Search Advertising Based Promotion Strategies for Online Retailers


 Allan O’Brien’
 3 years ago
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1 Search Avertising Base Promotion Strategies for Online Retailers Amit Mehra The Inian School of Business yeraba, Inia Amit ABSTRACT Web site aresses of small on line retailers are often unknown to customers. Therefore, web retailers use broacast an search avertising to inform customers of their existence. We fin that use of search avertising by a monopoly retailer may increase avertising costs an may not increase social welfare. In aition to the retailer s existence, customers may also be unaware of the quality of the prouct. A retailer selling a high quality prouct may want to signal this information to the customers. We fin that use of search avertising as a signaling evice is optimal when the quality ifferential between the high an low quality proucts is small. In a uopoly, there may be situations where one retailer is known to customers but its competitor is not. The profits of both retailers may increase if the known retailer uses its web site as a portal an charges a fee per transaction from the unknown retailer. When an unknown retailer competes with a known retailer in a large market, it uses more search avertising an less broacast avertising compare to the case when both retailers are unknown. This response is reverse if the size of the market is small. Keywors search, consumer search, search avertising, signaling, competition 1. ADVERTISING BY ONINE RETAIERS There has been a proliferation of web base retailers in the business to consumer electronic market segment ue to rising retail sales (aroun $17 billion in 005, see article in the Wall Street Journal [10]) an low costs of operating businesses on line. Many of these retailers are small an o not have the bran recognition to attract shoppers on their own. Avertising is very important for these retailers since this is the only way to get customer traffic on their web sites. A comment by the marketing irector of Jenson USA, an Ontario bicycle shop, while explaining the importance of avertising for their firm is pertinent in this regar (os WWW007  Thir Workshop on Sponsore Search Auctions, Banff, Canaa Copyright is hel by the author. Angeles Times [5]),It helps us reach customers that wouln t know our name otherwise. There are two moes of avertising available to on line retailers: Broacast avertising an search avertising. Retailers o broacast avertising by placing bannner or embee avertisements on websites that get customer traffic relevant to these retailers. To o search avertising, retailers use the services of search engines such as Google or Yahoo. Search avertising exploits the possibility of targeting customers base on their online search behavior. All signs are that this moe of avertising has been a huge success, both for the retailers an the search sites. Wall Street Journal [10] reports that 87% of online retailers in a survey sample use search avertising. In aition, an article in os Angeles Times [4] states that the strong earnings growth Google is enjoying is ue to the search avertising services it provies. Other search engines have similar moels riving their business growth. The first question we raise is how shoul retailers balance their investments in the two moes of avertising? If a retailer opts for search avertising, how much savings can be expecte in avertising bugets? The answer is interesting. We fin that use of search avertising may result in higher avertising bugets than if the retailer were using broacast avertising only. This is optimal because the retailer gets increase sales revenue which more than makes up for the aitional expense on avertising. From the stanpoint of social welfare, search avertising can be expecte to have a beneficial effect since it helps to provie better market coverage. owever, we fin that better targeting of customers through search avertising leas to increase in prices, which may be high enough to reuce social welfare. In some situations, the customers may not be aware about the quality of the prouct being sol by a retailer. This woul happen when the prouct being sol is not brane. Starting from the seminal works of Philip Nelson [8] an Richar Schmalensee [], it is well known that pricing an avertising spening may be use as signaling evices to convey to consumers that the prouct being sol is of high quality. owever, such signaling is costly because the retailer has to aopt suboptimal pricing an avertising. The availability of search avertising introuces an interesting question in this context. Does the mechanics of search avertising allow the retailer to signal high quality using a less suboptimal strategy as compare to avertising through broacast avertising? The answer to this question is positive, but only in certain situations.
2 Search avertising is also expecte to change the nature of competition on line. Small retailers can compete with big online retailers more effectively using search avertising. In response to the competition from small retailers, a big retailer like Amazon.com, which is well known among the customers, may follow a strategy to let its competitors use its web site as a portal an charge them for these services. We fin that such a strategy may be optimal for both retailers. Finally, we also look at how a retailer s strategy in using search an broacast avertising changes as customers become informe about the competing retailers.. ADVERTISING ITERATURE One of the important roles of avertising is to inform customers about his/her choices. In the context of Internet commerce, search avertising services are sol by intermeiaries such as Google, Yahoo, an Mysimon.com. Recent work by Baye an Morgan [1], Bhargava an Feng [] an Weber an Zheng [11] has concentrate on fining the optimal fee an the optimal esign for the intermeiary. Dewan, Freimer an Nelson [3] stuy how the ownership of the search engines impacts the market an social welfare. Mukhopahyay, Rajan an Telang [7] show that low quality search engines can survive in the market since search services are typically free of cost for the customers. owever, this literature ignores broacast avertising, which is available to retailers in the form of banner avertising on the Internet. This paper aresses this gap. By consiering both types of avertising simultaneously, we examine the traeoffs between their efficiency of market coverage an cost structure. If customers are unaware of the quality of the prouct, the amount of expeniture on avertising may signal the quality of the retailer s prouct. Important contributions in this research came from Nelson [8], Schmalensee [] an Milgrom an Roberts [6]. The essence of these papers is that when avertising is useful only for signaling, wasteful (or excess) avertising is use to signal high prouct quality. Recently Zhao [1] has shown that when broacast avertising plays the ual role of informing customers about the retailer an signaling, a high quality firm will o the reverse of what the previous literature states: It will reuce avertising to signal high quality. We exten this threa of research to examine the merits of signaling the quality of the prouct of a monopolist retailer with search avertising. Finally, we also moel uopoly competition between retailers. 3. MONOPOY RETAIER WIT A PROD UCT OF KNOWN QUAITY Our setting consists of a monopoly retailer that is selling a prouct of known quality. The customers willingness to pay for the prouct is represente by the parameter ρ, which is uniformly istribute between 0 an r with unit ensity. Each customer has the eman for one unit of the retailer s prouct. The retailer sells its prouct on the Internet. We consier the case of a retailer that is unknown to customers unless they see its avertisement or fin it on a search site. This is quite common for small regional sellers with a potentially large national market. We assume that the retailer informs the customers of its web aress in one of two ways: Broacast avertising such as banner an embee avertisements, an search avertising on search sites such as Google an Yahoo. Figure 1: Decision tree for the customer with a monopoly retailer Figure 1 shows the ecision tree of a customer in the process of buying the prouct. The noes inicate by circles are the event noes an those inicate by rectangles are the ecision noes. et a represent the probability with which a customer is expose to the broacast avertising of the retailer. If the price of the prouct is p an a customer with preference ρ knows the web aress of the retailer, she can buy the prouct an make a net surplus of ρ p. The lower branch of the ecision tree shows that of the customers expose to broacast avertising, only those with ρ p 0 will buy the prouct. In case the customer is not expose to broacast avertising, she will search for the retailer s web aress herself. If the retailer provies search base avertisements also, it is fairly easy to get its web aress by specifying some keywors to efine the prouct using the search sites. Therefore we assume that the customer will incur no search costs. Rational customers correctly anticipate the price put by the retailer, who calculates the profit maximizing price knowing that customers correctly anticipate this price. Thus a fulfille expectations equilibrium ensues. Because of this, only customers who value the prouct at ρ such that ρ p 0 will search for an buy the prouct. If the retailer oes not provie search avertising, the customer in unable to locate the web aress of the retailer as a small retailer oes not get a large number of click throughs an is therefore never important enough to have a substantially high ranking on the general search list provie by search engines. In this case, the customer cannot buy the prouct. By its very nature, broacast avertising is not targete. To get an iea about the cost of this type of avertising, consier a banner avertising campaign on a web site. The longer the avertisement runs, the more new customers are expose to it. At the same time, the frequent visitors to the web site are expose to the avertisement many times. The retailer pays for banner avertisements on the basis of number of impressions. Therefore, while repeate exposure of frequent visitors oes not increase the total number of customers expose to the avertisement, it results in aitional costs. So we assume that broacast avertising expense is increasing an convex in the fraction of customers expose to the avertisement. In particular, we assume that the retailer incurs a cost of ka for achieving a broacast aver
3 tising reach of a. Search avertising is a selftargete type of avertising because the customer is expose to the avertisement only when she consciously searches for the retailer s web site base on keywors escribing the prouct. The search site which carries the retailer s search avertisement charges a fee to the retailer for every customer who clicks on the hyperlink provie by the search avertisement. This type of charge reflects the pay per click metho of payment which is common in the search avertising inustry. et represent the pay per click charge for every customer who visits the retailer s web site through search avertising. Given the costs of search an broacast avertising, the retailer chooses its avertising policy (which avertising moes, broacast or search, to use an how much to avertise) an price. The customers then buy the prouct if they become aware of the retailer s web aress through avertisements an if they get a positive surplus from buying the prouct. et us examine the avertising policy more closely. The retailer may choose any combination of search an broacast avertising. Since broacast avertising costs are taken to be ka, some broacast avertising will always be provie. Thus there are two possible avertising policy choices for the retailer: One in which the retailer subscribes to both broacast an search avertising(ual moe avertising strategy), an the other in which it subscribes to only broacast avertising (single moe avertising strategy). Before we formulate the retailer s problem, we will list some restrictions on the parameter values to focus on situations of interest. Assumption 1. The pay per click fee is less than the highest reservation price, i.e., < r. Assumption. r < Min[ 4k, k]. This eliminates the uninteresting case of market saturation through broacast avertising where the retailer gets 100% market reach through broacast avertising alone. Note that for the assumptions 1 an to be feasible together, we must have < 4k k > Dual moe avertising strategy ere the retailer s strategy is to provie both broacast an search avertising. (r p) customers have a positive surplus from buying the prouct. A fraction (1 a) of these customers are not expose to the broacast avertising. So they use the search avertisement route to obtain the retailer s web aress. Thus the retailer incurs a search avertising cost of (1 a)(r p). Normalizing the marginal cost to 0, the profit function of the retailer is: π (r p)p ka (1 a)(r p) The retailer will maximize its profit with respect to the price p an broacast avertising reach a. The essian matrix of π is negative efinite ue to assumptions 1 an. Therefore, the profit function is jointly concave in a an p. The equilibrium values are: a (r ) 4k p k(r + ) r 4k π k(r ) 4k The parameter has an interesting effect on the equilibrium pricing an broacast avertising reach. As increases: 1 Equilibrium price increases if r < otherwise, 4k + an ecreases equilibrium broacast avertising increases if r > 8k 4k + an ecreases otherwise. The pricing behavior can be explaine as follows. As increases, the margin per customer for a given price ecreases. 4k + If r >, there are a consierable number of customers with relatively high valuations who are outsie the market ue to high prices. As increases, it becomes optimal to reuce prices an gain volume in the market. owever, if 4k + r <, then the optimal reaction is to increase the price to get a larger margin per customer from lesser number of customers. For explaining the effect on broacast avertising, note that an increase in increases the cost of getting a customer through search avertising. Therefore, one woul expect that broacast avertising shoul increase so that the marginal cost of getting a new customer through both avertising moes is balance. owever, if r < 8k, the opposite happens. The reason is that 4k + price increases with increase of for r < 8k 4k + (since 8k 4k + < ). Thus the market coverage reuces. 4k + Consequently, the marginal cost of getting a new customer through broacast avertising increases to be more than. ence broacast avertising is reuce. 3. Broacast Avertising Strategy The profit function of the retailer uner this strategy is: π b a(r p)p ka As before, the retailer will maximize its profit simultaneously with respect to the price p an broacast avertising reach a. Three critical points exist out of which two imply a 0 value for π b while the thir provies a positive value. Since π b is continuous, this thir point is the global maximum. The equilibrium values in this case are: a b r 8k p b r π b r4 64k Next we fin the conition when the ual moe avertising strategy is superior to broacast avertising only.
4 emma 1. The strategy to aopt ual avertising moes maximizes the retailer s profit when the pay per click fee < e (3k r p kr 4 (r 8k) ) r k Proof. We get this result by comparing π an π b. Search avertising is becoming ubiquitous ue to its targeting capabilities an many retailers feel that it is extremely effective in getting customers to their web sites. An important question for managers is whether employment of search avertising necessarily translates into smaller avertising costs. We answer this question in the next result. Proposition 1. When it is profit maximizing to provie search avertising through the ual moe strategy, then at the margin efine by emma 1 ( e ), the total avertising cost is more than the avertising cost in the single moe strategy with broacast avertising only. Proof. The total avertising cost in the ual moe strategy is k(a ) + (1 a )(r p ). In the single moe strategy with broacast avertising only, these costs are k(a b). Comparing these costs at e gives us the state result. This proposition points out that when the retailer chooses to get the customers through both avertising moes, it may be profit maximizing to increase the total avertising costs to reach the optimal number of customers in the appropriate customer segments. Interestingly, a recent article in the Wall Street Journal [?] states that this seems to be happening in the inustry. Our next observation comes from analyzing the behavior of equilibrium prices. It is easily seen that the price in the ual moe strategy, p, is higher than the price, p b, in the single moe strategy. igher price with the ual avertising moes implies that a larger fraction of customers are exclue from the market since they get a non positive surplus from buying the retailer s prouct. In the single moe strategy, although the price is lower, the section of the market not expose to broacast avertising is exclue from the market. Thus welfare may increase or ecrease with the availability of search avertisements. In particular, there is a possibility that welfare may reuce even when it is profit maximizing to employ the ual moe avertising strategy. The next proposition answers the question about welfare creation. Proposition. When a retailer aopts the ual moe avertising strategy, then at the margin efine by e, social welfare is reuce. Proof. The consumer welfare in the ual moe avertising strategy is CS Z r moe avertising strategy it is CS b a b p (x p )x, an in the single Z r p b (x p b)x. At e, the retailer profits in both avertising strategies are the same. Therefore, comparing CS an CS b at e gives us the statement of the proposition. Thus we fin that the increase in price with the ual avertising moes is so high that it always reuces social welfare at the margin when the firm switches to the ual moe strategy. Social welfare will be create only when the cost of search,, becomes low enough. 4. MONOPOY RETAIER WIT A PROD UCT OF UNKNOWN QUAITY In this section we consier a situation where the quality of a monopoly retailer s prouct is exogeneously fixe to be of either high or lwo quality. While the retailer knows the quality of its prouct, the customers are unaware of the actual quality. enceforth, we will refer to the retailer as the high quality (low quality) retailer if he sells the high (low) quality prouct. In this situation, the customers willingness to pay for the high quality retailer s prouct epens on their belief about the prouct s quality. If they believe that the prouct is of low quality, they will be willing to pay less than what the prouct is actually worth to them. Thus the uncertainty of customers about the quality of the retailer s prouct may have a negative impact on the high quality retailer s profit. Therefore, such a retailer has an incentive to inform the customers that its prouct is of high quality. In marketing literature, researchers have foun that suitable moification of the price an avertising spening from their optimal levels when the customers are aware that the prouct is of high quality constitutes an effective mechanism to signal the prouct s quality to the customers. Milgrom an Roberts [6] showe that when all customers observe a firm s avertisements, the firm signals by increasing the avertising expeniture. ater on Zhao [1] consiere the case where all customers o not observe the firm s avertisements, an only those customers who observe the firm s avertisements buy the prouct. In this case the firm signals by reucing its avertising expeniture, which is the reverse of what Milgrom an Roberts foun. To summarize, the high quality retailer may want to signal to the customers that its prouct is of high quality through a juicious mix of avertising an pricing policies. Observing these policies, rational customers arrive at correct conclusions about the actual quality of the prouct being markete. The intent of this section is to stuy the effectiveness of ual moe avertising visavis the single moe strategy with broacast avertising to signal the quality of the prouct for the high quality retailer. If the high quality retailer aopts an avertising an pricing policy that a low quality retailer is unwilling to aopt, an if such a policy provies higher profits to the high quality retailer than if it aopts any other policy an is mistaken to be a low quality retailer, then the high quality retailer will aopt such a policy. Since this policy will not be aopte by the retailer if it were a low quality retailer, the customers will be able to correctly infer the quality of the prouct being sol on observing the policy of the retailer. In other wors, a separating equilibrium will ensue. enceforth, the superscripts an stan for the type of retailer (high quality an low quality) an the subscripts an stan for the beliefs that customers form about the retailer s type on observing its policy. Therefore, in a separating equilibrium a retailer will make a profit of π if it is selling a high quality prouct an a profit of π if it is selling a low quality prouct. If a low quality retailer mimics the policies that a high quality retailer woul aopt, an is therefore mistaken to be a high quality retailer, it will earn a profit of π. In case a high quality retailer is unable to aopt a creible signaling policy, a pooling equilibrium will result in which the customers are unable to infer the quality of the prouct being sol. So they may mistake a high quality retailer to be
5 selling a low quality prouct. If this happens, a high quality an a low quality retailer woul earn profits of π an π respectively. In orer to enforce a separating equilibrium, the high quality retailer solves the following constraine optimization problem: max a,p s.t. π π π π π where the first constraint inicates that mimicry is not profitable if the retailer has a low quality prouct an the secon constraint inicates that the retailer of the high quality prouct makes a higher profit in a separating equilibrium than if it were mistaken to be a retailer of the low quality prouct in a pooling equilibrium. If the mimicry constraint is not bining, there is no threat that a low quality retailer woul mimic the policy of the high quality retailer. Essentially, the signaling is accomplishe for free in this case. For the problem to be of interest, signaling shoul be costly, which implies that the mimicry constraint must be bining. We will consier only these situations. In the forthcoming proof of emma, we will inicate the conitions uner which this will happen. As in the previous section the customers willingness to pay for the high quality prouct is ρ which is uniformly istribute between 0 an r with unit ensity. The marginal cost for the high quality prouct is c an for the low quality prouct it is 0, where c > 0. Implicit in our optimization problem is the fact that the high quality retailer may aopt either the ual moe avertising policy, or the policy of proviing broacast avertising only. If it aopts the ual moe policy, its profit function is as follows: π (r p)(p c) ka (1 a)(r p) The formulation of this profit function is base on two observations. First, the customers know the actual price being charge by the retailer before they click on the link provie by search avertising. Secon, the observation of price is alone is sufficient to convince the customers that the prouct is a high quality prouct. The first observation is base on the fact that many shopping web sites which provie search avertising services such as Fingift.net an Yahoo Shopping etc. isplay the prices of the retailers along with their links. Some prominent search services such as Google o not require retailers to isplay the prices. owever, it is in the interest of a high quality retailer to isplay its price along with the isplay of its link. Not oing so woul result in a eaweight loss for such a retailer because if the customers whose willingness to pay is greater than p o not click on the link the retailer looses potential buyers. If customers whose willingness to pay is less than p click on link, the retailer ens up paying a cost for each such customer who will not buy the prouct. A ranom search on Froogle inicate that myflavia.com, a retailer for coffee espresso machines isplaye its price of $ on the search link itself. The logic for the secon observation that price alone is sufficient to convince the customers that the prouct is of high quality will become clear in the forthcoming proof of emma. In view of the above iscussion, all customers with willingness to pay between r an p will buy the prouct, an the expeniture on search avertising is (1 a)(r p). The next lemma provies the signaling solution for the case when the high quality retailer aopts ual moe avertising: emma. With the ual moe avertising policy, the high quality retailer signals by lowering its broacast avertising compare to the case when the prouct quality is known to the customers. The optimal avertising, pricing an profits are: a D (r ) 4k p D π D p k(k(r ) π (4k )) (4k )k r ad k c k(r ) p k(k(r ) π (4k )) π 4k Proof. Suppose that customers use only the pricing information to ecie whether the retailer is selling a high or a low quality prouct. Is this a rational ecision? In what follows, we will show that the optimal choice of avertising reach by a low quality retailer who prices as if it were a high quality retailer, is the same as the avertising reach chosen if it were a high quality retailer. Therefore, mimicry of price implies mimicry of avertising reach. ence, observation of price alone is sufficient for the customers to ecie whether the prouct is of high or low quality. et p be the price chosen by the high quality retailer. The following function efines the profit earne by a low quality retailer when it mimics only the pricing of the high quality retailer an customers believe that the prouct is of high quality after observing this price: π (r p)p ka M (1 a M )(r p) The optimal broacast avertising reach a M is obtaine by solving the corresponing first orer conition which gives: p r a M k (1) We now consier the problem for the high quality retailer when the low quality retailer mimics only the pricing. We construct the relaxe problem without the constraint for the separating equilibrium. In emma 3 we will iscuss when the separating equilibrium is likely to exist. The lagrangian of the optimization problem for the high quality retailer is: (r p)(p c) ka (1 a)(r p) + λ π {(r p)p (ka M ) (1 a M )(r p)} The first orer conition of with respect to a is as follows: (ak (r p)) 0 From the above equation, we get p r ak Both the equations (1) an () give the price p chosen by the high quality retailer. Equating them we see that a M a. In other wors, mimicking the price is optimal only when the avertising reach is also mimicke. Therefore, observation of price alone is enough for the customers to conclue that the prouct is of high quality. Next we etermine what price is chosen by the high quality retailer to signal its quality, knowing that its choice of ()
6 avertising reach will also be mimicke. Substituting for p from Equation () an putting a M a in the mimicry constraint we obtain: a ( 4k kr k) + a(k ) + π 0 (3) Solving the above equation for a we obtain two possibilities: (r ) a 1 4k p k(k(r ) π (4k )) (4k )k an, a (r ) 4k + p k(k(r ) π (4k )) (4k )k To fin which one of these critical points constitute the global maximum (i.e give the high quality retailer a higher profit), we construct the unconstraine profit function of the high quality retailer as a function of a. This is one by substituting p r ak obtaine from the first orer conition of π (a, p) with respect to a. The function we construct is: ka `(r c) 4ak ( a) an its secon erivative with respect to a is k(1 4k ), which has a constant negative value ue to assumptions 1 an. Therefore, the unconstraine profit function is symmetric an concave an is maximize at a (r c) u. 4k (r c) (r ) Since c > 0, we have < 4k 4k. Therefore, a 1 a u < a a u, which implies that the high quality retailer gets a higher profit by choosing a 1. The corresponing price is arrive at using equation (). This completes the proof of the lemma. One final point to make is if a u < a 1, then the high quality retailer can maximize its profit by choosing a u as the optimal avertising reach, while simultaneously satisfying the mimicry constraint as it is slack at a u. From the expression of a u, note that this conition will happen if the marginal cost of the high quality prouct, c, is large enough. As mentione earlier, our analysis is confine to the interesting case where c is small so that the mimicry constraint is bining. The results in emma are reminiscent of Zhao [1] where the broacast avertising is reuce to signal a high quality prouct in a setting where the broacast avertising is the only moe of information for customers. Our next result establishes that a separating equilibrium will exist with the ual moe avertising policy. emma 3. When the ual moe avertising policy is aopte a separating equilibrium will exist if the cost of search avertising,, an the marginal cost, c, are small. Proof. We outline the solution to the relaxe problem with ual moe avertising for the high quality retailer in emma. If the constraint we i not consier, π π, is also satisfie with this solution, then a separating equilibrium will be establishe. Suppose that the highest reservation price for the low quality prouct is r, where r < r. Also, let be small enough so that ual moe avertising is the preferre policy for both the high an low quality retailers in a pooling equilibrium. From the analysis in section 3.1, then, π k(r ). Similarly, when the high quality retailer is (4k ) mistaken as a low quality retailer in a pooling equilibrium, it will aopt optimal avertising an pricing policies in anticipation of the pooling equilibrium, i.e., π k(r c ). (4k ) Substituting the values of π from emma, an π an π from the previous analysis in the constraint π π an simplifying, we obtain: c (r r ) + p (r r )(r + r ) Note that r > (r r ) + p (r r )(r + r ) > 0. Thus, if c is small enough the constraint π π will be satisfie an a separating equilibrium is establishe. If the high quality retailer aopts the policy of utilizing broacast avertising only to signal high quality, then the profit functions are as follows: π a(r p)(p c) ka π a(r p)p ka We assume as in Zhao [1] that the customers who are expose to broacast avertising, are also informe about the expense incurre on it. This problem is the same as that solve by Zhao. Therefore, qualitatively similar results are expecte. owever, in our formulation, the solution is algebraically complicate an is not easy to analyze irectly. Therefore, we will not provie its solution in an explicit form. We represent the optimal value of profit for this case by π B an the corresponing values of ecision variables by p B an a B. Now we concentrate on characterizing the situations where the high quality retailer prefers the ual moe avertising policy over the single moe policy with broacast avertising only to signal high quality. Our next proposition incorporates this result. Proposition 3. Dual moe avertising is more likely to be the optimal policy to signal the quality of the high quality prouct as the low quality prouct becomes more profitable i.e. as π increases. Proof. The solution to the high quality retailer s problem with the ual moe avertising policy is available from emma an emma 3. Next, we characterize the solution to the high quality retailer s problem when it chooses to aopt the single moe avertising policy with broacast avertising only. We consier the relaxe problem of the high quality retailer without the constraint for the separating equilibrium. The lagrangian is: Γ a(r p)(p c) ka + γ π {a(r p)(p) ka } The first orer conitions of Γ with respect to a an p are an, (r p)(p c) ak γ((r p)p ak) 0 (r + c p) γ(r p) 0
7 Eliminating γ from the above two equations we get p r ak (4) Substituting p from equation (4) in the mimicry constraint for this case, we arrive at π + 3a k ka 3/ r 0 (5) We can write π B From the mimicry constraint we have π a B (r p B )(p B c) k(a B ). a B (r p B )p B k(a B ). Therefore we have π B π a B c(r p B ). Similarly, we can write π D π (r p D )c. The conition for the profits with the ual moe avertising policy to be greater than the profits with the single moe avertising policy is: Substituting p D π D > π B (6) an p B using equations () an (4); an further using equation (5) to substitute for (a B ) 3 in the above inequality an simplifying we get: π > kr ad 3k(a B ) (7) The left sie of the above inequality is just π an so its slope with respect to π is 1. Next, we will show that the slope of the expression on the right sie of the inequality may become less than 1 as π increases. We obtain the expressions for the erivatives of a D an a B with respect to π by ifferentiating equations (3) an (5). These erivatives are: an, a D π a B π 1 a D ( 4k k) + (k kr ) (8) 1 p ka B (6p ka B 3r ) Although it is ifficult to see in our formulation of the problem, from Zhao (000) we know that a B a b, where a (r c) b (from analysis shown in section 3., but with 8k marginal cost c > 0). Therefore, the enominator of equation () is negative. ence, ab π () > 0. The erivative of the expression on the right han sie of Inequality (7) with respect to π is: kr a D π 6a B k ab π Substituting the value of the erivatives from equations (8) an () in this expression an simplifying we get r r ad (4k ) + 6ka B 6ka B 3 rp ka B The enominator of the first term is positive since we know from emma that a D (r ) 4k. The enominator of the secon term is negative since a B (r c), as 8k iscusse earlier. For the above expression to be weakly less than 1, we must have q «4k ka B + a D (10) If π is close to 0, then the low quality retailer will mimic any policy that a high quality retailer woul aopt. This is because any policy that gives a positive profit to the high quality retailer will certainly provie a positive (an higher) profit to the low quality retailer as its marginal cost is lower than that for a high quality retailer. The only way for the high quality retailer to stop mimicry by the low quality retailer is to avertise such that its own profits are zero. For this, the high quality retailer must choose a B 0 for the single moe broacast avertising policy an a D 0 for the ual moe avertising policy. In both cases, this will lea to an optimal price equal to r (see equations (4) an ()). This results in zero market size an zero profit for the high quality retailer. In this situation, the inequality (10) will not be satisfie because of the constant term on the right han sie. From the iscussion in the previous paragraph, we also know that as π 0, the left an right sie expressions in Inequality (7) go to zero. Further, we saw that the slope of the expression on the left sie (1) is less than the slope of the expression on the right (> 1) since Inequality (10) is not satisfie. Thus Inequality (7) cannot be satisfie if π is close to zero i.e. the ual moe policy cannot be the optimal policy. From earlier analysis, we know that ab π > 0. Therefore, the Inequality (10) may be satisfie as π increases i.e. the slope of the right sie of the expression in Inequality (7) may become less than 1. ence, the ual moe policy may become more profitable as π increases. From emma 3 we also know that that a separating equilibrium with the ual moe avertising policy will exist for some parameter range. This completes the proof of the statement in the proposition. The important insight from the previous proposition is that high quality retailers are likely to choose the ual moe avertising policy when face with the issue of ifferentiating themselves from a low quality retailer whose quality is relatively high. When oes the ual moe avertising policy become superior to the single moe broacast avertising only policy? To unerstan this, we have to first unerstan why signaling works. From the results in emma it can be shown that in the ual avertising moe, the high quality retailer signals by raising its price. Similarly, Zhao [1] shows that in the single moe avertising policy with broacast avertising only, the high quality retailer signals by raising price an reucing avertising reach. In both cases, these policies reuce the number of customers who can buy the prouct. If the low quality retailer mimics the policy of the high quality retailer, its profits are reuce much more than the high quality retailer s profits since it enjoys a greater profit margin per customer at a given price ue to lower marginal costs. Thus the tenency of the low quality retailer to mimic is checke by aopting pricing an avertising policies that reuce its profits much more than that of the high quality retailer. et us see when signaling through ual moe avertising
8 may work better for the high quality retailer. Inequality (6) can be written as a B (r p B )c > (r p D )c. Note that a B (r p B ) is the number of customers who buy the retailers prouct when it aopts the single moe avertising policy with broacast avertising. Thus a B (r p B )c is the aitional profit that the low quality retailer makes over the profit of the high quality retailer by mimicry. Similarly, (r p D )c is the aitional profit that the low quality retailer makes by mimicry when the high quality retailer aopts the ual moe avertising policy. The conition implies that the ual moe avertising policy becomes superior when the aitional profits mae by the low quality retailer uner the ual avertising moe become lower than the aitional profits mae by the low quality retailer uner the single moe policy. Essentially, the inherent avantage lies with the policy that provies lesser aitional profits to the low quality retailer if it resorts to mimicry. 5. DUOPOY The purpose of this section is to characterize the strategic choices of the retailers uner a competitive scenario. Competition can be in an asymmetric information setting, in which case the web site of one of the retailers is alreay known to customers an so it oes not require to invest in avertising; or it can be in a symmetric information setting, in which case customers are not aware of the web sites of both the retailers an so both of the retailers have to avertise. We moel both these scenarios. We are specifically intereste in situations where the cost of search avertisement,, is low so that ual moe avertising is the optimal strategy for a retailer whenever it requires to o avertising. The uopoly is moele as a Bertran competition between a retailer selling a high quality prouct (the high quality retailer) an a retailer selling a low quality prouct (the low quality retailer). The quality of the proucts are known to customers. The low quality prouct represents the base prouct an all the customers are willing to pay B for it. The premium that customers are willing to pay for the high quality prouct is represente by the parameter ρ which is uniformly istribute between 0 an r with unit ensity. As in the previous section, the marginal cost of low quality prouct is normalize to 0, an the marginal cost of the high quality prouct is c > 0. In our exposition, the subscripts an will represent the high an the low quality retailers respectively. In aition, there will be two superscripts for each variable. The first superscript will represent whether the customers know the high quality retailer (K), or o not know about it (U). The secon superscript with similar notations will represent whether the customers know the rival low quality retailer or not. To maintain consistency with the situation that the cost of search avertising is low, we make the following assumptions on the parameter values. Assumption 3. k > c Assumption 4. c > To explain our next assumption, similar to section 3.1, the pay per click fee plus the marginal cost of the high quality prouct is less than the reservation price. In aition, the highest reservation price is never so high so that it becomes optimal to saturate the whole market through broacast avertising alone. Assumption 5. c + < r < 4k 3k 4k + kc 4k We start by moeling the case of competition in an asymmetric information setting. 5.1 Asymmetric information about retailers The customers may be unaware of either the high quality retailer or the low quality retailer. First, consier the case where they know the low quality retailer only. When the high quality retailer prices at p UK an the low quality retailer at p UK, the inifferent customer (ρ I) between the high an low quality prouct is given by B+ρ I p UK B p UK. Thus ρ I p UK p UK an the market sizes for the high an low quality retailers are r ρ I an ρ I respectively. ere we assume that p UK < B so that all customers get a positive surplus from buying the low quality prouct. As in section 3.1, we also assume that a fulfille expectation equilibrium exists so that the customers will be charge the price that they expect to be charge. The profit functions of the two retailers, when the high quality retailer aopts the ual moe avertising policy, are: π UK π UK a UK + (1 a UK ) (p UK r (p UK p UK ) (p UK r (p UK p UK ) p UK )p UK c) (p UK c ) k(a UK ) The high quality retailer chooses a UK an p UK, while the low quality retailer chooses p UK in a simultaneous game. Both the profit functions are jointly concave in their respective ecision variables (from the assumptions). The equilibrium values are: a UK r (c + ) 6k p UK (k(c + + r) r ) 6k p UK k(c + + r) r 6k π UK k(4k )(r c ) (6k ) π UK ((k )r + (c + )k) (6k ) Besies avertising through the search an broacast moes, an interesting avertising possibility arises if the retailer whose web site is known to customers allows the unknown retailer to piggyback on its web site so that the unknown retailer oes not engage in avertising an instea pays a fixe fee per transaction, t, to the known retailer. Such a situation is seen at the Amazon.com web site where Amazon allows small (most of whom are unknown) sellers to be liste on its web site. The customers visiting Amazon s web site can buy either from Amazon or from the sellers liste on its web site. We use a secon subscript, P, to represent piggybacking. To ascertain that the prices of the low quality retailer with piggybacking, p UK P an p KU P, are less than B so that the customers get a positive surplus from the low quality prouct, we make another assumption.
9 Assumption 6. t < B r + c 3 The profit functions of the two retailers with piggybacking are: πp UK r (p UK P p UK P ) (p UK P c t) π UK P (p UK P p UK P )p UK P + (r (p UK P p UK P ))t The high quality an the low quality retailers choose prices p UK P an p UK P simultaneously. The profit functions are jointly concave in their prices ecisions. The equilibrium values are: p UK P p UK P (r + c) + 3t 3 r + c + 3t 3 πp UK (r c) πp UK (r + c) + rt As one above, we can also analyze the case when the customers know the web site of the high quality retailer only. Now the profit functions of the retailers when the low quality retailer aopts the ual moe avertising policy are: π KU π KU a KU r (p KU p KU + (1 a KU ) p KU ) p KU p KU (p KU c) p KU p KU (p KU ) k(a KU ) As before, the profit functions turn out to be jointly concave in their ecision variables. The equilibrium values are: a KU (r + c ) 6k p KU (k + (4k )(r + c)) 6k p KU k + (4k )(r + c) 6k π KU (k(c ) + r( 4k)) (6k ) π KU k(4k )(r + c ) (6k ) c r With piggybacking, the profit functions for this case are: πp KU r (p KU P p KU P ) (p KU P c) + (p KU P p KU P )t π KU P (p KU P p KU P )(p KU P t) The equilibrium values with piggybacking are: p KU P p KU P (r + c) + 3t 3 r + c + 3t 3 πp KU (r c) + rt πp KU (r + c) The next result states the importance of the piggybacking strategy for the retailers. Proposition 4. With piggybacking, both the retailers can achieve higher profits compare to the case when the unknown retailer aopts the ual moe avertising policy. Proof. First, consier the case when the high quality retailer is unknown an the low quality retailer is known. (r c) We have lim π UK. This represents the upper boun of the profits achievable for the high quality re 0 tailer with ual moe avertising because the retailer gets its customers at zero avertising costs. Further, we have πp UK (r c). Thus with the piggybacking strategy, the high quality retailer achieves profits that equal the upper boun on its profits with ual moe avertising. Further, πp UK (r + c) + rt. ence, if t is large enough, the low quality retailer can make profits exceeing the profits it earns when the high quality retailer aopts ual moe avertising. In the case when the high quality retailer is known an the low quality retailer is unknown, note that lim π KU 0 π KU (c + r) an π KU (r c) + rt. Using logic P P analogous to the one use above, we see that both the retailers can achieve higher profits with the piggybacking strategy. The constraint on increasing the value of t comes from Assumption 6. Therefore, if B is large enough, a transaction fee t > 0 can always be foun so that the known retailer can also improve its profits enough for piggybacking to be profitable for both retailers. 5. Symmetric information about retailers ere we moel the situation where neither retailer has the avantage of previous customer knowlege of its web site. As before, we assume a low search avertising cost so that both retailers aopt ual moe avertising. A customer can make a search specific to the high or the low quality prouct since the two proucts are ifferent an can be escribe separately on search sites. Assuming a fulfille expectations equilibrium, the profit functions of the two retailers are: π UU a UU r (p UU p UU ) (p UU c) + (1 a UU ) r (p UU p UU ) (p UU π UU a UU (p UU + (1 a UU )(p UU p UU )p UU p UU )(p UU ) k(a UU ) c ) k(a UU ) The two retailers ecie on their price an avertising simultaneously. The profit functions are jointly concave in terms of their ecision variables. The equilibrium values are: a UU a UU k(r c) r3 4k(3k ) k(r + c) r3 4k(3k ) p UU (4 6 k + 8k )r + ck(4k ) + 4k(3k ) 4k(3k ) p UU r(k ) k( (c + ) k(c + 3)) 4k(3k ) In the next result, we aim to efine the strategic response of a retailer as a function of whether the customers know its competitor or not.
10 Proposition 5. If the premium on the high quality prouct is high (large r), an if the customers are informe about a retailer s competitor, it will employ more search avertising an less broacast avertising compare to if the customers were not informe about the retailer s competitor. This strategic response is reverse if the premium on the high quality prouct is low. Proof. First, consier the case when the high quality retailer is unknown. The optimal expense incurre by this retailer on search avertisement when the low quality retailer is also unknown is ES UU (1 a UU ) `r (p UU p UU ) ; an when the low quality retailer is known, it is ES UK (1 a UK )(r (p UK p UK )). We fin that ES UK > ES UU r > 6(1k3 + 4ck c 3 k 4 k ), using some algebra. ( 4 18 k + 48k ) The optimal expense incurre by the high quality retailer on broacast avertising when the low quality retailer is also unknown is EB UU k(a UU ) ; an when the low quality retailer is known, it is EB UK k(a UK ). We fin that EB UK > EB UU r < (1ck + 6k 3c k 3 k) k + 48k We perform analogous calculations for the case when the low quality retailer is unknown an fin that similar results hol even for this case. Clearly, the nature of strategic response is not contingent on the quality of prouct being markete by the retailer. 6. CONCUSION Search avertising has emerge as a preferre way of avertising on the Internet. It s targeting capability ensures that only the customers who are intereste in buying a prouct are ever expose to the avertising message. The payment metho is also unique. The avertising fee becomes ue only when customers reaffirm their interest in buying the prouct by clicking on the link provie by the search avertisement. Shoul the targeting capability an cost efficiency of search avertising then enable online retailers to reuce their avertising bugets? The answer may be in the negative because it might be beneficial to spen more on avertising to get larger number of customers. Since search avertising allows for better targeting, retailers may want to increase their price. This price increase may cause a reuction in social welfare. When customers are uncertain about the quality of prouct being sol by the retailer, a retailer selling a high quality prouct may want to use price an avertising as signals of its prouct quality. It turns out that utilization of search avertising for signaling is more likely if the quality ifferential between the high quality an the alternative low quality prouct is small. This shows that the utility of search avertising as a signaling tool is limite an alternative means of signaling may be require if the quality ifferential between the high an low quality prouct is significant. In a competitive uopoly, both retailers may be better off if the retailer with an establishe bran value (i.e. who is known to customers) uses its web site as a portal. The retailer without the bran value lists its web site on the portal for a fee instea of resorting to avertising. If both retailers are unbrane, the relative amount of search an broacast avertising changes as the competing retailer becomes more establishe in the market. 7. REFERENCES [1] M. R. Baye an J. Morgan. Information gatekeepers on the internet an the competitiveness of homogeneous prouct markets. The American Economic Review, 1(3): , 001. []. K. Bhargava an J. Feng. Pai placement in information gatekeepers. Working Paper Series in Management Science an Information Systems, Smeal College of Business, Pennnsylvania State University, 00. [3] R. Dewan, M. Freimer, an P. Nelson. Impact of search engine ownership on unerlying market for goos an services. Proceeings of the 34th awaii International Conference on System Sciences, 001. [4] Google s profit soar on strong a sales; earnings jump nearly eightfol to $04 m on $1 billion in revenue in the fourth quarter. February, 005. [5] Search engines are powering a revenue; when the sponsore search concept was introuce, it was panne by iealists. now it s a river of online commerce. May 4, 004. [6] P. Milgrom an J. Roberts. Price an avertising signals of prouct quality. The Journal of Political Economy, 4(4):76 81, 186. [7] T. Mukhopahyay, U. Rajan, an R. Telang. Competition between internet search engines. Proceeings of the 37th awaii International Conference on System Sciences, 004. [8] P. Nelson. Avertising as information. The Journal of Political Economy, 8(4):7 754, 174. [] R. Schmalensee. A moel of avertising an prouct quality. The Journal of Political Economy, 86(3): , 178. [10] Online retail sales are expecte to rise to $17 billion this year. May 4, 005. [11] T. Weber an E. Zheng. A moel of search intermeiaries an pai referrals. Working Paper, Stanfor University, 005. [1]. Zhao. Raising awareness an signaling quality to uninforme consumers: A priceavertising moel. Marketing Science, 1(4):30 36, 000.
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