Vertical Differentiation with Variety-seeking Consumers

Transcription

1 Vertical Differentiation with Variety-seeking Consumers Robert Zeithammer UCA Anderson School of Management Rahael Thomadsen UCA Anderson School of Management Aril, 0 Abstract We analyze rice and quality cometition in a vertically differentiated duooly in which consumers have a reference for variety. The reference for variety is a consequence of diminishing marginal utility for reeated exeriences with the same roduct. We find consumer variety-seeking can either soften or intensify rice cometition, deending on the difference in firm qualities and the strength of consumer reference for variety. When the qualities are similar (or the consumer reference for variety is strong), rices and rofits are higher than would be obtained in the absence of variety seeking. On the other hand, if qualities differ enough (or the reference for variety is weak), stronger references for variety are associated with more-intense rice cometition and lower rofits. When firms set their qualities before cometing on rice and the range of feasible qualities is restricted such that variety-seeking softens cometition, cometing firms choose to minimally differentiate themselves from each other. The reference for variety can drive the firms to offer multi-unit discounts, and the greater rice-flexibility from these discounts does not necessarily reduce rofits relative to simle unit ricing. Contact: Robert Zeithammer, UCA Anderson School of Management, 0 Westwood Plaza, os Angeles, robert.zeithammer@anderson.ucla.edu. Both authors contributed equally.

2 . Introduction In several roduct categories, consumers care about both quality and the ability to samle different exeriences over multile consumtion occasions. For examle, skiers enjoy going to multile resorts during a single tri to the mountains, even when some of the resorts are objectively better in terms of size, service, and the quality of the runs. Art lovers on a weekend tri to New York may all refer the larger Metroolitan Museum of Art when they visit town for a single day, but most would also head to another museum if they visited for two weekend days even though seeing all of the art in the Met in a single day is difficult. Finally, suose you win a weekend of free dinners in Paris. If you care about quality, you surely wish to visit the to-rated restaurant in the city on one of your nights, but you would robably like to try another restaurant (by definition, lower quality) on the second night rather than go to the to-rated one again. A rich literature documents variety seeking behavior and examines its antecedents (Givon 984; McAlister and Pessemier 98; Kahn, Kalwani, and Morrison 986; McAlister 98). In the exerience-good settings we consider, consumers seek variety because varied exeriences rovide stimulation and reduce boredom (Faison 977), satisfy innate human curiosity (Raju 980), and imrove retrosective evaluation of the bundle of multile exeriences (Ratner, Kahn, and Kahneman 999). Note that consumers do not somehow tire of one quality level and want to exerience another quality level. Instead, they feel a diminishing marginal utility when they consume multile identical exeriences, and choosing variety hels them avoid the diminished utility. In this aer, we examine how such consumer references for variety affect cometition between two vertically differentiated firms. In addition to a different quality level, each firm rovides a distinct exerience and roduces multile units of its roduct. Consumers buy two units in the category and vary in their willingness to ay for quality. When they consume one unit from each firm, they obtain utility in a manner that is standard in vertically differentiated models. On the other hand, if a consumer buys two units from the same firm, she exeriences less utility from the second unit than from the first because of her reference for a variety of exeriences. The diminished marginal utility increases the desirability of choosing variety, that is, buying one unit from each firm, relative to a counterfactual world without references for variety. We offer three findings about how references for variety affect rice and quality cometition between the two firms: first, the reference for variety can either intensify or soften rice cometition. Second, the reference for variety sometimes results in both firms offering the same quality. Third, the reference for variety can drive the firms to offer multi-unit discounts, but allowing both firms to use such The diminishing marginal utility can also arise from satiation on incidental features secific to the each firm s roduct (McAlister 98; Feinberg, Kahn, and McAlister 99, Trivedi et. al. 994). Villas-Boas (004) demonstrates that variety-seeking behavior could also arise from a negative switching cost..

3 discounts does not necessarily intensify rice cometition it may soften it instead. In the rest of the Introduction, we exlain the intuition behind each finding and relate it to the literature. Intuitively, one might exect a consumer reference for variety to always soften rice cometition: consider the roblem of an avid weekend skier lanning a visit to a mountain town near two cometing ski resorts that offer similar qualities. Without references for variety, the firms would be selling similar roducts, which would lead to low margins due to intense rice cometition arising from most skiers choosing the cheaer resort. owever, with a reference for variety, avid skiers will choose to ski at each of the resorts once even if one resort s rices are slightly higher than the other s. Therefore, consumer variety seeking reduces downward cometitive ressure on rices. Seetharaman and Che (009) reach a similar conclusion in a two-eriod horizontally differentiated model in which consumers exerience an additional staying cost if they consume the same good for both eriods. Our first main finding is that this intuition only works when the qualities of the two resorts are similar enough; counterintuitively, consumer references for variety can intensify rice cometition when they are dissimilar. When the quality difference between the two firms is big enough, for examle, the inferior ski resort has a much lower quality than the suerior resort because of its low elevation or diminished snowfall, the cheaer inferior resort attracts some quality-insensitive consumers for both days. In contrast to the situation with similar qualities, the avid skiers now ski at the better resort for the entire weekend, and variety seeking characterizes the behavior of consumers with an intermediate willingness to ay for quality. These intermediate consumers get enough utility from the first day at the better resort to ay for its higher quality, but the discounted utility of the second day is less than the utility they obtain from the other inferior yet cheaer resort. Each firm thus ends u cometing to sell both its first and its second units, and rice cometition becomes more intense than if consumers did not refer variety. Intuitively, cometition emerges between the first unit of the inferior firm and the second unit of the suerior firm. Because references for variety diminish the effective quality of the second suerior unit, it is less differentiated from the first unit of the inferior firm, intensifying cometition. Given the close relationshi between the amount of vertical differentiation and the effect of references for variety on rice cometition, a question arises regarding the extent to which the two resorts wish to be vertically differentiated. Should an inferior resort remain differentiated or should it imrove its quality to be more like the suerior resort? In our second main finding, we show that when the range of qualities available to firms is narrow enough, both resorts offer the same quality in equilibrium. This result contrasts with Feinberg, Kahn, and McAlister (99), who ioneered research on the sulyside imlications of consumer variety seeking and found that firms should always differentiate from each other in the sense that they should increase the value of their unique features and osition away from rivals. owever, their model is not an equilibrium model and does not consider rice cometition. Our

4 results also contrast with the basic equilibrium result in vertically differentiated markets without a taste for variety, which shows that firms differentiate themselves to soften rice cometition (Shaked and Sutton 98, Moorthy 988). The intuition behind our result is that variety seeking can soften cometition more when the two firms roducts are less differentiated, and this softening is stronger than the softening firms can obtain from differentiation. In a searate roosition, we show that the softening of rice cometition due to consumer references for variety is so strong that not only does the inferior firm benefit from increasing its quality to the suerior firm s level, but the suerior firm is better off as well. Therefore, heling the inferior firm imrove is a win-win strategy. In a comlementary aer, Sajeesh and Raju (00) examine the imact of variety seeking on location cometition in a two-eriod horizontal otelling model. They show that if a subset of consumers have a reference for variety, than equilibrium levels of roduct differentiation will be lower than the level that would be obtained without a consumer reference for variety, but not to the minimum differentiation we find. In contrast with our results, Sajeesh and Raju s model finds the resence of variety-seeking consumers always reduces rofits. Guo (006) resents another related model in a horizontally differentiated setting by examining a duooly with forward-buying consumers who are uncertain of their future references. Such consumers sometimes make multile urchases mimicking the behavior of variety seeking to remain flexible at the time of consumtion. Guo shows this behavior can also soften rice cometition. In some of the industries we consider, sellers offer multi-unit discounts. For examle, large ski resorts sell two-day tickets for less than twice the rice of a one-day ticket. In our third main finding, we show our first finding is robust to the resence of multi-unit discounts: stronger references for variety continue to soften rice cometition when qualities are similar and to intensify rice cometition when qualities are dissimilar. In both settings, at least one firm uses a discount, and the effect on rofits again deends on the extent of vertical differentiation and the strength of reference for variety.. Model We model the cometition between two firms as a two-stage game. In the first stage, the firms simultaneously select quality q from an interval of feasible qualities. In the second stage, the firms set rices simultaneously, and consumer demand is realized. We now outline the notation of our model before discussing our assumtions in detail. Firms: Two firms exist with identities j =,. Each firm rovides a distinct exerience and sets its own quality level. In the first stage, firm j selects quality q q, q, where 0 j q. The fixed cost Cq of selecting a given quality level is weakly increasing and convex in q: Cq Cq 0, 0. In the second stage, each firm j charges a rice j for each unit of its good. We assume the marginal costs of 3

5 roduction are constant across the two firms, so they can be normalized to zero without loss of generality. When the two firms select different qualities qj q j in the first stage, we label the firms (for low ) and (for high ) according to the relative magnitude of their qualities. This conflation of identity and quality into a single index will clarify our exosition of the second-stage ricing game. Consumers: Consumers have utility for u to two units of the good, and they differ in their marginal utility for quality θ: consumer tye θ is distributed across the oulation uniformly on the [0,] interval. We normalize the utility of consuming no units to be zero. When consumer θ buys only one unit of the good and chooses firm j, his utility is standard U q. When consumer θ buys two j j j units of the good, he cares about the identities of both roducts because of his reference for a variety of exeriences. If the consumer buys one unit from each firm, he obtains a utility of (when the two firms select different qualities j j U q V j j stage, the utility is U V units from firm j is q q in the first ). The indirect utility of consumer θ who buys two U q, where δ < reflects the rate at which erceived quality is j j j diminishing across units of the same firm s roduct. As is common in these tyes of models, we assume β is large enough that all consumers buy two units of the good in equilibrium. Further, because β aears additively in all two-unit utilities, we dro it from any utility calculations in the rest of the aer. Two quality ranges: As noted in the Introduction, we show consumer behavior and the intensity of rice cometition deend crucially on the relative difference between the two firms qualities and the degree of diminishing marginal utility δ. We analyze the following two regions of the (q, q, δ) arameter sace for which the rice cometition equilibrium is tractable to us: Definition : For any fixed δ, two firm qualities 0 are similar if when 8 0 7, where. 39 4, and dissimilar 4 From a consumer s ersective, similar qualities imly >δ, so the variety bundle is the highest-utility consumtion alternative: all consumers would choose to urchase one unit from each firm if the two firms charged the same rice. In contrast, dissimilar qualities imly <δ, and two units are the highest-utility consumtion alternative. Note the definition intertwines the difference in qualities with the strength of reference for variety: for examle, an alternative interretation of similar qualities is that the reference for variety needs to be strong enough for a given fixed air of qualities. 4

6 aving outlined the model, we now discuss its key assumtions. The main dearture from standard models of vertical differentiation (Shaked and Sutton 98, Moorthy 988) is the diminishing marginal utility for multile units of the same firm s roduct (δ<) that catures a reference for variety described in the Introduction. We further assume the reference for variety is roortional to the reference for quality (θ), consistent with the notion that connoisseurs exerience a greater taste for variety comared to casual users. That is, we exect ski enthusiasts to value skiing at different resorts more than casual skiers, and for foodies to lace the highest value on trying new restaurants. The main dearture from revious models of cometition with a consumer reference for variety is our focus on vertically differentiated firms and their inherent asymmetry. Our model thus alies in markets in which consumers care more about quality and novelty than about other attributes. In articular, consumers care more about having a variety of exeriences than about which articular exerience they have. For examle, two ski resorts may have different scenic views in addition to different overall qualities, but the skiers care much more about quality and seeing a variety of views than about looking at one view versus the other. This concetualization of variety-seeking is consistent with the concetualization of the need for trying new exeriences to combat boredom or to satisfy curiosity, ala Faison (977) or Raju (980). Another dearture from revious models of cometition with a consumer reference for variety (Seetharaman and Che 009, Sajeesh and Raju 00) is that we abstract from dynamic considerations and examine a static model in which the rice of the first unit is the same as the rice of the second unit. This assumtion acknowledges menu costs and the fact that in the industries we consider ski resorts, amusement arks, and restaurants rices do not tend to vary on a consumtion-exerience basis within the time frames we consider, such as a weekend. One can also think of our consumers as lanning and urchasing both units of the good ahead of the actual exeriences as in Guo (006).. Consumer behavior Suose the two firms offer different qualities qj q j. We assume market coverage, so consumers have three urchase choices: units of, units of, or one of each, which we call variety. We denote the utilities from these choices as U, U and U V, resectively. The following inequalities determine the otimal decision of a consumer θ: UV U () Many of our results continue to hold when we consider a constant additive disutility from reeated urchases instead. In articular, firms would still earn ositive rofits if they both offered identical qualities, and the rofits increase with a stronger reference for variety. Please contact the authors for details. 5

7 U U () The U V vs. U comarison deends on whether >δ or <δ. We discuss the two cases in turn. When and are similar (Definition ) then >δ, and the utility comarison becomes UV U (3S) Figure rovides an illustration of consumer behavior. When and are similar, high-θ consumers choose variety, whereas the rest of the consumers buy two units of the cheaer good. To understand this attern, note that when the suerior good is cheaer ( < ), no one buys two low-quality units, and consumers choose between variety and two high-quality units. On the other hand, when the suerior good is more exensive ( > ), no one buys two units of it: whoever refers {, δ} to {, δ} will also refer the variety bundle {, } to {, δ} because it gives more quality (>δ) for less money ( + < ). Therefore, > makes the consumers choose between variety and buying two low-quality units. Figure : Consumer behavior similar qualities different qualities > > θ buy variety ( and ) buy x (cheaer) buy variety ( and ) buy x (cheaer) buy x buy variety ( and ) buy x buy x Note that equal rices ( = ) make all consumers choose variety under similar qualities, so consumer behavior transitions continuously from one ordering of rices to the other. In other words, the demand functions of both firms are continuous at =, but the sloes of the demand functions change at that oint. Also note that if the differences in rices are high enough, consumers will only urchase the cheaer roduct, and the more exensive roduct can be foreclosed out of the market. Now consider the U V vs. U comarison when and are dissimilar: 6

8 UV U (3D) Figure (right side) illustrates consumer behavior under dissimilar qualities. Comaring equation (3S) with equation (3D), we see that the variety bundle {,} is the highest-quality consumtion alternative in similar-quality scenarios, so variety seeking behavior occurs at the to; that is, the consumers with high value on quality (θ) choose variety. In dissimilar quality settings, the variety bundle {, } is inferior to buying two units of (because < δ), so the consumers with high θ buy two units. Variety seeking behavior instead emerges in the middle of the θ sectrum because the variety bundle becomes a middlequality otion with a mid-level rice. 3 Therefore, unlike in the case of similar qualities, dissimilar qualities allow all three consumtion choices to occur at a given set of rices. To comlete the descrition of consumer behavior, we note that the similar qualities case with ==q catures the behavior when both firms offer the same quality q. In such a case, high-θ consumers still choose variety, whereas low-θ consumers buy two units of the cheaer good; if both firms charge equal rices, all consumers urchase one unit from each firm.. Price cometition We first show that when the two firms have similar qualities (er Definition ), both firms rofit more than they would in the absence of a consumer reference for variety (δ =), and rofits for both firms increase with the consumer reference for variety (i.e., as δ decreases). We then show the oosite result occurs under dissimilar qualities: both firms rofit less than they would without a consumer reference for variety, and rofits of both firms decrease as δ decreases. Price cometition with similar qualities When the two firms have similar but not equal qualities ( ), no ure-strategy ricing equilibrium exists because the high-quality firm s demand curve is kinked the wrong way at = : the sloe of its demand curve is steeer when > than when <. The kink results from a switch in the tye of indifferent customer at = : when >, the indifferent consumer is deciding between variety and two units of the (cheaer) low-quality good. owever, when <, the indifferent consumer is deciding between variety and two units of the (cheaer) high-quality good. One result of this kink is that the high firm wants to undercut high and overshoot low, destroying the ossibility of a ure-strategy equilibrium. More details are available from the authors. Although no ure-strategy equilibrium exists, the game does have a tractable mixed-strategy equilibrium: 3 This assumes that the inferior good is cheaer, as it will be in equilibrium. When <, all (), (), and (3D) thresholds are negative, so all consumers consume two units of the high-quality good. This cannot occur in equilibrium because the low-quality firm can rofitably deviate by lowering its rice. 7

9 Proosition (Price cometition with similar qualities): When the firms have similar qualities, an equilibrium exists in which the low-quality firm sets a rice of and the highquality firm lays a mixed-strategy, ricing at Pr UP, and DOWN UP with robability UP with robability Pr Firm rofits are increase as δ decreases (i.e., as reference for variety increases)... Profits of both firms The roofs of all roositions aear in the aendix. The intuition behind Proosition is that, which is between and, makes the high-quality firm indifferent between undercutting and overshooting. The low-quality firm s demand in the face of a UP high-quality firm mixing between two oints is concave, and Pr is set such that is the low-quality firm s best resonse to the high firm s mixed strategy. such a case, Proosition also covers cometition between two firms that offer equal qualities ( = = q). In UP DOWN and the game has a ure-strategy equilibrium. The ure-strategy equilibrium is ossible because equalizing the firm qualities removes the kinks in the demand functions. Profits and rices are continuous as aroaches because the ure-strategy equilibrium is the limit of the equilibrium in Proosition. The equal-quality case clearly demonstrates how the consumer references soften rice cometition: in the absence of tastes for variety (δ =), the firms earn zero rofits when they offer identical roducts. When consumers have a taste for variety, the firms earn ositive rofits and these rofits increase as δ decreases. We summarize the equal-quality results in a corollary: Corollary: When ==q, a ure-strategy equilibrium exists such that q q. The equilibrium of Proosition has intuitive comarative statics: the high firm earns greater equilibrium rofits than the low firm and is more likely to overshoot than undercut the low firm s ure strategy. Also, greater references for variety increase both firms rofits. Intuitively, the reference for variety softens cometition by ensuring a higher-riced firm gets ositive demand if rice differences are small enough. As we will see below, this intuition only holds when the firms offer similar qualities. q 8

10 Price cometition with dissimilar qualities When the two firm qualities are dissimilar in the sense of Definition, a ure-strategy ricing equilibrium exists with the low-quality firm charging less than the high-quality firm: Proosition (Price cometition with dissimilar qualities): When the firms select dissimilar qualities <, a unique ure-strategy Nash equilibrium exists with Firm rofits are 9 9 Profits of both firms decrease as δ decreases (i.e., as reference for variety increases). and. The comutations behind the equilibrium in Proosition are standard, and the equilibrium ossesses many of the standard roerties of rice-cometition equilibria in vertically differentiated markets as originally described by Shaked and Sutton (98): the high-quality firm charges a higher rice and earns higher rofits than the low-quality firm, and rofits for both firms increase as the amount of vertical differentiation increases. The arallel is more than qualitative the rofit functions resented in Proosition reduce to (twice, for two units) the rofit functions from Shaked and Sutton when δ =. In contrast with the similar-qualities case, consumer references for variety intensify the rice cometition here. This contrast is a result of variety seeking behavior shifting from the to to the middle of the θ sectrum: because the variety bundle is a middle-quality otion under dissimilar qualities, the firms have to comete for two sets of marginal consumers: high θ consumers decide between variety and two units, and low θ consumers decide between variety and two units. In other words, the firms comete intensely to sell the consumer the second unit, and each firm s second unit effectively cometes with the cometitor s first unit. The crucial match-u is between the second suerior unit that delivers δ erceived quality and the first inferior unit that delivers. Note that the smaller the δ (i.e., the stronger reference for variety is), the less differentiated these two units are, and so rice cometition intensifies. 9

11 .3 Equilibrium quality choice aving analyzed the rice cometition in the second stage, we now solve the first stage of the game where firms choose qualities. We focus most on the case where qualities are constrained to be similar. 4 We then briefly discuss what haens under dissimilar qualities. Proosition 3 (Quality cometition equilibrium with similar qualities): Suose the range of feasible qualities qj q, q is restricted to similar qualities; that is, 4 q q. Then a unique ure-strategy 4 first-stage equilibrium exists in which both firms select the same quality min qq,, where q is either the lower bound q when C q or the quality level above q, where Cq., A crucial comonent of the forces behind Proosition 3 is that when < and C the low-quality firm wants to increase its quality to at least that of the high-quality firm. Similarly, each firm wants to raise its quality level if both firms have equal qualities qq q, as long as C q. Therefore, the qualities of both firms rise as they best resond to each other, until they reach the oint at which Cq, unless this value of q falls outside the feasible range. In equilibrium, the firms will always choose the same quality, leading to minimum differentiation. Proosition 3 contrasts with the basic result in vertically differentiated markets without a taste for variety, where Shaked and Sutton (98) and Moorthy (988) show firms want to differentiate themselves to soften rice cometition. Our result is in the same direction as the findings of Sajeesh and Raju (00), who find references for variety reduce the equilibrium level of roduct differentiation in a horizontaldifferentiation model, although they do not find minimum differentiation as we do. Under Sajeesh and Raju s model, margins for each firm shrink to zero under minimum differentiation, so the underlying mechanics driving the results are different in the two settings, and variety seeking aears to soften location cometition more in vertical settings than in horizontal ones. The intuition behind Proosition 3 is that references for variety soften rice cometition the most when the firms have the same qualities, because each firm easily sells one unit to every consumer, but a unilateral rice-reduction does not convince many consumers to urchase a second unit. As the quality of the inferior firm decreases, the suerior firm has more success selling some consumers a second unit, and so rice cometition intensifies. Comaring our results with the monooly benchmark with zero 4 Restricting the range of feasible qualities is often realistic because of technology or legal constraints. For examle, health standards set a minimum allowable quality level of restaurants. In resort industries, natural conditions such as snowfall or sunshine fix a large comonent of the quality, often restricting nearby resorts to offer similar qualities. 0

12 marginal costs further clarifies the intuition by showing that minimum differentiation arises from equilibrium considerations rather than from the structure of demand. In the Aendix, we show the monoolist selects maximally different qualities to rice discriminate. In contrast, two cometing firms benefit more from creating increased consumer value. Therefore, the equilibrium of Proosition 3 is a result of active rice cometition; the two firms do not somehow imlement the monooly strategy and slit the rofits. Proosition 3 aears to be consistent with an intuition that the references for variety create an additional dimension of differentiation for the second units, and it is the additional differentiation that allows both firms to make rofits with equal qualities. This intuition is valid in broad terms, but the relationshi between vertical differentiation and the strength of variety-seeking is more subtle than a relationshi between two generic dimensions of differentiation. Secifically, the references for variety only mimic additional differentiation when the two roducts have similar qualities. When the roducts have different qualities, the references for variety reduce the effective vertical differentiation because stronger references for variety make the second suerior unit more similar to the first inferior unit it cometes with in the market. Thus, the extent to which references for variety mimic differentiation along another dimension deends on the level of differentiation between the firms. Proosition 3 relies on the low-quality firm making more money as it increases its quality u to the high-quality firm s level. The reduction in rice cometition from bringing the firm qualities closer together is so strong that even the higher-quality firm benefits as aroaches : Proosition 4 (Imroving the weaker cometitor is win-win): When two firms have similar, but not equal, qualities, the higher-quality firm benefits from an increase in the lower-quality firm s quality. The roof of Proosition 4 is simle: 4 0. Thus, both firms are better off under minimum differentiation. In other words, both firms roviding an equal level of quality is not just an equilibrium outcome but also a win-win scenario for both firms. We summarize the rofits from Proositions, 3, and 4 with C=0 and q (so both firms choose quality q in equilibrium) in Figure. Both firms earn the greatest rofits under minimum differentiation, and the rofits decrease as the reference for variety decreases (i.e., as δ increases). We now briefly consider the case where the two firms have dissimilar qualities. In such a situation, rofits increase for both firms with greater levels of differentiation (at least in a local sense); that is, rofits for both firms are higher as the quality of is higher or the quality of is lower. The reasons for the contrast between the results under similar qualities and the results under differentiated

13 qualities is that if the roducts start out differentiated enough that middle-θ consumers choose variety then differentiating further increases the amount of differentiation between the second unit of and the first unit of, leading to softer cometition. In contrast, under similar qualities, greater quality differences lead to lower differentiation between a second unit of and a first unit of. Note that we limit our analysis to two restricted sets of feasible qualities from Definition because an intermediate (greater than similar, but smaller than dissimilar) range of relative qualities 4, 4 exists with no ure-strategy ricing equilibria, and no mixed strategy equilibria are tractable to us. We hoe that future work can address this ga in our analysis, and we conjecture that rice cometition is so intense in the intermediate region that endogenous equilibrium qualities never end u there. Based on this conjecture, it makes sense to ask whether rofits are higher under minimum versus maximum vertical differentiation. Comaring the rofits from minimum vs. maximum differentiation, we find that the low-quality firm refers minimum differentiation to maximum differentiation when δ is low enough (customers have a strong-enough reference for variety seeking). Figure : Equilibrium rofits under similar qualities Π : Π : rofit ( Π ) δ=0. δ=0.3 δ=0.5 δ=0.7 quality of the low-quality firm () δ=0.9 q Note to Figure: Each line shows the relationshi between the low firm s quality (conditional on = q ) and rofits for different δ. Each line starts at the lowest ossible under Definition of similar qualities.

14 3. Extension: Volume Discounts In some of the industries we consider, some sellers offer multi-unit discounts. For examle, large ski resorts often sell two-day tickets for less than twice the rice of a one-day ticket. We examine the imact of volume discounts on the intensity of rice cometition for two quality configurations: = = q (identical qualities) and < δ (dissimilar qualities). Our first main finding is robust to volume discounts: stronger references for variety continue to soften cometition when qualities are identical and intensify rice cometition when qualities are dissimilar. We also comare the rofits under volume discounting to rofits under unit ricing, and we find another dichotomy: volume discounting intensifies rice cometition when qualities are identical, but it softens it when qualities are dissimilar. Suose the firms can discount the second unit, and let the discounted rice of two units from firm j be (+λ j ) j for some 0. The utility comarisons of equations () and () change to: j V U U (λ) U U Consider first what haens in the similar-qualities case. Equation (3S) changes to V U U (3Sλ) The consumer behavior is analogous to the similar-qualities unit-ricing situation illustrated in Figure, with high-θ customers choosing variety. No ure-strategy equilibria exist under similar qualities, and no tractable mixed-strategy equilibria exist when is slightly less than. In the identical-quality case (relevant because it is the equilibrium configuration under unit ricing; see Proosition 3), we find a tractable symmetric mixed-strategy equilibrium: (λ) Proosition 5: When the firms offer identical qualities ( = = q) and each firm can offer a volume discount 0, a symmetric mixed-strategy Nash equilibrium exists in which both firms include the j second unit for free with the first unit (λ j = 0). Each firm draws its two-unit rice from the distribution with a c.d.f. of F exected rofits are q 4 q q on the suort 4 q q,, and each firm s 4 4, which is less than the equilibrium rofit under unit ricing. The roof roceeds by first solving the game between two firms restricted to including the second unit for free with the first unit. We then consider a deviation to any smaller second-unit discount by one 3

15 of the firms, and show such a deviation cannot be rofitable. Intuitively, given a fixed effective two-unit rice of, the second-unit discount becomes a transfer to variety seekers who have a high i i willingness to ay, but only for the first unit from each firm. Thus, the best resonse to an oonent who offers the second unit for free with the first unit is to follow suit. Both firms thus resort to ure bundling in equilibrium desite having the freedom to use a fully non-linear ricing schedule. Comaring rofits between Proositions and 5, volume discounting clearly reduces rofits (by a factor of four). owever, as in Proosition, rofits of both firms increase as δ decreases (i.e., as reference for variety increases). Therefore, the effect of the strength of reference for variety on rice cometition we found in Proosition is robust to the resence of multi-unit discounts in the case of equal qualities. Moreover, the fact that rofits remain ositive means the reference for variety continues to soften rice cometition even when the firms can use volume discounts: if consumers instead cared only about quality and the firms offered roducts with identical qualities, Bertrand rice cometition would wie out all rofits. When qualities are exogenously set at dissimilar levels, the analysis simlifies because a urestrategy equilibrium exists. From a consumer-behavior ersective, the only change from section is the cutoff between buying variety and buying two units: UV U (3Dλ) As in the roof of Proosition 5, we show firms that can set any multi-unit discounts obtain the same equilibrium rofits as they would if they were restricted to include the second unit for free with the first unit (even though only the high-quality firm actually discounts in equilibrium). Unlike in the equalquality case, discounting softens cometition here: Proosition 6: When the two firms offer dissimilar qualities and each firm can set a volume discount 0 j, an equilibrium exists in which charges 6 for each unit (λ =) and offers the second unit for free with the first unit (λ =0), for which it charges 3. The equilibrium rofits are Each firm s rofit exceeds its rofit under unit ricing No consumers choose variety in the equilibrium because λ =0 and any customer who has bought two high-quality units will never buy any low-quality roducts (, so buying even one unit of would involve an exense without any incremental benefit). Therefore, the cometition over two-unit 4

16 bundles j 0 is akin to a standard unit-demand duooly with the difference in roduct qualities being the difference between the utilities of the two bundles,. When the firms can use any volume discounts, some consumers choose variety if λ > 0, but we show the high-quality firm always wants to engage in ure bundling to get rid of variety-seeking behavior. The low firm, on the other hand, weakly refers unit ricing: when the high firm lays its equilibrium strategy, only the total rice of the low-quality bundle matters, but λ > 0 makes the full-rice cometition for the second unit less intense than the discounted λ cometition for the first unit. Since λ =0 in equilibrium, both firms make the same rofits they would earn if they were both restricted to offering ure bundles (λ j =0). Unlike in Proosition 5, allowing the firms to use multi-unit discounts softens cometition relative to simle unit ricing. Intuitively, discounting is less cometitive with dissimilar qualities because no consumers choose variety in equilibrium and the rice cometition evolves as if the sellers were selling vertically differentiated roducts with a single marginal customer in the middle. Although the level of rofit changes comared to those in Proosition, rofits of both firms decrease as δ decreases (i.e., as reference for variety increases). Therefore, the direction the reference for variety has on rice cometition in Proosition is robust to the resence of multi-unit discounts. 4. Discussion In a vertically differentiated duooly, consumer reference for variety can have substantial effects on three managerially imortant outcomes: rice cometition, quality cometition, and the rofitability of discounting. We find that the direction of all three effects deends closely on whether two units of the suerior-firm roduct deliver more or less utility than a variety bundle (i.e., one unit from each firm). When the firm qualities are similar enough and/or the reference for variety is strong enough that the variety bundle rovides the highest consumtion utility, consumer references for variety soften rice cometition (and increase rofits). The reduction in rice cometition is so strong that ufront quality cometition results in both firms choosing identical qualities. The quality cometition result runs counter to the rincile of vertical differentiation established by Shaked and Sutton (98) and Moorthy (988). The intuition for our result is that when firms roduce roducts of the same quality, they find it difficult to sell many customers a second unit of the good without steely decreasing their rices, so they choose not to target that market. We therefore redict co-located cometitors in exerience goods with strong customer references for variety, such as restaurants or resorts, are more likely to offer similar qualities than those in markets in which customers do not have references for variety. For examle, imagine two restaurants in an isolated city where tourists often send a weekend. Variety seeking is strong in the restaurant industry in that tourists would rather visit two restaurants than the same restaurant twice, so we 5

17 would exect the restaurants to offer identical qualities. Consider instead the market for motel rooms in the same city. Consumers do not value variety as much in that industry, so we would exect firms to offer different qualities, as in Mazzeo (00). Note the result that firms want minimum differentiation (if the scoe of differentiation is limited enough) is not roagated urely through firms choosing to increase their qualities; the high-quality firm is better off if the lower-quality firm chooses a higher quality rather than a lower quality. In other words, the suerior firm would be willing to exend resources to imrove its rival s roducts. In the restaurant examle, suose one of the two chefs is excellent and the other is also very good, but not as great. Our model demonstrates that the excellent chef has an incentive to hel the weaker chef become a better cook, as long as the weaker chef has a similar-enough initial quality. In the resulting equilibrium, the restaurants offer the same quality, charge the same rice, and all consumers choose variety. When qualities are not only similar but actually identical, the consumer reference for variety gives both firms an incentive to use buy-one-get-one-free discounts. Allowing both firms to use volume discounts reduces rofits relative to unit ricing, but stronger references for variety continue to soften cometition. All three effects of consumer references for variety are reversed when the firm qualities are dissimilar enough and/or the reference for variety is weak enough that two high-quality units rovide more consumtion utility than the variety bundle. Then, consumer references for variety intensify rice cometition (and reduce rofits) whether or not firms can use volume discounts. Counter-intuitively, our model redicts that seemingly very differentiated cometitors, such as a fancy restaurant and a izza ub, in a setting that involves multile urchase oortunities (e.g., a small, isolated resort town), may be cometing more on rice than they would if they were both located in an area that served only non-reeat customers (e.g., an interstate highway sto). Also, we find that allowing both firms to use volume discounts increases rofits relative to unit ricing, and that the lower-quality firm does not offer any discount in equilibrium. One may hyothesize that giving each firm more degrees of ricing freedom would intensify rice cometition (as it does under equal qualities). But under dissimilar qualities, volume discounts increase rofits because they combat the rofit-destroying variety-seeking behavior. Finally, regarding quality choice, when firms are differentiated enough, rofits for both firms locally increase with greater amounts of differentiation. 6

18 References Faison, Edmund W. J The Neglected Variety Drive: A Useful Concet for Consumer Behavior, Journal of Consumer Research, 4(3), Feinberg, F. M., B. E. Kahn, and. McAlister. 99. Market Share Resonse When Consumers Seek Variety. Journal of Marketing Research 9(): Givon, Moshe Variety Seeking through Brand Switching Marketing Science 3():. Guo, iang Consumtion Flexibility, Product Configuration, and Market Cometition, Marketing Science, 5 (), Kahn, B.E., M.U. Kalwani, and D.G. Morrison Measuring Variety-seeking and Reinforcement Behaviors Using Panel Data. Journal of Marketing Research 3(): Klemerer, Paul Markets with Consumer Switching Costs. Quarterly Journal of Economics 0(): Mazzeo, Michael. 00. Product Choice and Oligooly Market Structure. RAND Journal of Economics 33(): -4 McAlister, eigh. 98. A Dynamic Attribute Satiation Model of Variety-Seeking Behavior. Journal of Consumer Research 9(3): McAlister, eigh, and Edgar. A. Pessemier. 98. Variety Seeking Behavior: An Interdiscilinary Review. Journal of Consumer Research 9(3): 3. Moorthy, K. Sridhar 988. Product and Price Cometition in a Duooly, Marketing Science, 7(), Raju, P. S. 980, Otimum Stimulation evel: Its Relationshi to Personality, Demograhics, and Exloratory Behavior, Journal of Consumer Research, 7(3), 7-8. Ratner, Rebecca K., Barbara E. Kahn, and Daniel Kahneman Choosing ess-preferred Exeriences for the Sake of Variety. Journal of Consumer Research 6(): 5. Sajeesh, S., and Jagmohan S. Raju. 00. Positioning and Pricing in a Variety Seeking Market. Management Science 56(6): Seetharaman, P.B., and ai Che Price Cometition in Markets with Consumer Variety Seeking. Marketing Science 8(3): Shaked, Avner, and John Sutton. 98. Relaxing Price Cometition through Product Differentiation. Review of Economic Studies 49(): 3 3. Trivedi, Minakshi, Frank M. Bass and Ram C. Rao "A Model of Stochastic Variety-Seeking." Marketing Science 3(3), Villas-Boas, Miguel Consumer earning, Brand oyalty, and Cometition, Marketing Science 3 ()

19 Aendix: Proofs of the Proositions Proof of Proosition : The equilibrium can be exosed most clearly in terms of the following quantities: D,C, B C, A D. Under this notation, Assumtion is equivalent to A BD 4C. et AB, and note that C D because AB is the geometric mean of C and D. We first show the high firm is indifferent between undercutting and overshooting this : the otimal undercutting deviation is down down and yields a rofit of C 8 down. The undercut to 4C the market because B A B (see roof of Proosition ) down does not drive the low firm out of B down down B A Demand 0 AB B A 3B, C which is in turn imlied by Assumtion. The otimal overshooting deviation is roof of Proosition ), which yields a rofit D u A A B (see u. Comaring the two rofits, we find that 4D C D D D C C DC AB. Since the high firm is u down indifferent between undercutting and overshooting AB, any mixed strategy that lays u with down robability ρ and with robability -ρ is a high firm s best resonse to AB. To close the equilibrium construction, we find ρ such that AB is the best resonse of the DOWN UP low firm. When the high firm lays a mixed strategy with a suort,, the rofit of the low firm is obviously increasing for small rices ( continuous at and u ), decreasing for large rices ( down down down, the maximum must be somewhere in the, u u down where the function is: min, C u ), and u interval, down. D C down u u Since C imly an increasing, the maximum must be either at or down down down down somewhere in the, C interval. To find the best rice in, C, let down B A B u A A B, and note that the rofit function for C simlifies down u A B to which is concave. The first-order condition is A B A B AB 3AB 4 A B. Solving for ρ for = AB in turn yields A * A B. Plugging ρ*

20 back into the rofit function yields * AB AB. When the high firm lays ρ*, the first-order down down condition for the low firm has an interior solution inside the, C is obvious, and firm refers to lay = AB to B interval: BA B AB B A AB B A 3B, which is imlied by similar qualities (Def. ). The low A AB * AB A B, which is u u u. exactly the definition of similar qualities. In equilibrium, the high firm makes A B, which exceeds the equilibrium rofit of the low firm because the arithmetic mean always exceeds the geometric mean (Cauchy): AB AB AB AB. Finally, the 0 and 0 comarative statics are obvious. Now substitute ==q in the rofit functions and kees track of firm identities: u down and q q. Neither firm s demand function has a kink now, and the rofit functions are the same. Therefore, only can be a ure-strategy equilibrium. The rofit functions are also concave, so the unique candidate rices q are indeed equilibrium rices. QED Proosition. Proof of Proosition : The demand functions consumer behavior imlies are Demand where R, Demand R R R. Therefore, the rofit functions are and R R. The local (within the ordering of the cutoffs) best-resonse functions are therefore, R, and candidate rices for equilibrium are R 4 R R. It is 3 3 easy to check that both marginal consumers lie within the suort of θ: 0 and. The second constraint holds because

21 4 6 The rofits in the candidate equilibrium are R, R.The above situation is an 9 9 equilibrium whenever the high firm does not want to deviate u to make money only on the variety seekers. The consumer behavior then becomes 0, : both eriods and, : variety seek. The best such deviation is The best deviation yields a rofit of D C CD DC DC 3D 5CD, where D and C. 6 D C 3D 5C D 6D C, so it is rofitable when D, which reduces to 9D 34CD39C 0 and holds for C=0 and is 6 9 decreasing for ositive C in C, so a cutoff C*<D exists, beyond which this deviation is not rofitable. For all C>C*, the above candidate equilibrium is an equilibrium. The cutoff is C D 0.D. To 39 R rove the comarative static in δ, it is sufficient to show that 0. R increases in δ: R 3 0. QED Proosition Proof of Proosition 3: Each firm is maximizing C and C q C q. It is straightforward to confirm that are both concave, so we can rely on first-order analysis. Differentiating from Proosition with resect to shows that each firm wants to deviate from qq q qsuch that Cq because. Differentiating from Proosition with resect to q shows that the lower-quality firm would always refer to raise its quality u to any such that such that C because and 0 is increasing in q, and so so C 0 for every <. Therefore, either C q firms run into the uer bound of the feasibility constraint or there is a q q and neither firm wants to raise its quality further. QED Proosition 3 C means that C q and both such that Cq, 0