Int. J. of the Economics of Business, Vol. 19, No. 1, February 2012, pp. 25–51
A Comparison of Bundling and Sequential Pricing in Competitive Markets: Experimental Evidence
JOHN ALOYSIUS, CARY DECK and AMY FARMER
ABSTRACT Technological advances enable sellers to identify relationships among offered goods. Sellers can leverage this information through pricing strategies such as bundling and sequential pricing. While these strategies have primarily been studied under monopoly assumptions, the strategies are available to competitive firms as well. This paper reports on a series of laboratory experiments comparing bundling and sequential pricing while varying the underlying relationship between the goods in markets where a fraction of buyers comparison shop. The results indicate that sequential pricing is generally as profitable to the seller; however, there is evidence that sequential pricing may be more harmful to consumers than bundling when the goods have complementary values or the buyer’s values are positively correlated. Key Words: Pricing Strategy; Bundling; Sequential Pricing; Experimental Methods. JEL classifications: C9, D4, L1.
1. Introduction Each basket of goods purchased at many major retailers is recorded.1 This vast volume of data enables retailers to identify the underlying distribution of buyer values and the relationships between those values through data mining
The authors wish to thank Scott Burton, Yongmin Chen, Robert Letzler, Donald Lichtenstein, John List, Bart Wilson, and participants at the FTC Conference on Microeconomics, the Southern Economic Association Annual Meetings, and a seminar at Chapman University for helpful comments and suggestions on an earlier draft of this paper. Financial support from the Center for Retailing Excellence and the Information Technology Research Institute, both of the Sam M. Walton College of Business, is gratefully acknowledged. John Aloysius, University of Arkansas, Department of Information Systems, 1 University of Arkansas, Fayetteville, AR 72701; e-mail:
[email protected]. Cary Deck, University of Arkansas, Department of Economics, 1 University of Arkansas, Fayetteville, AR 72701; e-mail:
[email protected]. Amy Farmer, University of Arkansas, Department of Economics, 1 University of Arkansas, Fayetteville, AR 72701; e-mail:
[email protected]. 1357-1516 Print/1466-1829 Online/12/010025–27 Ó 2012 International Journal of the Economics of Business http://dx.doi.org/10.1080/13571516.2012.642637
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techniques such as cluster detection and market basket analysis (see Berry and Linoff, 2004). Some goods are complements (customer values for the bundle are greater than the sum of the values for the individual products) and in other cases the goods are substitutes (customer values for the bundle are less than the sum of the valuations for the individual products). For example, a computer and a printer are complements, since customers have added utility for a printer when they have a computer and vice versa. Separately, individual buyers may have positively or negatively correlated values for two goods. For example, someone interested in a given topic is likely to have a high value for books on that topic, while an uninterested person is likely to have a low value for these books. Additivity between values for two goods and the correlation of values for two goods are distinct concepts. Again referring to the book example, two books covering the same content may be substitutes, whereas two books presenting different perspectives on the topic may be complements. With an understanding of buyers’ values, multi-good sellers choose a portfolio of prices in order to maximize profit. For example, a seller can engage in pure components pricing by setting a single price for each good. Alternatively, a seller could engage in mixed bundling by offering standalone prices for the individual goods as well as a price for a bundle of goods.2 Bundling has a long history in the economics literature, going back to Stigler (1968). Adams and Yellen (1976) develop the now common modeling framework and demonstrate how mixed bundling could increase monopoly profits even with independent goods. In their interdisciplinary survey of bundling, Stremersch and Tellis (2002) make two pertinent observations. First, the literature has focused primarily on profit maximization by a monopolist (p. 60).3 Second, one of the most promising areas of further research appears to be the impact of competition on the impact of bundling (p. 71). They also highlight the distribution of customer conditional reservation prices as the likely predominant condition for optimality of bundling. While academic analysis has primarily focused on monopoly sellers, competitive firms commonly use price bundling as a strategic marketing tool. Be it consumer durables (e.g., computers and printers), consumer packaged goods (e.g., a shrink-wrapped package of shampoo and conditioner), services (e.g., cable TV and Internet), firms use bundling as a means to improve measures of business performance, including profits and market share. As an alternative strategy to bundling, Aloysius et al. (2009) introduced the notion of sequential pricing with discrimination, where sellers observe the order in which buyers are quoted prices and condition subsequent price quotes on previous purchase decisions. There is considerable evidence in the popular press that retailers are trying to exploit their ability to monitor customers using technology to price discriminate (see, e.g., Clifford, 2010a, 2010b) and there are advocacy groups, such as Consumers Against Supermarket Privacy Invasion and Numbering, who oppose it. Current technologies such as the enhanced drivers’ licenses in the states of Washington and New York or RFID tags in previously purchased items such as clothing can also allow a seller to recognize a unique individual and price accordingly (Bustillo, 2010). Impulse purchases have long been known to be pervasive (Rook, 1987) and market basket analysis gives the retailer a means to predict what a customer might buy (Good B) given that they have already expressed their intent to purchase something else (Good A). Therefore if a retailer knew that a customer had
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purchased (or expressed the intent to purchase by putting it in their shopping basket) Good A, this revealed preference would be the basis for a suggestion that might trigger an impulse purchase. New technologies such as item level Radio Frequency Identification (RFID) tags allow a seller to track which items a customer intends to purchase (and thus which ones they do not) and adjust prices accordingly as a shopper moves around a store.4 Online retailers can use electronic “shopping carts” in a similar manner. The same technology that enables Amazon to make a recommendation based upon search history also enables it to charge a premium (or offer a smaller discount) to buyers who are more likely to have a high value for the item. Aloysius et al. (2009) report that sequential pricing generates greater monopoly profit than mixed bundling when the goods are either close substitutes or have highly positively correlated values. The theoretical complexity of monopoly bundling or sequential pricing, as discussed in the next section, is exacerbated under competition where some customers comparison shop. However, such a set-up is arguably more representative of what is occurring in the naturally occurring economy than either extreme assumption of only informed shoppers or only uninformed shoppers. As this intractability does not preclude retailers from engaging in these practices, it should not discourage researchers from studying the practices’ implications in this pertinent setting. The methodology of experimental economics provides an ideal tool for understanding market behavior in such situations. As described by Smith (1994), laboratory experiments provide a means for establishing empirical regularities, comparing environments (i.e., endowments, preferences, and costs), and comparing institutions (i.e., the set of actions available and how actions lead to outcomes). That is, through experiments we can identify how market outcomes change as a function of changes to buyers’ value structures (environment) and the pricing capabilities of the sellers (institution). Further, this type of research does not rely upon the auxiliary assumption of fully rational agents, the appropriateness of which has been called into question by recent research (e.g., Ellison, 2006). Our paper uses controlled laboratory experiments to explore the implication of bundling and sequential pricing in competitive markets. We examine the environment by a comparison of markets with independently valued goods, markets in which goods have positively correlated values, and markets in which goods are complements. We examine the institution by comparing different pricing strategies (bundling, sequential pricing with discrimination, and sequential pricing without discrimination). By establishing systematic deviations observed in these comparisons, we hope to extend beyond current theory and give guidance to theorists who seek to know in advance where their attention may best be directed as they attack these difficult problems (Smith, 1994). These deviations could lead to new theoretical models that incorporate previously ignored factors that may influence behavior and outcomes (e.g., fairness), or incorporate more realistic assumptions of rationality (e.g., quantal response). The remainder of the paper is organized as follows. The next section reviews the relevant literature providing mathematical detail where useful for our experimental study. The third section extends the theoretical development to the case where some customers comparison shop a la Varian (1980). The fourth section describes the experimental design, and the fifth section presents
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the findings. As a prelude to the results, we find that sequential pricing is generally as profitable to sellers as bundling, but sequential pricing can be more harmful than bundling in some environments. In all cases, the symmetric Nash equilibrium bidding strategy does not accurately describe aggregate behavior. A final section contains concluding remarks.
2. Bundling and Sequential Pricing The core theoretical work on product bundling is due to Adams and Yellen (1976), McAfee et al. (1989), Schmalensee (1984), and Stigler (1968).5 The general result is that customers with a high degree of asymmetry in product valuations will buy an individual product that they favor, while customers with less extreme product valuations will buy the bundle. This allows a seller to raise single item prices without losing all of the displaced customers (as some buy the bundle). The literature on bundling is beginning to clarify optimal pricing strategies, issues related to effective deployment of those strategies, and the environment in which these strategies may be deployed (Estelami, 1999; Guiltinan, 1987; Noble and Gruca, 1999; Simon and Dolan, 1998).6 Venkatesh and Kamakura (2003) present an analytical model of contingent valuations and find that the degree of complementarity or substitutability determines whether products should be sold as pure components, pure bundles, or mixed bundles. They also find that, typically, complements and substitutes should be priced higher than independently valued products. In their model, a customer has a value for good A, vA fA(vA), and for good B, vB fB(vB). The customer’s value for buying both goods depends upon the degree of substitutability or complementarity, h, so that vAB = (1 + h)(vA + vB). With mixed bundling, the customer simultaneously observes the prices of PA, PB, and PAB. The customer will purchase the bundle if vAB PAB P max (0, vA PA, vB PB) with similar conditions holding for purchasing items A and B separately. A buyer who cannot obtain a non-negative surplus from making a purchase will not buy anything and earn 0. The monopolist produces each item at constant marginal costs of cA and cB respectively. Given the framework above, now consider a seller’s price setting problem. We introduce the notation RiA , RiB , and RiAB to denote the region of possible buyer values from which a buyer would choose to purchase A, B, and i the bundle AB given PAi , PBi , and PAB . Of course, these regions depend upon the joint distribution of preferences. Therefore monopoly profit is given by Z Z Z Z m pm ¼ ðPAm cA Þ f ðvA Þf ðvB Þ þ ðPAm cA Þ f ðvA Þf ðvB Þ þ ðPAB cA cB Þ Z
RAB
RA
Z m
m
RB
m
f ðvA Þf ðvB Þ:
The optimization problem is conceptually straightforward. Differentiating the profit function with respect to PA, PB, and PAB yields three first order conditions, which must be satisfied simultaneously. While a general solution is unattainable, Venkatesh and Kamakura (2003) use a uniform distribution and numerically solve for the solution.
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In contrast to bundling where prices are set simultaneously, Aloysius et al. (2009) introduce sequential pricing where customers observe one price at a time. Without loss of generality, one can assume that the good A purchase decision is made first. They consider two cases: one in which the seller sets a single price for the second good and one in which the seller can condition the price of the second good on the purchase of the first good. Retailers are already offering customized prices based on characteristics of the buyer such as their past buying history and demographics (Clifford, 2010a). To use these characteristics, however, requires the retailer to identify unique customers through loyalty cards, credit cards, or some other means. The current research, however, has the retailer monitoring behavior (revealing preference for a Good A) in real time, which is not only technologically feasible but is something retailers have already begun doing (Bustillo, 2010). In the case where the seller prices good B without information regarding the purchase of A, the consumer will buy A iff PA 6 vA. A consumer who chooses not to purchase A will buy B iff PB 6 vB, whereas if A was purchased, then the consumer will buy B iff PB < (1 + h)(vA + vB) vA, which can be expressed as vB > (PB h vA)/(1 + h). When the seller sets PB, he or she knows the probability that A will have been purchased, conditional on the price of A and the distribution of preferences. Thus the seller sets the price of A knowing the probability A will be bought and therefore how that probability will affect the subsequent purchase of B. Solving the problem in reverse, the seller sets the price of B conditional on the chosen price of A and the corresponding probability that A was purchased. This yields the optimal price of B as a function of PA. Given that response function, the seller maximizes expected total profit as a function of the prices, where PB = f(PA). Aloysius et al. (2009) work through the exercise in the case of uniform distributions. Specifically, when fA(vA) U[0,100] and fB(vB) U[0,100], the two period expected profit maximization problem written as a function of PA is: Z
100
Z
PB hvA =1þh
1 dvB dvA þ ðPB cB Þ 2 100 0 0 Z 100 Z PA Z 100 R 100 1 PB hvA 1 dvA dvB þ ðPA cA þ PB cB Þ dvB dvA 2 100 1 þ h 1002 PB PA 0
maxPA EðPA Þ ¼ ðPA cA Þ
where the terms are profit from customers who buy only A, only B, and both goods respectively. Aloysius et al. (2009) present numerical solutions for the optimal prices as a function of h. If instead the seller can condition the good B price on whether or not the consumer has purchased A, then there will be two separate optimal response functions for setting the price of good B depending on whether good A was purchased or not. Each case yields an optimal expected profit from the sale of B, and the seller will take these optimal responses and corresponding profits into account when setting PA. Using the uniform distribution and the implied probability of a purchase of subsequently purchasing good B depending upon PA, Aloysius et al. (2009) show that the profit maximization problem in terms of PA becomes:
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J. Aloysius et al. Z PA 1 CB CB2 1 dVA þ 25 dVA 100 100 2 400 0 PA Z ½200 2CB þ ð300 þ PA Þh2 100 1 dVA : þ 1600ð1 þ hÞ PA 100 Z
maxPA EðPA Þ ¼ ðPA CA Þ
100
The novelty of sequential pricing as described by Aloysius et al. (2009) is that the information regarding the intent to purchase one item is used to price another item on the same shopping experience without having to identify the customer. Other studies of dynamically priced goods have been confined to single goods and do not consider cross category effects on other goods. Cope (2007) presents dynamic strategies for maximizing revenue in Internet retail by actively learning customers’ demand responses to price. Zhang and Krishnamurthi (2004) provide a decision support system of microlevel promotions in an Internet shopping environment that provides recommendations as to when, how much, and to whom to give price promotions. The system derives the optimal price promotion for each household on each shopping trip by taking into account the time-varying pattern of purchase behavior and the impact of the promotion on future purchases. There are several examples of sellers using customer behavior to infer preferences and using that information either to drive revenues or for customer relationship management. Montgomery et al. (2004) show how clickstream data about the sequence of pages or path navigated by web buyers can be used to infer users’ goals and future path. There is a literature on behavior-based price discrimination in which firms use information about consumers’ previous purchases to offer different prices and/or products to consumers with different purchase histories (for a survey, see Fudenberg and Villas-Boas, 2006). Empirical data show that even the information contained in observing one historic purchase occasion by a customer boosts net target couponing revenue by 50% (Rossi et al., 1996). Better ability to predict preferences has been shown to potentially reduce price competition (Chen et al., 2001). Acquisti and Varian (2005) show analytically that it is optimal to price so as to distinguish between high-value and low-value customers. There is empirical evidence that competing firms have been able to price discriminate profitably by charging different prices across consumer segments (Basenko et al., 2003). Moon and Russell (2008) develop a product recommendation model based on the principle that customer preference similarity stemming from prior purchase behavior is a key element in predicting current purchase. These studies exploit customer revealed preference for a good in order to set prices for future purchases of that good. 3. A Model of Competition The previous work of Aloysius et al. (2009) and Venkatesh and Kamakura (2003) addresses bundling and sequential pricing for monopolies respectively. In this section, we extend the analysis to examine these pricing strategies in a more realistic setting with imperfect competition. To introduce competition into multiple product markets, we follow Varian’s (1980) model of informed and uninformed buyers. We assume that a fraction 1 a of the customers are fully informed of all competitor prices. These comparison shoppers can be
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thought of as those people that seek out price information, say by looking at advertisements in print media or by using pricebots or other online price comparison tools. The remaining customers visit a single seller. These loyal buyers may be considered to have an idiosyncratic preference for a given seller, high search or travel costs, and so on. Each of the n firms acts as a monopolist to the a /n customers who are loyal to that seller, but the seller is unable to determine which customers comparison shop and which do not. The problem faced by an uninformed potential customer with values vA, i vB, vAB who observes simultaneously the prices of PAi , PBi , and PAB from seller i is straightforward. The customer will purchase the bundle AB if i vAB PAB maxð0; vA PAi ; vB PBi Þ. Similar conditions hold for purchasing items A and B separately. A buyer who can obtain a non-negative surplus from making a purchase will not buy anything and earn 0. The problem faced by an informed customer is more complex. The informed customer will purchase the bundle AB from seller i if j i vAB PAB [maxð0; vA PAi ; vB PBi ; vA PAj ; vB PBj ; vAB PAB Þ8 j 6¼ i, with similar conditions holding for purchasing item A only or item B only. Any tie between sellers is assumed to be broken randomly. Therefore an informed buyer makes the best decision from the 3n + 1 choices and cannot create a bundle by purchasing components from different sellers.7,8 Let Pm denote the expected profits that a monopolist would earn from setting the monopoly prices. Since a firm could simply act as a monopolist to its loyal, uninformed customers, any competitor can guarantee itself a security profit of a Pm/n. We first note that there are no pure strategy equilibria nor are there any mass points in the symmetric mixing distribution because the probability of a tie would lead some seller to cut its price or revert to monopoly pricing. Any strategy in the support of the mixed strategy equilibrium must generate the same expected payoff, which we denote by P⁄ where P⁄ P a Pm/n. If every strategy generates P⁄ by definition of a mixed strategy, then the expected value of the entire game will also be P⁄. Thus the joint distribution function gðPA ; PB ; PAB Þ that characterizes the equilibrium must satisfy: Z Z Z Z Z Z i gðPA ; PB ; PAB Þ EðjPAi ; PBi ; PAB Þ¼ gðPA ; PB ; PAB Þ ¼ : ð1Þ Venkatesh and Kamakura (2003) show that, for general h, a closed form solution does not exist in the relatively simple monopoly problem. We do note that if a = 0 then there is no competition and the equilibrium is for i m PAi ¼ PAm ; PBi ¼ PBm , and PAB ¼ PAB 8i. Of course, the monopoly prices are a function of f(vA), f(vB), cA, cB, and h. On the other hand, if a = 1 and all customi ers comparison shop, the equilibrium is PAi ¼ cA ; PBi ¼ CB and PAB ¼ cA þ cB 8i. Without directly solving for gðPA ; PB ; PAB Þ we can identify price strategies that are not in the support of the symmetric mixed strategy equilibrium. Since a seller could focus exclusively on its uninformed customers, if gðPA ; PB ; PAB Þ[0 then it must be that the strategy ðPA ; PB ; PAB Þ generates a profit of at least (a Pm/n)/(1 a + a /n) from loyal shoppers where the denominator is the probability a firm is visited by either an informed or an uninformed shopper. Any time a seller chooses a price that generates less
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profit, it is direct evidence that the seller is not playing the symmetric mixed strategy Nash equilibrium. As we will discuss in the experimental results, there is compelling evidence that subjects in fact do not play the symmetric Nash equilibrium strategy. The competitive markets with sequential pricing are similar. With or without discrimination, loyal customers visit one seller, make a good A purchase decision, and then observe a possibly conditional price for good B. That is, without sequential price discrimination, shoppers at seller j would observe PBi , but with sequential price discrimination shoppers would observe either PBi jA if vA PAi 0, as the shopper would have bought good A or PBi j:A otherwise. By contrast, comparison shoppers first observe the price of good A from each seller and then visit the seller offering the largest non-negative buyer surplus from good A (i.e., comparing vA PA across sellers and visiting the seller offering the best deal if it beats buying nothing and receiving a surplus of 0), with ties between sellers again broken randomly. Comparison shoppers who purchase good A from seller i then observe the possibly conditional good B price of that specific seller and make a purchase if it increases their buyer surplus (i.e., (1 + h)(vA + vB) PAi PBi P vA PAi for the nondiscriminatory case and (1 + h)(vA + vB) PAi PBi jA P vA PAi with discrimination). Informed customers who do not purchase good A never visit a seller and thus never have the opportunity to purchase good B. In this set up (and consistent with the bundling discussion above), customers are assumed to be shopping for good A and learn about good B during the shopping experience. In this respect, good B can be thought of as an impulse purchase, and thus sellers engaging in sequential pricing become an effective monopolist in the good B market for those customers that visit their outlet. One could assign the informed buyer who does not purchase A to a randomly selected store, but this approach is unappealing without a compelling reason why the buyer would observe the store’s Web site or go visit the physical location in such situations. We believe that this potential loss of customers is an important implication of using a sequential pricing strategy that was not apparent from previous theoretical research on monopolies, but is nonetheless a real issue for competitive firms; that is, when pricing good A, the possibility of lost customers in market B factors into the pricing decision. Again, there is no pure strategy equilibrium nor are there mass points in the symmetric mixed strategy equilibrium. As before, a seller could focus on its loyal customers and earn a profit of least a Pm/n, where Pm now denotes monopoly profit under the appropriate form of sequential pricing. The equilibrium is again characterized by an equation similar to (1), but where gðÞ is only over PA, as the good B prices are determined by PA. As before, any price strategy that does not generate an expected profit of least (a Pm/n)/(1 a + a /n) cannot be supported in equilibrium. Further, to be consistent with equilibrium behavior, it must be that the sellers are playing the optimal good B price response(s) to the chosen PA. In the event that the firm can condition the price of good B on the purchase of good A, the optimal prices are the same here as under monopoly. When sellers cannot set conditional prices, the optimal good B price will differ from the monopoly case; this situation involves a change in the probability that a customer observing PB will have purchased good A due to the existence of comparison shoppers. Ultimately, there is once again
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compelling evidence that subjects do not play the symmetric mixed strategy Nash equilibrium. As with bundling, one can construct the theoretical benchmarks for the case of no comparison shoppers (a = 0) and only informed buyers (a = 1). When there is no competition then the equilibrium is for PAi ¼ PAm ; PBi ¼ PBm m without discrimination and PAi ¼ PAm ; PBi j:A ¼ PBjA , and PBi jA ¼ PBmjA 8i. Again, the monopoly prices are a function of f(vA),f(vB), cA, cB, and h. On the other hand, if a = 1 and all customers comparison shop, the equilibrium is PAi cA 8i and the price of good B would be a function of f(vA), f(vB), cA, cB, and h, assuming that firms are not allowed to price below cost. 4. Experimental Design To explore the impact of bundling and sequential pricing in competitive markets, a total of 36 laboratory sessions were conducted. The sessions consist of four replicates of each of the nine treatments in a 3 3 between subjects design. The first factor of the design is the relationship between two experimental goods, A and B. In the “independent values” condition, the buyer’s values for the two goods are independent and the value of the bundle made from purchasing both goods is the sum of the values of the separate items (i.e., h = 0). Specifically, vA U[0,100] and vB U[0,100] in the independent values case. For the “complements” condition, the single item values are the same as in the previous case but the value from buying both items is 1.3 (vA + vB), that is h = 0.3. The third condition involves positively “correlated values,” wherevA and vB are jointly distributed according to the density func1 c 6 50 c 7651 for vA, vB integers [0,100]. For this distion f(vA,vB) = if jvA vB j else 0 tribution, the correlation is q = 0.5.9 Bundle values are additive in the correlated values condition (i.e., h = 0). This distribution is admittedly arbitrary, as is the uniform distribution; however, this distribution has the advantage of being easy to describe to subject sellers.10 The second factor in the experimental design was the pricing strategy available to the sellers. In the “Bundling” condition, seller i could post PA, PB, and PAB for good A alone, good B alone, and the bundle consisting of goods A and B respectively. Notice that sellers could engage in pure bundle pricing by setting PAB 6 PA, PB, and could engage in pure components pricing by setting PAB = PA + PB. In the “Sequential Pricing with Discrimination” condition, sellers could post PA for good A and PB|A and PBj:A for good B depending on whether or not the buyer purchased good A. In the “Sequential Pricing without Discrimination” condition sellers could post PA and PB for goods A and B respectively. Note that sequential pricing without discrimination is not the same as pure components pricing because while the seller does not observe behavior, the buyer will not observe the price of B at the time the decision is being made to purchase good A. This timing difference for buyers generates different pricing strategies for sellers. For simplicity, the marginal cost of producing both types of goods was cA = cB = 0, and therefore profit and revenue are identical. Given the parameters and assumed distributions for buyer values the theoretical benchmarks discussed in the previous section are as follows. With mixed bundling a monopolist would charge PAM = PBM ¼ 67, 83, 52, and
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M PAB ¼ 87, 109, 88 for the cases of independent values, complements, and correlated values respectively. A perfectly competitive firm facing only informed customers would charge PA = PB = 0 and PAB = 0. A monopolist that engaged in sequential pricing without discrimination would charge PAM ¼ 50; 43; 45 and PBM ¼ 50; 63; 45 in the cases of independent values, complements, and correlated values respectively, while a firm facing only informed customers would charge PA = 0 and PB = 50, 72.5, 45 in those respective settings. Monopolists that engaged in sequential pricing with discrimination would charge PAM ¼ 50; 44; 45, PAMjB ¼ 50; 76; 50 and PBMj:A ¼ 50; 50; 36 in the cases of independent values, complements, and correlated values respectively. The firm facing only informed customers would charge PA = 0 and PB|A = 50, 72.5, 45 in the cases of independent values, complements, and correlated values respectively. At a price of PA = 0, every customer buys good A and thus no one observes PB|A, which could be anything in equilibrium. Each session involved n = 4 seller subjects posting prices for 750 paid market periods.11 In each period, a new buyer would visit the market having drawn a realized value pair (vA, vB) from the appropriate distribution and make a purchase decision. Since buyers make one purchase decision, there is no incentive for them not to reveal their willingness to buy truthfully. Therefore, the buyer role was automated, a common practice in posted offer market experiments where demand withholding is not a critical element of the design (see Davis and Holt, 1993). With this buyer automation, each period lasted only three seconds. The use of nearly continuous posted offer markets provides considerable seller experience and “improve[s] the drawing power of underlying equilibrium predictions” (Davis and Korenok, 2009, p. 465).12 Our choice of n is somewhat arbitrary; however, previous experimental work has suggested that four firms are sufficient to avoid collusion (see Holt, 1995, p. 407). Following Varian (1980), the markets consist of two types of buyers. Loyal (or uninformed) customers account for a = 80% of the market, so each seller served as a monopolist to a /n = 20% of the market. Comparison (or informed) shoppers account for 1 a = 20% of the market. A buyer’s type is independent of its (vA, vB) realization. Therefore, conditional on a particular seller being visited, there is a 50% chance that the seller is in direct competition for a comparison shopper. Thus, as described in the previous section, no subject seller should select a set of prices that generate less than Pm/2. With the optimal monopoly prices (discussed above) and the resulting profits for each treatment,
Table 1. Security profits by treatment Pricing strategy
Value relationship
Bundling
Independent values Positive correlation Complements Independent values Positive correlation Complements Independent values Positive correlation Complements
Sequential pricing without discrimination
Sequential pricing with discrimination
q
h
0 0.5 0 0 0.5 0 0 0.5 0
0 0 0.3 0 0 0.3 0 0 0.3
Security profit = Pm/2 27.6 26.2 35.4 25.1 25.6 29.5 25.1 25.9 30.2
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it is straightforward to calculate the security profits, which are presented in Table 1. While the profit differences in Table 1 are not nominally large, these profits are per period expected profits, and our sellers are competing for 750 periods. Subject sellers could adjust their prices at any point during the experiment and received feedback about the prices charged and profit earned by each rival after every period. During the experiment, subjects had an onscreen tool that would identify which potential uninformed customers would buy each good and the expected profit based upon a subject specified pricing strategy.13 Value combinations that would lead to purchases of good A only were shaded in yellow, while value combinations that would lead to the purchase of good B only were in blue. Value combinations such that the person would buy both A and B were shaded green. Combinations for which the person would not buy anything were white and areas shaded black could not occur given the distribution of values. Subjects were recruited from undergraduate courses at a state university. While many of the participants were in the business school, students from other disciplines participated as well. The students were recruited directly from classes and through the laboratory’s subject database. Some of the subjects had prior experience in experiments; however, none had previously participated in any related experiments. Each laboratory session lasted 90 minutes, including approximately 30 minutes for the self-paced written directions and the completion of a comprehension handout.14 After completing the handout, responses were checked by an experimenter and any remaining questions were answered. Once all of the participants were ready, the actual experiment began. At the conclusion of the experiment, subjects were paid based upon their earned profit at the rate $400 in profit = US $1. The average salient payment was approximately $18.00. Participants also received a fixed payment of $7.50 for arriving on time and participating in the study. Subjects were paid in private and were dismissed from the experiment once they had collected their money. Multiple sessions occurred concurrently in the laboratory to prevent subjects from being able to identify which other participants were sellers in the same market. 5. Experimental Results The analyzed data consist of 72,000 market pricing decisions.15 Of course, observations from the same subject or even from the same session are not independent. Therefore, linear mixed effects models are utilized to control for the repeated measures present in the data at the period level. Non-parametric permutations tests are utilized for comparisons at the session level, since each session is independent. We first note that all of our competitive markets generate greater consumer surplus and lower profits than under monopoly. It is not surprising that by introducing competition into these environments, surplus is redistributed from sellers to buyers. However, in this setting there are only four sellers and 80% of customers are loyal, leaving only 20% of the population of consumer over which to compete. Even with such a small degree of competition, these pricing strategies do not seem to insulate the sellers from competitive pressures. We
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see this very clearly in the sequential pricing game where sellers dramatically lower the price of good A in order to be able to compete in the good B market. Below we analyze each pricing strategy, but it is important to note that one of the main contributions here is to adapt these strategies to a competitive environment. In so doing, it is clear that these seller strategies do not seem to harm consumers by protecting sellers from the effects of even a small level of competition. The next question is how bundling and sequential pricing compare. The results are discussed in separate subsections for each value relationship (independently valued goods, positively correlated goods, and complementary goods). Within each subsection, we report a series of results. First we compare the seller profit, buyer surplus, and overall efficiency across pricing strategies.16 Next we summarize the pricing decisions for each pricing strategy. Given the structural differences between sequential pricing and bundling, we evaluate bundling separately, but we do compare the other two strategies directly to evaluate the effect of discrimination. We do not make comparisons across environments because the total surplus available differs and this relationship is not a choice variable for sellers. The final subsection discusses the consistency of behavior with the symmetric Nash equilibrium mixed strategy. 5.1. The Case of Independently Valued Goods Figure 1 shows the average realized seller profit and buyer surplus by session for each of the pricing strategies, while Figure 2 shows the distribution of prices for each pricing strategy. Table 2 provides the average seller profit, buyer surplus, and efficiency by pricing strategy and the results of permutation tests for comparing the welfare measures across pricing strategies. Based upon the permutations test, seller profit is significantly greater (p = 0.043) with bundling (average profit of 39.0) than with sequential pricing without discrimination (average profit of 30.7), but does not differ between bundling and sequential pricing with discrimination or between sequential pricing with and without discrimination despite the fact that security profits are 10% greater under bundling than either sequential pricing strategy. The statistical results also indicate no significant difference between pricing strategies with respect to either buyer surplus or efficiency. The lack of an effect on efficiency between bundling and sequential pricing without discrimination is due to the fact that the significant changes in seller profit are being offset by the more variable changes in buyer surplus. Sellers in the bundling treatment could engage in mixed bundling, pure components, or pure bundling. Overwhelmingly, they engaged in mixed bundling (83% of observations) and rarely engaged in pure component pricing (3% of observations). Given the symmetry of the market, it is reasonable to expect that sellers in the bundling treatment would set PA = PB, and in fact this is what was observed.17 Therefore, we combine the single item prices in the left portion of Figure 2 and in reporting that the average single item price was 39.9, while the average price for a bundle was 55.3. The 31% = 1 – 55.3/(2 39.9) bundle discount is similar to the 35% offered under monopoly. These prices represent the typical price that a loyal uninformed customer would observe. For comparison shoppers, the average minimum single item price fell to 27.6 and the lowest bundle price fell to 37.0 (a bundling discount of 33%).
Comparison of Bundling and Sequential Pricing in Competitive Markets Seller Profit
Buyer Surplus
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Monopoly Profit
125 100 75 50 25 0
a. Bundling 125 100 75 50 25 0
b. Sequential Pricing with Discrimination 125 100 75 50 25 0
c. Sequential Pricing without Discrimination
Figure 1. Profit and buyer surplus by session with independent values. For both sequential pricing conditions, good A prices tend to be much lower than good B prices, as sellers are competing for customers via good A prices (see Figure 2). There is also evidence of subjects using a leader pricing strategy, as a substantial proportion of sellers (regardless of whether or not they could price discriminate) priced at or close to marginal cost.18 In this environment of independently valued goods, the ability to price discriminate should not be exercised when sellers are engaging in sequential pricing, as the purchase of good A reveals no information to the seller about the buyer’s marginal value of subsequently purchasing good B. In fact, given the structure of
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J. Aloysius et al. Single Item Price Bundle Price
0.5
0.4
0.3
0.2
0.1
0 0-10
11-20
21-30
31-40
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a. Bundling 0.5
0.4
Price of Good A Price of Good B without A Price of Good B with A
0.3 0.2 0.1 0
0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90+
b. Sequential Pricing with Discrimination 0.5
Price of Good A
0.4
Price of Good B
0.3 0.2 0.1
0 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90+
c. Sequential Pricing without Discrimination
Figure 2. Distribution of prices by pricing strategy with independent values.
the buyer values, sequential sellers should charge 50 for good B (i.e., PB|A = PB|A = 50 with discrimination and PB = 50 without discrimination). Because of this result, there is no reason for the price of good A to differ based upon whether or not sellers could subsequently discriminate. The average price of good A is only 18 when sellers cannot base the price of good B on the good A purchase decision as reported in Table 3. This amount increases to 21.6 = 18 + 3.6 when sellers do have the ability to set conditional prices for good B, but as predicted this difference is not significant
Comparison of Bundling and Sequential Pricing in Competitive Markets
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Table 2. Welfare effects for goods with independent values Average across sessions Seller profit
Pricing strategy
Buyer surplus
Efficiency
Bundling 39.0 52.8 Sequential pricing with discrimination 34.2 52.5 Sequential pricing without discrimination 30.7 59.5 p-values for permutations tests for differences between pricing strategies Comparison Seller Buyer profit surplus Bundling versus sequential pricing with discrimination 0.429 0.957 Bundling versus sequential pricing without discrimination 0.043 0.214 Sequential pricing with discrimination versus sequential pricing 0.514 0.386 without discrimination
0.85 0.79 0.84 Efficiency 0.249 0.657 0.257
Table 3. Linear mixed effects estimation of sequential pricing for goods with independent values Average good A pricei Model: PAijt = a0 + a1PDj + ei + ej + eijt Intercept Estimate t-statistic p-value
18.0 6.23
