool as given. As in many other sequential-search models, our market model has a trivial equilibrium in which all fi rms post a price equal to the highest willingness to pay, p = 1, and consumers choose not to search at all. This is the equilibrium characteriz
33、ed by Diamond (1971) and known since then as the “Diamond Paradox”. However, if search costs are suffi ciently low (see below), there is also a uniform-price market equilibrium with active search, and we will focus on this equilibrium. 4 Proposition 1 In a uniform-price market equilibrium with activ
34、e search, consumers stop if and only if the value of a match with the current fi rm is at least v= 1 s 2s E(q) (1) where E(q) is the expectation with respect to the population of fi rms in the search pool. Firms charge the uniform price p= 1 v= s 2s E(q) (2) Proof. Our proof is a minor extension of
35、a derivation by Wolinsky (1986). Let us begin with the consumers stopping rule. Because all fi rms charge p, consumers face a stationary environment. Therefore, their stopping decision obeys a cutoff rule. That is, there exists v 0,1, given by E(q) Z 1 v (v v)dv = s such that in equilibrium, consume
36、rs stop if and only if the current match value is v v . The L.H.S represents the incremental expected benefi t from one more search, while the R.H.S represents the cost of one more search. The proof is standard and therefore omitted. Solving this equation yields the expression for v. Now consider th
37、e pricing decision of a fi rm of type q. If the fi rm deviates from the equilibrium price p to another price p, a consumer who samples the fi rm and learns that the match value is v 0 will buy the fi rms product if v p v p because the R.H.S of this inequality represents the consumers reservation sur
38、plus con- ditional on a positive-value match. Thus, the probability that the consumer will buy at p is 1 p v+ p, by the assumption that v is drawn from U0,1 (ignoring the possibility of corner solutions, which is easy to dismiss). Therefore, the fi rm will choose p to maximize p (1 p v+ p) 5 In equi
39、librium, the solution to this maximization problem coincides with p, yielding p= 1 v To see how our model relates to Wolinsky (1986), think of the consumers “eff ective search cost” of a consumer as the total expected cost that a consumer incurs before reaching a positive-value (i.e., relevant) matc
40、h. This is precisely s/E(q). The model due to Wolinsky (1986) is a special case in which q = 1, hence the eff ective search cost coincides with s. The gross profi t-per-click that a fi rm of type q0earns in active-search equilibrium (i.e., excluding the transfer to the search engine) is q0 p (1 v) =
41、 q0 2s E(q) The conversion rate - namely, the expected stopping probability - is Eq (1 v) = Eq s 2s E(q) = p2s E(q) Note that the inverse of this probability is the expected duration of search. Turning to consumer welfare, note that consumers fi nd it optimal to enter the market and face the uniform
42、-price equilibrium only if their ex-ante expected surplus from searching in the pool is non-negative. The ex-ante expected surplus is equal to the expected value of the item that will ultimately be purchased, minus its equilibrium price minus the expected search costs. This amount is given by E(v |
43、v v) p s p2s E(q)= v p By Proposition 1, this reduces to 1 s 8s E(q) (3) This means that the uniform-price equilibrium with active search exists if and only if E(q) 8s. 6 3.2The Optimal Price-Per-Click In this sub-section, we assume that the uniform-price equilibrium with active search is played (wh
44、enever it exists) in the search pool induced by any given price-per-click. Let us characterize this search pool. Given that the search engines price-per-click is r, a fi rm of type q0chooses to enter a pool if and only if q0 2s E(q) r The expectation in E(q) is taken with respect to the set of fi rm
45、s that choose to enter the search pool. If a fi rm of type q 0 prefers to enter, then any type q00 q0strictly prefer to enter. It follows that given r, the set of fi rm types that choose to enter is q,1, where q is defi ned as follows: q 2s Eqq(q) = r(4) This equation may have multiple solutions. We
46、 will assume that in this case, the search engine is free to select its most desirable solution. Recall that the search engines expected revenue is the price-per-click r multiplied by the expected number of clicks in the induced equilibrium, which is the inverse of the conversion rate. This leads to
47、 our fi rst main result. Proposition 2 The search engines problem can be reformulated as follows: choose the critical type q 0,1) to maximize q Eqq(q) 3 2 (5) subject to the constraint that a uniform-price market equilibrium with active search exists in the search pool induced by q- i.e. Eqq(q) 8s T
48、his maximization problem involves a subtle trade-off . When the search engine sets r in a way that eff ectively increases q, this has several implications. First, the change in the profi t-per-click is ambiguous. On one hand, the equilibrium product price goes 7 down because a higher-quality search
49、pool creates a more competitive environment. On the other hand, the conversion rate goes up. Both are equilibrium implications of the increase in the quality of the search pool, and they have opposite eff ects on the fi rms profi t-per-click. Second, the increase in qlowers the expected number of clicks (because it is the inverse of the conversion rate). This lowers the search engines total profi t. Note that the domain in the search engi