Price promotions as a threat to brands

Inderst, Roman; Obradovits, Martin Article — Published Version Price promotions as a threat to brands Journal of Economics & Management Strategy Provided in Cooperation with: John Wiley & Sons Suggested Citation: Inderst, Roman; Obradovits, Martin (2023) : Price promotions as a threat to brands, Journal of Economics & Management Strategy, ISSN 1530-9134, Wiley, Hoboken, NJ, Vol. 33, Iss. 1, pp. 53-77, https://doi.org/10.1111/jems.12550 This Version is available at: https://hdl.handle.net/10419/288265 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/4.0/ Received: 17 September 2021 | Revised: 20 May 2023 | Accepted: 30 May 2023 DOI: 10.1111/jems.12550 ORIGINAL ARTICLE Price promotions as a threat to brands Roman Inderst 1 |Martin Obradovits 2 1 Chair of Economics and Finance, Johann Wolfgang Goethe University Frankfurt, Frankfurt, Germany 2 Department of Economics, University of Innsbruck, Innsbruck, Austria Correspondence Roman Inderst, Chair of Economics and Finance, Johann Wolfgang Goethe University Frankfurt, Frankfurt, Germany. Email: [email protected] Abstract Manufacturers frequently resist heavy discounting of their products by retailers. Since low prices should increase demand and manufacturers could simply refuse to fund deep price promotions, such resistance is puzzling at first sight. We develop a model in which price promotions cause shoppers to evaluate the relative importance of quality and price against a market‐wide reference point. With deep discounting, consumers perceive quality differences as less pronounced, eroding brand value and the bargaining position of brand manufacturers. This reduces their profits and may even lead to a delisting of their products. By linking price promotions to increased one‐stop shopping and more intense retail competition, our theory also offers an explanation for the rise of store brands. 1|INTRODUCTION “We take loss leading of our brands very seriously.”This exemplary statement was delivered by a spokesperson of Foster's, who justified the company's blitz action to withdraw key stock from two Australian supermarket chains after learning of their promotion to sell Foster's beer brands below cost. 1 Staying with the country of the initial quote, also leading brand manufacturers of bread and milk reported trading losses and the need to cut cost, naming discounted prices at competing retailers as the primary reasons. 2 Turning to another country, in a well‐known case in 2014, Lidl, one of the largest German discounters, stopped selling Coca‐Cola, with both sides citing different views about the product's store price as reason. This was preceded by heavy discounting of Coca‐Cola at the discounter. 3 In light of Germany's notoriously competitive food retailing environment, manufacturers frequently express concerns about the impact of price wars on their brand value and profits. 4 The above examples echo brand manufacturers' general fears of losing profits and brand equity when retailers heavily discount their products. However, given that price discounts should drive demand for manufacturers' products and that, at first glance, there is no reason why manufacturers would need to fund such deep price promotions, manufacturers' resistance may come as a surprise. To shed light on this phenomenon, we set up an analytically tractable model of multiproduct retail competition incorporating manufacturer–retailer negotiations, retailers' product‐stocking decisions, consumer one‐stop shopping, and retail‐price promotions. Precisely, our model combines the following four key elements. First, to capture retail competition with frequent price promotions, we employ a “model of sales,”as in Varian (1980) or Narasimhan (1988). Second, due to limitations either in consumer attention or advertising space, such promotions take place only in one product category, following Lal and Matutes (1994). 5 We can thus compare implications for this promoted category and other categories. Third, as we are interested in the distribution of profits between retailers and manufacturers, we model the manufacturer–retailer channel via vertical contracting. Fourth, next to a benchmark model where J Econ Manage Strat. 2024;33:53–77. wileyonlinelibrary.com/journal/jems | 53 This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made. © 2023 The Authors. Journal of Economics & Management Strategy published by Wiley Periodicals LLC. consumers exhibit standard (rational) preferences, we build on recent advancements in behavioral economics and employ a model of consumer reference‐dependent (relative) preferences. Our main results are as follows. First, when consumers exhibit standard preferences, we show that brand manufacturers' fears are indeed unfounded in our model. As retailers' lower prices expand demand, manufacturers would even tend to benefit when their products are used for promotions, rather than being adversely affected by the retailers' margin loss. Thus, from the viewpoint of classical economics, our model does not support the claims of brand manufacturers that heavy retailer discounting erodes the value of their brands. In contrast, our model can explain manufacturers' resistance to deep discounts when consumers, faced with frequent price promotions, do not have “fixed”preferences, but form their relative preferences for price and quality with respect to a market‐wide reference point. Specifically, our consumer choice criterion of “relative thinking”builds on the concept of “salient thinking”introduced in Bordalo et al. (2013), as subsequently adapted to imperfect retailing competition in Inderst and Obradovits (2020). 6 A key property of the applied consumer choice rule is that as the price level in the promoted category decreases, the same quality difference becomes less important in the eyes of shoppers who compare offers across retailers. Retailers' deep discounting thus undermines brand manufacturers' quality advantage over low‐quality rivals' products and thereby their bargaining power vis‐à‐vis retailers. This may lead to lower profits and possibly even to a delisting of their products, such as in favor of store brands. Importantly, the depth of discounts offered in the promoted category—and thereby, the overall equilibrium outcome—is tightly linked to the extent of consumer one‐stop shopping, that is, the size of consumers' baskets at individual shopping trips. Expressing our results in relation to consumers' degree of one‐stop shopping, we find the following. First, when consumers have standard preferences, brand manufacturers in promoted categories are not disadvantaged relative to brand manufacturers in other categories, and all brand manufacturers' profits are independent of the degree of one‐stop shopping. This continues to hold even when consumers exhibit relative thinking, provided that the degree of one‐stop shopping is fairly small. Second, when consumers are relative thinkers and thesizeoftheirshoppingbasketexceedsacertainthreshold,the resulting deep discounting of promoted manufacturers' products leads to a weakening of their bargaining position with retailers. This is because stocking a low‐quality substitute (e.g., a store brand/private label) becomes relatively more attractive for retailers in the face of consumers' diminished perception of quality differences. From that point onwards, brand manufacturer profits are lower in the promoted category than in nonpromoted ones, and they keep decreasing as the extent of one‐stop shopping grows. Yet, also in the promoted category, all retailers still stock the branded high‐quality product. Lastly, eventually a point is reached where the average price level in the promoted category becomes so low that affected brand manufacturers lose all their bargaining power vis‐à‐vis retailers. They then make zero profit in equilibrium, and retailers remove their products with positive probability, replacing them with low‐quality alternatives. Our mechanism may thus shed new light on some general trends that have shaped retailing over the last decades, especially in the food sector. Since in our model retailers replace branded high‐quality products with lower‐quality variants in the promoted category when the extent of consumer one‐stop shopping is sufficiently large, our model provides a possible explanation for the widely observed long‐term growth of private labels. 7 This is consistent with an increasing consumer preference for one‐stop shopping, as claimed by some authors and policy reports (see, e.g., Baye et al., 2018; Johansen & Nilssen, 2016, and the references therein). Also, again following the main thrust of our model and argument, an increase in retail competition reduces the bargaining power of brand manufacturers, as they can then no longer bank on their superior quality or investment in brand value. In our concluding remarks, we argue how this should have far‐reaching implications for brand manufacturers' product positioning and investment strategies. To our knowledge, this paper is the first to analyze the impact of heavy discounting by retailers on the profits of manufacturers whose brands are promoted, in contrast to profits of manufacturers in nonpromoted categories. We acknowledge that the literature has identified alternative explanations for why manufacturers would want to prevent heavy discounting of their products (and possibly even impose a minimum resale price). For example, manufacturers may want to ensure sufficient margins to retailers so as to incentivize services, or, in the language of Telser (1960), to ensure “fair trade”among retailers. 8 Such theories seem most applicable to service‐intense products or to new‐product introductions. Our model instead focuses on the conflict of interest between manufacturers and retailers. Moreover, our showcased mechanism, by which deep discounting negatively affects manufacturer profits, is such that manufacturers could not fully escape these negative implications by adopting retail‐price‐maintenance (RPM) strategies—provided that they are not anyhow prohibited by antitrust laws. 9 This follows from the fact that the 54 | INDERST and OBRADOVITS mechanism depends on the average price in the considered category, as this affects the relative importance of quality and price. In particular, in our model, a retailer's price‐cutting of a particular product does not by itself undermine a consumer's perception of the product's quality or brand value. 10 To fully defend the value of their brand and thereby their bargaining position vis‐à‐vis retailers, brand manufacturers in a given category would have to act in concert to prevent that their products are heavily discounted. But such horizontal agreements would clearly fall foul of antitrust laws. Hence, when manufacturers are rightly concerned that retailers' intense price promotions reduce their bargaining position and destroy brand value, they would need to rely on the support of regulation, such as through the establishment of minimum sale prices. 11 But even when such regulations are not (yet) in place, manufacturers may be able to constrain retailers by raising the awareness of policymakers or the general public. Another insight of our model is that brand manufacturers, particularly those of promotion‐intense products, should be aware of increasing retail competition. This could be triggered by the entry of hard discounters or, potentially, also by the rise of alternative shopping formats, such as online retailing—even more so if this forces retailers to compete more aggressively on few, particularly visible products. The underlying concept of context‐dependent preferences has gained wide acceptance in behavioral economics and marketing, with literature dating back to at least Monroe (1973). 12 Several authors in marketing have also related this to Kahneman and Tversky's (1979) seminal Prospect Theory (e.g., Diamond & Sanyal, 1990). Much of this literature has however focused on how a single firm's offers can shape consumer perceptions. For example, Huber et al. (1982) show that the choice among two alternatives can crucially be affected if a third, dominated alternative is added (the so‐called “attraction effect”). Similarly, Simonson (1989) demonstrates that adding an alternative that is particularly good on one dimension, but bad on another (e.g., a product with very high quality, but also a very high price), may tilt consumers' choice among the initially available alternatives (“compromise effect”). Departing from this, our paper contributes to the burgeoning literature in behavioral industrial organization investigating the impact of context‐dependent or reference‐point‐dependent consumer preferences in strategic market environments. Like us, many recent works build on the seminal formalization of “salient thinking”developed in Bordalo et al. (2013). 13 Moreover, several of these articles have also shown that such preferences can lead to distorted consumer choices, prices, and ultimately firms' product choices. For instance, Bordalo et al. (2016) find that depending on the specific technological relationship between product quality and the corresponding marginal costs of production, consumers' biased attention may induce “commoditized”price‐salient equilibria (where product quality is distorted downwards relative to the rational benchmark) or “decommoditized”quality‐salient equilibria (where the opposite is the case). Other articles in this vein include Herweg et al. (2017), Johnson (2017), Helfrich and Herweg (2020), Apffelstaedt and Mechtenberg (2021), Dertwinkel‐Kalt and Köster (2022), and our companion work in Inderst and Obradovits (2020). Notably, the present contribution builds on our earlier framework in Inderst and Obradovits (2020), where we also study retail competition with salient‐thinking consumers. Next to the application of this consumer choice criterion to a workhorse model of imperfect competition (Varian, 1980), the main focus of that article was the analysis of the effects of a prohibition of loss leading. Compared with Inderst and Obradovits (2020), we now introduce a vertical structure (and the respective manufacturer–retailer contracting) as well as additional, nonpromoted categories in retailers' offers. This allows us to analyze and compare manufacturers' offers in promoted and nonpromoted categories, and how these are affected when promoted products are deeply discounted due to consumer one‐stop shopping. Moreover, we can determine the distribution of profits among retailers and manufacturers. Vertically related markets are also examined in Helfrich and Herweg (2020) and Dertwinkel‐Kalt and Köster (2022). However, both of these articles focus on the effects of vertical restraints in online retailing. For example, Dertwinkel‐ Kalt and Köster (2022) demonstrate that, in a setting where price differences across sales channels (offline and online) lead consumers to undervalue product quality, a monopolistic upstream manufacturer may find it optimal to bias product quality away from the (rational) first best to counteract the associated profit loss. Under some circumstances, vertical restraints can then correct market outcomes. Similar considerations are also at the heart of Helfrich and Herweg (2020); in contrast to the present contribution, neither article takes into account multiple (promoted and nonpromoted) brands or a profit comparison between those. The remainder of this paper is organized as follows. Section 2sets out the model. Section 3solves the baseline case where consumers follow a standard choice criterion, thereby setting up the respective puzzles. Section 4presents the main analysis under relative consumer preferences. Section 5concludes by deriving from our results potentially testable hypotheses as well as managerial implications. All proofs are relegated to Appendix A. In Appendix B,we INDERST and OBRADOVITS | 55 outline several alternative consumer choice rules that are equivalent to the choice concept of salient thinking employed in the main analysis. Appendix Cconsiders a variation of our baseline model with elastic demand. 2|MODEL SETUP 2.1 |Retail competition We consider a market where N = 2 possibly multiproduct retailers compete for final consumers. 14 The retailers may stock a single product in each of ≥I 1 different product categories, 15 with the respective products supplied by manufacturers that compete for shelf space at the retailers (see below). Consumers are one‐stop shoppers and thus make all their purchases at a single retailer. 16 We abstract from retailers' own (handling) costs, which however can be included without affecting results. It is convenient to denote the respective sets of retailers and product categories also by N and I . The price of the product offered by retailer ∈n N in product category ∈ iI is denoted by pn i, and we suppose that the product's respective quality can be described by a real‐valued variable q n i . When this does not cause confusion, we will sometimes omit the superscript i denoting the specific product category. 17 2.2 |Manufacturers For simplicity, we assume that in each product category ∈ iI , only two different product variants exist: a low‐quality product with quality q > 0 Land constant marginal costs of production ∈cq(0, ) LL and a high‐quality product with quality q q> HL and constant marginal costs of production ∈ccq(, ) HL H . 18 We denote qq Δ =− qHL and cc Δ =− cHL . For each product category, we further suppose that the low‐quality variant can be supplied by at least two undifferentiated manufacturers, or that it represents a private label (that can be produced by the retailers themselves). Because of this, we assume that in each product category, retailers can procure the respective low‐quality variant at cost cL. In contrast, motivated by our introductory examples, we suppose that in each product category, there is a single high‐quality brand manufacturer that negotiates with retailers (see below for our specification of the brand manufacturer–retailer negotiations). We focus on the interesting case where the brand manufacturers' products provide a strictly higher surplus, Δ >Δ qc . Otherwise, the retailers would always stock the low‐quality variant in each product category, irrespective of consumers' (rational or relative) preferences. 2.3 |Brand manufacturer–retailer negotiations It is well known from the large literature on vertical contracting and channel management that the equilibrium characterization depends crucially on whether retailer competition can be affected through the strategic choice of wholesale contracts. 19 In this paper, we abstract from such issues of optimal channel management by choosing a specification that results in marginal wholesale prices equal to marginal costs. Precisely, we assume that even when a manufacturer supplies both retailers, he negotiates separately (through independently acting agents) with them. 20 Another way to obtain such a result is to have a “dedicated”manufacturer for each retailer, so that the setup becomes that of competing vertical chains. 21 As the intricacies of bilateral negotiations are also not the subject of our model, we stipulate that in each bilateral meeting, the manufacturer's agent makes a take‐it‐or‐leave‐it offer in the form of a two‐part tariff contract. This contract specifies a fixed fee Tn itogether with a constant (per‐unit) wholesale price w n i . 2.4 |Consumers We follow Varian (1980) by assuming that a fraction ∕λ ( 1−) 2 of consumers can only shop at their (local) retailer n (for ∈n{1, 2}), such that a total fraction λ1 − of consumers does not compare offers. In contrast, the remaining 56 | INDERST and OBRADOVITS fraction λ of consumers, called “shoppers,”is free to choose any retailer, so that λ also captures the intensity of competition. We next stipulate that only the offer in category i = 1 is observed before a consumer enters the respective shop. 22 Shoppers thus observe offers qp ( ,) nn 11 across both retailers, while nonshoppers only observe the respective offer of their (local) retailer. No consumer observes offers in categories i > 1 before entering a shop, though consumers hold (rational) expectations qp ( , ) n i n i   for all i > 1 . Once in a shop, a consumer then observes all of this retailer's offers and decides which products to buy. We normalize consumers' (common) outside option to provide zero utility/surplus and assume that they demand at most one unit in each product category. We describe consumers' choice rules next. 2.5 |Consumer choice with rational preferences In our baseline analysis, we suppose that consumers have standard (rational) preferences. This means that the actual and perceived utility a consumer derives from purchasing any product i , now dropping retailer subscripts, is given by uqp=− iii . This is compared with the outside option of not‐buying, which yields zero utility. Hence, given their expectations of the product offers in categories i > 1 , shoppers will frequent the retailer n for which  qp qp ( −)+ ( − ) nn i n i n i11 >1   (1) is largest. 23 Nonshoppers have no choice and thus simply visit their (local) retailer. Once in a store, each consumer purchases all products i that provide a nonnegative net utility. 2.6 |Consumer choice with context‐dependent preferences Here, we follow closely the concept of “salient thinking,”as applied also in Inderst and Obradovits (2020), which in turn builds on the seminal framework provided by Bordalo et al. (2013). As we discuss in Appendix B, the resulting consumer choice criterion can however also be given alternative foundations, which is why we will subsequently refer to it more broadly as “relative thinking.” As a first guiding principle, relative thinking can only occur when consumers are faced with at least two different but comparable options, such that a relative evaluation is even possible. We thus stipulate that relative thinking may only apply when making comparisons within the same product category. Since nonshoppers cannot choose between retailers, and shoppers may only observe different offers in product category i = 1 , it follows directly that relative thinking may only matter for shoppers through retailers' offers in category i = 1 . Note next that if both retailers stock the same product quality in i = 1 , then either their offers are exactly the same (such that relative thinking does not matter), or one retailer's offer is strictly dominated. For the latter case, as in Inderst and Obradovits (2020), we assume that relative thinking will then not apply either, since dominated options are not relevant for a comparison (a dominated option will never be chosen, so it should be discarded by consumers). Suppose hence that the two retailers offer different qualities in category i = 1 . Following Bordalo et al. (2013), we may then define a “reference product”that has the average quality Q = qq+ 2 LH and the average price P= pp+ 2 LH of the two offers (where pp< L H , as otherwise, the low‐quality product would be strictly dominated). Take now, first, the low‐ quality product. For this product, its low price, rather than its low quality, is salient when p P q Q < , LL that is, when its price is relatively lower (in percentage terms), compared with the average price P in the consideration set, than its quality, compared again to the average quality Q . When instead the converse holds strictly, its lower quality is salient. Similarly, for the high‐quality product, its high quality is salient when q Q p P > , HH INDERST and OBRADOVITS | 57 while its high price is salient when the converse holds strictly. As is easy to check, for both products, the same attribute must be salient. 24 Namely, substituting for Q and P , price is salient for both products when p p q q < , L H L H(2) while quality is salient for both products when the converse of (2) holds strictly. 25 We next stipulate that consumers compare products only on the salient attribute, so that they prefer the (lower‐ priced) low‐quality product in category i = 1 if (2) holds, while they prefer the high‐quality product in i = 1 if the converse of (2) holds strictly. While this may seem somewhat stark, as the nonsalient attribute is basically fully neglected, this heavily simplifies the analysis. 26 Based just on retailers' offers in category i = 1 , shoppers would thus form their preferences over retailers accordingly. While in general one would have to specify how this preference carries over when also including shoppers' expectations qp ( , ) n i n i   of the offers provided in categories i > 1 , for our purposes it is sufficient to assume that, in the expectation of equal offers in categories i > 1 across retailers, consumers choose the retailer based on their preference in category i = 1 . Finally, in line with the earlier discussion, the described decision criterion applies only to choices that can indeed be compared along the two attributes, price and quality. We thus follow Inderst and Obradovits (2020) and suppose that consumers evaluate offers correctly with respect to their outside option (of value zero). Hence, once in a shop, where within a category consumers can no longer compare different offers, a purchase is made if and only if the respective utility from that category exceeds the consumer's reservation utility of zero. 27 2.7 |Sequence of moves The game proceeds as follows. In t = 1 , at each retailer n=1, 2 and for each product category i , the corresponding brand manufacturer with high quality qH and costs c H and at least two nonbrand manufacturers with quality q L and costs cLcompete by simultaneously offering contracts to the respective retailer. In t = 2 , retailers simultaneously choose for each category ∈ iI which product to stock, that is, which contract to accept, and at which prices pn ito offer these to consumers. Finally, in t =3 , consumers choose which retailer to frequent and which bundle to purchase. Precisely, of the fraction λ1 − of nonshopping consumers, half frequents retailer 1 and half frequents retailer 2. The fraction λ of shopping consumers decides which retailer to visit, depending on, first, observed qualities and prices qp ( ,) nn 11 in category i = 1 and, second, on retailers' anticipated choices qp ( , ) n i n i   in categories i > 1 . Once in a shop, a consumer purchases the product in category ∈ iI if and only if ≥ q p− 0 n i n i . 3|BENCHMARK ANALYSIS In our benchmark analysis, we suppose that consumers have standard preferences, so that shoppers choose the retailer for which (1) is highest. Most of the subsequent analysis for the baseline model follows well‐established results (see Narasimhan, 1988; Varian, 1980), which is why we can be short, though all remaining gaps are filled in the proof of Proposition 1. 3.1 |Product choices Consider first products in categories i > 1 . Recall that even shoppers do not observe the offers of these products before entering a shop, but only that of the promoted product in category i = 1 . It is thus optimal for all retailers to set (monopolistic) prices pq= n i n ifor products in all nonpromoted categories i > 1 . As consumers rationally anticipate that pq= n i n i  for i > 1 , they anticipate to realize zero surplus on these products. Since Δ >Δ qc , it is next obvious that the high‐quality product must be stocked in all categories i > 1 by both retailers. Otherwise, the respective brand manufacturer and retailer could jointly achieve a higher surplus in this category (with the retailer serving at least its 58 | INDERST and OBRADOVITS locked‐in consumers), such that a profitable deviation would exist. We now extend this insight to category i = 1 . To see this, suppose to the contrary that in some candidate equilibrium, at least one retailer ∈n{1, 2} would instead choose q q= nL 1and some price p n 1 . In this case, the retailer and the high‐quality manufacturer could however jointly realize strictly higher profits by offering instead qH at a price p+Δ nq 1 , so that this leaves consumers indifferent (and thus does not affect expected demand), while the margin would increase by Δ −Δ > 0 qc . 3.2 |Vertical contracting So as to avoid double marginalization, in equilibrium products are provided to the retailer at a marginal wholesale price that is equal to marginal cost. Depending on the chosen quality q n i , the retailer's marginal cost of offering product i is thus either w c= n i L or w c= n i H . Given manufacturer competition for the provision of the low‐quality product, the respective offers will not contain a positive fixed part: low‐quality products are thus offered by manufacturers at cost. In contrast, the offer of the respective high‐quality manufacturer at retailer n may contain a fixed part T> 0 n i . When this offer is accepted, Tn iis thus the profit of the high‐quality manufacturer. By optimality, the specification of Tn iwill leave the respective retailer just indifferent between acceptance and rejection. To determine Tn i, as offered by the brand manufacturer in category i , we can leave all other fixed fees constant. Recall now that consumers do not anticipate to get a positive surplus from any product in categories i > 1 , so that shoppers only need to compare offers in category i = 1 . Intuitively, when all retailers stock the same quality in all categories, including i = 1 , with standard preferences the pricing equilibrium shares the key features of Varian (1980). In particular, a retailer realizes the same profits as when choosing the highest feasible price also for the product in i = 1 ,pq= n H 1,thereby attracting only its share of nonshoppers ∕λ ( 1−) 2 . Thus, all profits that could be realized with shoppers are fully competed away in equilibrium; compare below for the precise characterization of the (mixed‐strategy) pricing equilibrium. Hence, equilibrium profits for each retailer equal gross profits ∕qcI λ ( −)(1−) 2 HH minus the sum of fixed fees  T in i . When the retailer instead stocks a low‐quality product in some category i , the deviating gross profit equals the sum of ∕qcI λ ( −)( −1)(1 −) 2 HHand now ∕qc λ ( −)(1 −) 2 LL . The difference is extracted by the respective manufacturer i ,so that ∕Tλ=(Δ−Δ)(1 −) 2 n iqc . Note that this holds irrespective of the product's category, thus both for the promoted category i = 1 and for all other categories i > 1 . This will be markedly different with relative thinking. 3.3 |Promotions We finally turn to the characterization of equilibrium pricing in the promoted category. The considered demand system does not afford an equilibrium where all retailers choose pure strategies. 28 Dropping for convenience the superscript i = 1 , we denote retailers' pricing strategies for the promoted product in i = 1 by the cumulative distribution function (CDF in what follows) Fp( ) nnwith support pp [ ,] nn. In line with the literature, we refer to choices pp< nn as promotions. The lower boundary pnthus denotes the deepest promotion of retailer n . With symmetry, p p = n is obtained from retailers' indifference between setting p and attracting all shoppers or setting pq= H and attracting only loyal customers:                  pc I q c λλqcI λ [ (−)+( −1)( −)] 1− 2+=(−)1− 2 , HHHHH which solves for                                pc q c I λ λ =+(−)1−2 1+ . HHH(3) Promotional depth qp − H is strictly increasing in the scope of products I that consumers purchase during their one‐stop shopping trip. For a retailer to be indifferent over all ∈ppq[, ] H, the (symmetric) pricing strategy Fp Fp()= ( ) nnof its rival must satisfy INDERST and OBRADOVITS | 59                     pc I q c λλFp π [ (−)+( −1)( −)] 1− 2+(1−())= . HHH Substituting () πqcI=( −) HHλ1− 2 , it follows that               Fp λ λ qp pc I q c ()=1−1− 2 − −+( −1)( −). H HHH (4) As I increases, this shifts the distribution of (promoted) prices downwards in the sense of first‐order stochastic dominance, thus making lower prices more likely. Note that retailers' equilibrium pricing also shifts downwards (in the sense of first‐order stochastic dominance) when there are more shoppers in the market (higher λ ), as does the deepest promotion p derived in (3). We summarize our equilibrium results in the following proposition. Proposition 1. In the benchmark case with rational consumers,we have the following unique characterization of equilibrium product choice,profits,and prices: (i) Quality: Both for the promoted category i = 1 and for all other categories i > 1 ,the brand manufacturers' (high‐quality)product is chosen. (ii) Prices: Nonpromoted (high‐quality)products in categories i > 1 are always offered at prices equal to consumers' willingness to pay,pq= n i H .Instead,the price for the promoted product in i = 1 depends on the extent of one‐stop shopping ( I )as follows: The lowest price at which it is offered in equilibrium, p as given by (3), is strictly decreasing in I ,so that the depth of promotion increases.The full pricing strategy Fp() is given by (4). (iii) Profits: At each retailer n and for all product categories i ,that is,again independent of whether i = 1 or i > 1 , the respective (high‐quality)brand manufacturer realizes the same profit ∕λ Π =Π=(Δ−Δ)(1 −) 2 i MMqc . Each retailer earns ∕πqcI λ=( −)(1−) 2 nLL . Proof. See Appendix A. □ 3.4 |Discussion of the benchmark case We note first that when setting I= 1 , one recovers the single‐product analysis of retail competition in the seminal work of Varian (1980). While retail prices in categories i > 1 are unaffected, when I increases, prices in the promoted category i = 1 decrease and, at a certain point, can even drop below the respective marginal wholesale price, c H . In fact, for the lowest promoted price, p , this is immediately evident from the derivation in (3). However, this does not affect either the profits of the manufacturer in category i = 1 or the provision of quality. For the benchmark case with rational consumers, results are thus not consistent with the fears of brand manufacturers that profits decline when their product is deeply discounted by retailers. We summarize this observation as follows. Corollary 1. When consumers maximize expected utility (1), brand manufacturers realize the same profits irrespective of both the extent of one‐stop shopping ( I )or whether their product is used for promotions ( i = 1 )or not ( i > 1 ). At this point, it is instructive to briefly mention the results of an extension of our baseline model where demand is elastic as consumers have heterogeneous reservation values (see Appendix Cfor the full analysis). Then, as the extent of one‐stop shopping increases and as thus promotion discounts in category i = 1 increase, the brand manufacturer in this category becomes strictly better off, and it is also strictly better off than other brand manufacturers. With standard preferences and now elastic demand, we thus arrive indeed even at the opposite prediction to the aforementioned fears of manufacturers. 60 | INDERST and OBRADOVITS ENDNOTES 1 The Sydney Morning Herald, March 23, 2011, “Beer war as Foster's takes on chains to stop sale of $28 cases,”https://www.smh.com.au/ business/beer-war-as-fosters-takes-on-chains-to-stop-sale-of-28-cases-20110322-1c5cd.html, accessed August 26, 2021. 2 The Sydney Morning Herald, November 22, 2011, “Heinz hits out at home brands,”https://www.smh.com.au/business/heinz-hits-outat-home-brands-20111121-1nr1l.html, accessed August 26, 2021. In the same article, as the title suggests, Heinz' CFO blamed “relentless promotional pressure”at the two national discounters, Coles and Woolworths, as the main reason for bad financial performance. 3 Welt, January 29, 2014, “Coca‐Cola kämpft sich zurü ck in das Lidl‐Regal”[“Coca‐Cola fights its way back to the Lidl shelf”], https:// www.welt.de/wirtschaft/article124337516/Coca-Cola-kaempft-sich-zurueck-in-das-Lidl-Regal.html, accessed August 26, 2021. 4 For example, Welt, January 29, 2017, “Unilever kritisiert ‘Brandrodung’im Supermarkt”[“Unilever criticizes ‘fire clearing’in the supermarket”], https://www.welt.de/wirtschaft/article161630067/Unilever-kritisiert-Brandrodung-im-Supermarkt.html, accessed August 26, 2021. 5 In our already rich model, we however do not endogenize which of the considered product categories is used by retailers for promotions. 6 As in the present context the same choice criterion as under “salient thinking”can also be obtained with other concepts used in the literature, we refer to it more broadly as “relative thinking.”See Appendix Bfor a discussion of these alternative concepts. 7 There is by now a large literature documenting and analyzing the spread of store brands. For an early survey, see, for example, Bergès‐ Sennou et al. (2004). Various rationales have been proposed for why retailers introduce store brands, for example, so as to exert downwards pricing pressure on national brands (Mills, 1995; cf. Chintagunta et al., 2002, for an empirical analysis). In our model, instead, retailers are only reactive to external forces (e.g., the increase in one‐stop shopping). As, in line with the literature, shoppers in our model exhibit the same preferences, at present our model cannot be immediately extended to the case where in a given category store brands and national brands are simultaneously offered by a given retailer. 8 Compare the seminal work by Telser (1960), Mathewson and Winter (1984), and Marvel and McCafferty (1984). Overall, the literature on minimum resale prices or resale price maintenance is too large to review here. Other identified rationales for such practices include a facilitation of tacit collusion, a softening of downstream competition to ensure overall higher channel profits, or exclusion of upstream rivals. 9 RPM is severely restricted in the European Union, where some countries even treat it similarly to anticompetitive practices prohibited per se. Since the 2007 Leegin‐decision of the US Supreme court, which clearly ruled against a per se prohibition of RPM, in the United States matters are less clear‐cut—also as some states, like, California under the Cartwright‐Act, still seem to practice such a prohibition. 10 Indeed, such a mechanism would seem more reasonable with luxury products, where a high price may itself be a vital trait of the product (e.g., as it communicates to others the owner's income and wealth or as it ensures that there is only a small, selective group of such owners). See, however, Dertwinkel‐Kalt and Köster (2022) for a model where price variation across different retail channels leads consumers to focus on price, rather than quality. 11 An obvious example is the prohibition of loss leading (i.e., below‐cost selling). In the United States, federal law does not restrict loss leading, but several states, such as California, have enacted respective laws. Other countries have stricter rules or specifically forbid below‐cost selling in food retailing. An interesting example is that of Germany where, following the aggressive loss leading of Walmart after its market entry, the law was changed to explicitly ban this practice in food retailing. Other European countries that have restrictions on below‐cost pricing include Belgium, France, and Ireland. 12 Possibly the most widely known evidence of such preferences relates to an experiment conducted by Tversky and Kahneman (1981). They document that 68% of subjects were willing to drive 20 min to save $5 on the purchase of a calculator when the price was $15, but less than half of this fraction (29%) were willing to do so to save again $5 when the price was instead $125. 13 Other noteworthy choice concepts describing different forms of reference‐point‐dependent preferences have been introduced, among others, in Kőszegi and Szeidl (2013) and Bushong et al. (2021). 14 We focus on a retailing duopoly merely for expositional simplicity. All our results readily extend to competition among N > 2 ex ante symmetric retailers. Details are available from the authors upon request. 15 Note that as all customers have the same preferences, as we will specify below, there would be no benefit from stocking multiple products in any given product category. An extension with heterogeneous consumer preferences must be left to future research. 16 We do not model consumers' choice for one‐stop shopping. An increase in I may have exogenous reasons, in particular when considered over a longer time horizon, such as caused by a change in mobility. 17 Usually, this will be the case for the “promoted”category i = 1 (see below). 18 The model could easily be extended to allow for different quality levels q Li, and q Hi,(and corresponding constant marginal costs) in each category, albeit this would make some subsequent expressions less transparent, and does not yield any additional insights. 19 An obvious case is that of a monopolistic (brand) manufacturer who can commit to observable offers to all retailers and thereby dampen retail competition by a high marginal wholesale price (together with a low inframarginal price or even a negative fixed transfer). For a recent discussion of various models with such observable contracts, see Inderst and Shaffer (2019). INDERST and OBRADOVITS | 67 20 Models where a supplier or retailer negotiates through independent agents are widely used in the literature. Admittedly, such an approach, where a player cannot orchestrate a simultaneous deviation across all his agents, may not be realistic in some contexts. On the other hand, some recent contributions have provided a foundation for this, such as through an appropriate extension of the respective game form (see, e.g., Inderst & Montez, 2019). 21 We will briefly return to this interpretation at the end of Section 4.2. 22 As discussed in the Introduction, only products in category i = 1 are prominent. For our purposes, it is inconsequential whether consumers' inability to observe retailers' offers in other categories is due to limited attention or memory or whether it follows from limits to advertising space. 23 In case of indifference, we assume that shoppers choose randomly which retailer to visit. 24 This property would also extend to more than two offers (as long as strictly dominated offers are deleted from the consideration set; cf. Inderst & Obradovits, 2020). 25 If (2) holds with equality, both attributes are equally salient for both products, giving rise to rational preferences. 26 We have also solved the model for the case where such discounting occurs only to some degree, where all subsequently derived insights survive, provided that this discounting is sufficiently strong. Details are available from the authors upon request. Inderst and Obradovits (2020) derive results for arbitrary discounting of the nonsalient attribute, though without the additional manufacturer–retailer layer that is at the core of the current analysis. 27 This assumption corresponds to the overarching notion that consumers do not have a fixed valuation for an offer, but that this depends on the choice context. In our particular application, the first choice context is that of selecting which store to frequent, which is based on observed promotions from all retailers. The second choice context relates to the decision in the store. 28 If ≤ppq= nH 1was the (symmetric) deterministic equilibrium price, each retailer would either find it profitable to marginally lower its price and thereby attract all shoppers, or to increase its price to extract (more) rent from its locked‐in consumers. 29 Recall that by construction, when stocking high quality in i = 1 , a retailer is indifferent between choosing any price in the support pq [ ,] H , given the rival retailer's mixed pricing strategy. 30 Note that I ˜ strictly decreases in λ , with → IIlim ˜= λ 1  . Hence, for any II>  , there exists some ∈ λ (0, 1 ) where II> ˜ for all λ λ> . 31 In fact, the increase in profits resulting from such a deviation from the candidate equilibrium would be ∕λ ( Δ−Δ)(1 −) 2 qc . 32 From a technical perspective, the proof shows that retailers are indifferent as to which product to stock in i = 1 and what corresponding price (in the respective support) to set. Moreover, it shows that there are no profitable price deviations outside the characterized supports. This takes into account that if (and only if) two different qualities are offered, shoppers' relative thinking is triggered. 33 More precisely, when we impose equality on the first condition, we can write this as qsc q c qc I q cXs qsc q c qc I q cXs qsc I q cXs q s c I q c Xs Xs Xs [( −′− +[( −)−(−)]) + ( −1)( −)] ( ′) =[( −″− +[( −)−(−)]) + ( −1)( −)] ( ″), i. e. , [( −′− )+( −1)( −)] ( ′) =[( −″− )+( −1)( −)] ( ″)+(Δ−Δ)[ ( ″)−(′)]. LLHHLLHHn LLHHLLHHn LLHHn LLHHn q cn n From this, our second inequality follows as Δ >Δ qc and as clearly Xs Xs(″)> (′) nn . 34 Indeed, some contributions in the literature, such as Azar (2014), start right from such a (re)formulation. 35 However, while then the optimal choice is indeed (generically) a corner solution, with x> 0 nonly for the product where the respective “quality‐per‐dollar” ∕ q p nn is highest, xn would now depend on pn. 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We may then write the expected demand of this retailer as a function of consumers' (perceived) net surplus s n, which is sqp=− , nLn given the anticipated monopolistic pricing at all products i > 1 . Given the anticipated strategies at all other retailers ≠nn′, in an equilibrium retailer n faces some expected demand Xs() nn (which, at this point, we need not derive explicitly). Take now some equilibrium price p n(i.e., a price for i = 1 in the respective support of retailer n ) with expected demand Xq p(− ) nLn . Consider a deviation to q q= n H and the choice of a price pp=+Δ nn q  , which thus realizes the same expected demand. In case the high‐ quality manufacturer offered his product at the wholesale price w c= n H , the retailer's increase in profit (gross of T n) would then be at least πλ N Δ =1−(Δ−Δ)>0 . nqc INDERST and OBRADOVITS | 69 By setting (e.g.) ∕Tπ=Δ 2 nn , the respective high‐quality manufacturer can thus ensure that its (deviating) offer is accepted for sure and that it generates strictly positive profits, which results in a contradiction to the claim that retailer n offers low quality for product i = 1 in equilibrium. We next turn to wholesale contracts. We wish to support an equilibrium where marginal wholesale prices equal marginal costs. Take first i = 1 and note that, for a given wholesale price w n 1 set by the respective brand manufacturer, the retailer's optimal price p n 1 solves                 () () pw I qcXqp−+( −1)( −)− . nnHHn Hn 11 1 (A1) When w c= n H 1 , the retailer thus maximizes                 () () pc I qcXqp−+( −1)( −)− , nHHHn Hn 11 which are indeed the joint profits of retailer n and the respective high‐quality manufacturer for any w n 1 . This property extends also to the providers of products i > 1 . Then, the respective objective function of the retailer becomes                 () ()() pc I qc qwXqp−+( −2)( −)+ −− , nHHHHn inHn 11 (A2) which equals that in (A1). Next, given marginal wholesale prices equal to marginal brand manufacturer costs, the determination of fixed fees follows from the argument in the main text as follows. For this we show that when a retailer rejects the offer of the high‐quality manufacturer of any category i , the deviation profit, gross of the fixed fees Tn jfor all other manufacturers j , is obtained by attracting only the respective locked‐in fraction of consumers. We show this first when i = 1 . Consider generally any two levels of net utility that a retailer may offer to consumers, ss′<″.We show that when offering s ′ is weakly preferred for a retailer that (on‐equilibrium) chooses q q= nH 1 , offering the lower net utility is strictly preferred when the retailer deviates to q q= n L . Formally: Making use of the expression Xs( ) nfor expected demand, as well as prices pqs ′=− ′ HH and pqs ″=−″ HHwith high quality and prices pqs ′=− ′ LLand pqs ″=−″ LL with low quality, we claim that ≥qsc I qcXs qsc I qcXs [ (−′− )+( −1)( −)] ( ′)[(−″− )+( −1)( −)] ( ″ ) HHHHn HHHHn implies qsc I q cXs qsc I q cXs [ (−′− )+( −1)( −)] ( ′)>[( −″− )+( −1)( −)] ( ″) , LLHHn LLHHn which indeed holds from Δ >Δ qc . 33 As we already know that offering zero net utility ( pq= n H ) yields the equilibrium profits, offering zero net utility (now pq= n L ) must then indeed be uniquely optimal when deviating to q q= n L . From the respective expressions for π , we then obtain from a retailer's indifference, which must hold by optimality for the manufacturer, that Tλ =(Δ−Δ)1− 2 . nqc 1 We can now apply this argument also to all categories i > 1 , after noting the equivalence of the respective expressions as used already when we compared (A1) with (A2). □ Proof of Lemma 1. Consider a candidate equilibrium where retailers stock high quality in all categories. From this, we determine a retailer's deviation profits. Suppose thus that retailer n , instead of choosing q q= n H in 70 | INDERST and OBRADOVITS category i = 1 , deviates to q q= n L . Then, given the rival retailer's anticipated choice of q q= n H ′ in the same category and the corresponding product price drawn from ⋅F( ) as given in (4), when setting an arbitrary price p L , the deviating retailer n makes an expected deviation gross profit of                                                         πpq p c I q c λλFpq q pc I q c λIq c q qpc I qc (; )=[ −+( −1)( −)] 1− 2+1− = [−+( −1)( −)]1− 2(−) −+( −1)( −) , nLL L LHHL H L LLHHHH H L LHHH where the last equality follows from inserting ⋅F( ) and simplifying. It now holds that ∂ ∂ πpq p (;) nLL L has the same sign as ≡ η Iq qcc I q cq q () −−(−1)( −)Δ, H L LH HH L which is, in particular, independent of p L . Hence, the deviation gross profit πpq(; ) nLL is monotonic in p L .If ≥ η I() 0 , which is equivalent to ≤              Iq qc I Δ Δ−Δ −= , H q qc HH  the optimal deviation price is the highest feasible price pq= L L , yielding thus a maximal deviation gross profit of πqq q c I q c λ (; )=[ −+( −1)( −)]1− 2 . nLL L LHH If instead η I()< 0 (i.e., II>  ), the optimal deviation price is p q q L H , which guarantees that all shoppers are attracted. The corresponding deviation gross profit is then                                       πq qpq q qpc I q c λ ;= −+( −1)( −)1+ 2. nL H L L H LHH □ Proof of Proposition 3. In Lemma 1, we have derived the optimal deviation pricing strategy and from this the corresponding profits when a retailer deviates to stocking q L in category i = 1 . Recall now that the brand manufacturer in i = 1 can extract as a fixed fee (and thereby, profit) the difference of the retailer's gross profit when stocking qH at the marginal wholesale price c H , πqqcI λpc I q c λ ()=( −)1− 2=[ −+( −1)( −)]1+ 2 , nHH HH HH and the retailer's maximal deviation profit. Hence, when ≤II  , the brand manufacturer in i = 1 makes a profit of qcIλqc I q c λ λ Π=( −)1− 2−[−+( −1)( −)]1− 2 =(Δ−Δ)1− 2, MHHLLHH qc 1 INDERST and OBRADOVITS | 71 that is, the same as other brand manufacturers. But when II>  , the brand manufacturer in i = 1 makes a profit of                                                                                                                                         pc I q c λq qpc I q c λ pqq qcc λ λλIqqc λλIqqc λ λλqqcI q qc λλqqcII Π=[ −+( −1)( −)]1+ 2−− +( −1)( −)1+ 2 =−−(−)1+ 2 =1+ 2(Δ−Δ)−Δ(−) =1− 2(Δ−Δ)−Δ(−)+ (Δ−Δ) =1− 2(Δ−Δ)−Δ(−)−(Δ−Δ) Δ(−) =1− 2(Δ−Δ)−Δ(−)( −), MHHHL H LHH HL H HL qc q H HH qc q H HHqc qc q H HH qc H qHH qc q H HH 1  as stated in the proposition. Clearly, this is strictly lower than other brand manufacturers' profits of (Δ−Δ ) λqc 1− 2. Moreover, Π M 1 is clearly strictly decreasing in I , with I Π ()= (Δ−Δ ) Mλqc 1 1− 2  and I Π (˜)=0 M 1,as claimed. □ Proof of Proposition 4. In the subsequent lemma, we provide a full characterization of the equilibrium (product and pricing) strategies in category i = 1 , which implies the statements in the proposition. □ Lemma 2. If the converse of (7)holds such that II>˜,no equilibrium exists in which both retailers stock the branded product or the low‐quality product in category i = 1 with probability one.There exists a unique symmetric equilibrium involving mixed product strategies such that either retailer stocks the branded product in i = 1 with probability ∈                         α λ λ q Iqc qcqc *=1− 2 (Δ−Δ) (−1)( −)Δ+−(0, 1) , qc H HHq LHHL where α I *(˜)= 1 and α I *( ) strictly decreases in I . The equilibrium pricing strategies are as follows.Conditional on stocking qH in i = 1 ,a retailer draws his price in i = 1 from the CDF                                         Fp α λ λ qp pc I qc ()=1−1 * 1− 2 − −+( −1)( −) HH HH HHHH with support                         pp qq [ ,]= Δ Δ, . HH c qHH Conditional on stocking q L in i = 1 ,a retailer draws his price in i = 1 from the CDF () Fp α ()= 1− 1−* LL λ λ qp pc I q c 1− 2 −Δ − −+( −1)( −) HcL LLHH 72 | INDERST and OBRADOVITS with support                         pp p q [ ,]= −Δ,Δ Δ , LLcc qL where p is given in (3). In this equilibrium,the brand manufacturer in i = 1 charges no fixed fee and consequently makes zero profit. Proof. Recall from the main text that for II>˜, no equilibrium exists in which both retailers stock the branded product in i = 1 for sure or where both retailers stock the low‐quality quality product in i = 1 for sure. In what follows, we confine ourselves to proving existence of the outlined symmetric mixed‐strategy equilibrium in product choice (and pricing). The proof for why this is also the unique symmetric equilibrium is slightly more subtle and is available from the authors upon request. For existence, note first that when retailers stock different products in i = 1 in the candidate equilibrium, then firms' price distributions are such that ∕∕ q pqp< HH L L with probability one (as ∕∕ q pqp= HHL L , ≥pp H H and ≤pp LL ). Hence, a retailer stocking qH in i = 1 (at marginal wholesale price c H ) and setting some price ∈ppp[,] HHHonly attracts the shoppers if its rival stocks the high‐quality product as well and chooses a price higher than p H (which has joint probability α Fp *(1 −() ) HH ). Therefore, such a retailer's expected gross profit is given by                              πpq p c I q c λλα Fp qcI λ (; )=[ −+( −1)( −)] 1− 2+*(1 −()) =( −)1− 2, nHH H HHHH H HH where the second equality follows from inserting ⋅F() Hand simplifying. If instead a retailer stocks q L in i = 1 and sets some price ∈ppp[,] LLL, the retailer attracts the shoppers whenever the rival stocks qH in i = 1 (probability α* ) or when the rival stocks q L in i = 1 and chooses a price higher than p L (joint probability αFp ( 1−*)(1 −() ) LL). Therefore, such a retailer's expected gross profit is given by          {} {} πpq p c I q c λλα α Fp pc I q c λλαFp qcI λπpq (; )=[ −+( −1)( −)] 1− 2+[ *+(1−*)(1 −( ))] =[ −+( −1)( −)] 1− 2+[1−(1 −*)()] =( −)1− 2=(;), nLL L LHHL L LLHHL L HHn HH where the third equality follows from inserting ⋅F( ) Land simplifying. As a first implication, note that the retailers are indeed indifferent between stocking qH in i = 1 and setting any price ∈ppp[,] HHH, or stocking q L in i = 1 and setting any price ∈ppp[,] LLL. A further implication from this indifference is that the brand manufacturer in i = 1 can indeed not charge a positive fixed fee. Further, retailers cannot profitably deviate by stocking qH in i = 1 and pricing above pq= H H (as this would imply zero demand) or stocking q L in i = 1 and pricing below p L (as already by setting pp= L L , the shoppers are attracted with certainty). It remains to show that the retailers do not wish to deviate by stocking qH in i = 1 and pricing strictly below p H (giving them a chance to attract the shoppers even when the rival stocks q L in i = 1 )orby stocking q L in i = 1 and pricing strictly above p L (risking to lose the shoppers also when the rival chooses qH in i = 1 , but realizing a higher margin on each sale of i = 1 ). We prove this next. To see the former, note that for pp< H H , a retailer's expected gross profit is given by INDERST and OBRADOVITS | 73                                         πpq p c I q c λλαFpq q (; )=[ −+( −1)( −)] 1+ 2−(1 −*) , nHH H HHHL H L H as the mass λ of shoppers is attracted unless the rival stocks low quality in i = 1 and prices below p H q q L H (joint probability αFp ( 1−*)( ) LH q q L H ). Plugging in ⋅F( ) Land simplifying yields                              πpq p c I q c λIq c pcIqc (; )=[ −+( −1)( −)] 1− 2 (−) −+( −1)( −) nHH H HHHHH H q qLHH L H for pp< H H . The derivative of πpq(; ) nHH with respect to p H has the same sign as q cqc I qc−+( −1)( −)Δ . LHHLHHq This is strictly positive for II>  , which is true since by assumption II>˜and it holds that II ˜>  . We have thus shown that it is indeed not profitable to deviate to prices p H below p H . If instead a retailer stocks q L in i = 1 and chooses a price ∈ppq(,] LLL , its expected gross profit is                                                         πpq p c I q c λλα Fp q q (; )=[ −+( −1)( −)] 1− 2+*1− , nLL L LHHH L H L as the mass λ of shoppers is only attracted when the rival retailer stocks qH and chooses a price that exceeds p L q q H L (joint probability α Fp *(1 −()) HL q q H L ). Inserting ⋅F() Hand simplifying yields                              πpq p c I q c λIq c pcIqc (; )=[ −+( −1)( −)] 1− 2 (−) −+( −1)( −) nLL L LHHHH L q qHHH H L for all ∈ppq(,] LLL . The derivative of πpq(; ) nLL with respect to p L now has the same sign as qc q c I q c − [−+( −1)( −)Δ] , LHHLHHq which is strictly negative as III>˜>  . Hence, also deviation prices p L above pLare not profitable. Taken together, we have thus shown that the outlined symmetric strategies indeed constitute an equilibrium, while no equilibrium exists where in i = 1 either the high‐or the low‐quality product is chosen with probability one. We finally note that all CDFs and probabilities used in the construction of the equilibrium are well‐behaved as follows: α I *(˜)= 1 (as is easy to check), so that ∈ α I *() (0,1) , which is also strictly decreasing in I for II>˜, Fp Fp()=()=0 HHLL,Fp Fp()= ()= 1 HHLL, and Fp( ) HHand Fp() LL are strictly increasing in their arguments for ∈ppp[,] HHHand ∈ppp[,] LLL, respectively. □ APPENDIX B: ALTERNATIVE FOUNDATIONS FOR CONSUMERS' CHOICE RULE As discussed in the Introduction, the notion of context‐dependent preferences has been formalized in various ways in the literature, and we do not claim that our formalization based on “salient thinking”(building on Bordalo et al., 2013 and the adaptation to imperfect competition in Inderst & Obradovits, 2020) is generally preferable. In fact, in our specific context, the same outcome would be obtained from alternative specifications, as we will briefly outline in this appendix. 74 | INDERST and OBRADOVITS For this, suppose first that when comparing two offers, it is simply the relative difference in qualities and prices that matters (“pairwise relative thinking”). To make this precise, note that for two undominated offers with different qualities, the high‐quality offer has a ⋅ 1 00 qq q − HL L percent higher quality than the low‐quality offer, but also a ⋅ 1 00 pp p − HL L percent higher price. Suppose now that a consumer prefers the cheaper low‐quality offer when the difference in quality is relatively lower than the difference in prices in this (percentage) sense, that is, when qq q pp p −<− . HL L HL L (B1) Reorganizing inequality (B1), we can alternatively say that the consumer prefers the low‐quality offer when q p q p > L L H H (B2) and the high‐quality offer when the converse holds strictly. In other words, consumers may also compare offers in terms of the respective “quality‐per‐dollar,”and choose the offer that provides the highest value in this sense, for example, low quality when condition (B2) holds. 34 It is immediate that conditions (B1) and (B2) are equivalent to our earlier condition (2). Finally, we note that this choice logic also pertains when consumers derive a constant marginal utility from quality and maximize consumption with respect to a binding fixed budget constraint, as motivated from a theory of mental accounting (Thaler, 1985). To see this, suppose that consumers choose quantities ≥x0 nso as to maximize ∈  xq p(− ) nNnnn subject to the (binding) category‐specific resource constraint ≤ ∈  xp E nNnn (where E is the budget allocated to the considered category in the mental account). When the constraint binds, we are again back to our choice criterion of salient/relative thinking. 35 APPENDIX C: BENCHMARK MODEL WITH ELASTIC DEMAND In this appendix, we consider a straightforward extension of our benchmark model in which all consumers had the same reservation value for shopping (of zero). Instead, we now suppose that consumers differ in their reservation values. Our aim is to show that in such a model variant, the brand manufacturer's profit in the promoted category i = 1 is strictly increasing in the degree of one‐stop shopping I , and that its profit is strictly larger than the profits of the brand manufacturers in all other categories i > 1 . Suppose henceforth that the consumers have heterogeneous reservation values ≥θ0 , where θ is distributed according to some atomless CDF G θ() , with G (0) = 0 and strictly positive density ≡gθGθ() ′( ) in the interior of its support. To guarantee that the subsequent analysis is well‐behaved, we further assume that ∕gθGθ() ()is weakly decreasing, which is, for example, satisfied if the density of consumer reservation values is (weakly) decreasing in their size. Following the logic from our baseline model, we start by observing that, first, for all products the more efficient high quality will be stocked and, second, that in equilibrium marginal wholesale prices equal marginal costs. Observe next that a retailer's expected (gross) profit with any nonshopping local consumer is πppcI qcGqp()=[ −+( −1)( −)] ( −) . HHHH (C1) Since, by assumption, ∕gG is weakly decreasing, it is easy to see that pπp=argmax ( ) mp is uniquely determined and results in (per‐consumer) expected profits of ππp=( ) mm . Thus, when a retailer only attracts nonshoppers, its maximum profit is π λm 1− 2(gross of any fixed fee paid to the manufacturer). We now turn to the derivation of manufacturer profits. Take i = 1 with respective profits Π M 1 . From the respective indifference condition for each retailer, we now have that () λππ Π =1− 2− , MH mL m 1 INDERST and OBRADOVITS | 75 where π H mdenotes the maximum profit when the retailer stocks qH at cost c H and πL mdenotes the respective maximum profit when the retailer instead stocks q L at cost cL. Using uniqueness of the respective prices p H m and p L m and applying the envelope theorem, it follows that                 ()() d dI qc λGq p Gq p Π=( −)1− 2−− − . M HHHH mLL m 1 To show that the profits of the brand manufacturer in i = 1 increase with the extent of one‐stop shopping, it thus remains to prove that q pqp−>− HH mLL m, that is, pp−<Δ. H m L mq(C2) To see this, it is now convenient to denote more generally pqc(, ) m as the “monopoly price”when, at i = 1 , quality q is stocked at cost c . With this, we rewrite ppcIqcGqp pcIqcGqp pcIqcGqp pq c =argmax [( −+( −1)( −)) ( −)] =argmax [( −Δ − +( −1)( −)) ( −(−Δ))] −Δ =argmax [( −(Δ+)+(−1)( −)) ( −)] −Δ =(,Δ+)−Δ, L mpLHHL pqL HHLqq pqL HHHq mHqL q where the second equality follows because fx fx h h a rg max ( ) = (arg max ( + )) + xx . Hence, plugging in ppq c=(,Δ+)−Δ L mmHqL q , the requirement (C2) transforms to ppqc pq c=(,)<(,Δ+). H mmHHmHqL This is true as ∂ ∕∂pqc c(, ) >0 m and as cc Δ +> qL H from Δ >Δ qc . With respect to manufacturer profits, it remains to prove that, with elastic demand, Π >Π Mi M 1for i > 1 . To see this, we have to derive Π i M , using again retailer indifference. For this, we now make use of expression (C1) as follows. On equilibrium, the retailer's gross profits are π λm 1− 2. Off equilibrium, after rejecting the offer of one manufacturer in some category i > 1 , the retailer's maximum profits are again obtained by targeting only nonshoppers and choosing the respective optimal “monopoly”price p , thereby now realizing (per‐consumer) profits pc I q c q cGq pmax [ −+( −2)( −)+( −)] ( −). pHHHLLH We denote these per‐consumer profits by π HL m, , indicating that high quality is offered in category 1 (as well as in I− 2 additional categories), while in one (nonpromoted) category low quality is offered. Consequently, we have, for i > 1 , () λππ Π =1− 2− , i MH mHL m, so that Π >Π Mi M 1holds if and only if ππ< L mHL m, . This is the case if pc I q cGq p pc I q c q cGq pmax [ −+( −1)( −)] ( −)<max[ −+( −2)( −)+( −)] ( −). pLHHLpHHHLLH Recall that the maximizer of the first expression is denoted by p L m . Clearly, the second expression is bounded from below when we substitute some arbitrary price p ′ , such as pp ′=+Δ L mq . The second expression is thus bounded from below by                 () pcI qcGqp−+( −1)( −)− , L mLHHLL m 76 | INDERST and OBRADOVITS