Manufacturer-Retailer Pricing Competition Across Multiple Product Categories: An Equilibrium Framework

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1 Manufacturer-Retailer Pricing Cometition Across Multile Product Categories: An Equilibrium Framework Benjamin Kartono Nanyang Technological University This aer investigates ricing cometition between manufacturers and a common retailer across multile roduct categories using an equilibrium framework. Rather than assuming a standard Nash equilibrium outcome to the channel s ricing game, the allows for deendencies in ricing behavior between channel members and is flexible enough to accommodate deviations from a Nash equilibrium. Results suggest that accounting for ricing behavior across multile roduct categories affects cometitive intensity and the distribution of channel rofits, suggesting that manufacturer and retailer ricing decisions across the two categories are deendent and involve cross-category coordination. Imlications of the results for managerial ractice are discussed. INTRODUCTION The study of cometitive interactions between channel members has received considerable attention in the marketing and economics literature. Issues such as the coordination of channel decisions, rice cometition among channel members, vertical contracting, and bargaining ower between manufacturers and retailers, among others, have been studied. Much of the extant research on channel interactions has examined the issue for secific industries or within a single roduct category. The objective of this exloratory aer is to extend the existing research on channel cometition by develoing an emirical that accounts for the effects of cross-category interactions between channel members cometing in multile roduct markets, within an equilibrium, game-theoretic framework. In articular, the aer examines whether manufacturers and retailers tend to coordinate their ricing decisions across different roduct categories and if doing so enables them to comete more effectively by realizing a higher ercentage of channel rofits. In addition, rather than assuming a standard Nash equilibrium outcome to the channel s ricing game, the allows for deendencies in ricing decisions between the channel members via the estimation of a set of conduct arameters that cature the nature of the cometitive interactions in the channel and allow these interactions to vary according to the data, making the more flexible to ossible deviations from a Nash equilibrium and more reflective of the actual nature of the channel cometition. In the theoretical literature, various issues ertaining to channel interactions have been studied. Jeuland and Shugan (98) looked into the roblem of coordinating of various decision variables among channel members within the context of managing and otimizing channel rofits in a single-manufacturer, singleretailer channel, and McGuire and Staelin (98) examined the extent to which the substitutability of a manufacturer s roducts may affect its distribution structure. Choi (99) examined channel interactions between multile cometing manufacturers and a common retailer, and he demonstrates how an Journal of Alied Business and Economics vol. () 0 7

2 indeendent retailer can be a owerful layer in the market, unlike comany-owned retail stores or exclusive franchises or dealershis. Along the same lines, Lee and Staelin (997) studied the issue of rice leadershi and roduct line ricing for various s of channel interactions involving multile layers, including a two-manufacturer, two-retailer, while Iyer and Villas-Boas (00) develoed a theoretical of bargaining ower to examine its effects on vertical coordination between channel members. While these and similar studies have contributed significantly to our theoretical understanding of channel cometition, they are generally confined within the context of a single roduct category, and do not consider firms simultaneous marketing decisions across multile roduct categories. The emirical literature on channel interactions has also mainly looked into cometition within a single roduct category: Besanko et al. (998) studied the imortance of treating rices as endogenous variables in an alication of the Choi (99) of cometitive ricing between two manufacturers and a common retailer, Kadiyali et al (000) and Sudhir (00) also used a two-manufacturer, singleretailer framework to build equilibrium s of cometitive ricing behavior, and Villas-Boas (00) studied different s of vertical contracting in a market with multile manufacturers and multile retailers. More recently, Villas-Boas and Zhao (005) develoed comrehensive equilibrium s to study the level of manufacturer cometition, channel interactions, and the retailer s roduct-category ricing behavior in the ketchu market, and Draganska et al. (00) examined the relative bargaining ower between manufacturers and retailers by develoing a that exlains why channel ower has shifted from manufacturers to retailers in recent years. While these and other aers in the emirical literature have rovided valuable insights on the nature of channel cometition between manufacturers and retailers, one limitation of these studies - as with the theoretical literature - is that they are largely done within the context of individual roduct categories. In ractice, firms may not make their marketing decisions in any one roduct category indeendently of their decisions in the other roduct categories that the firm is cometing in, and if so, such cross-category effects need to be taken into account. In addition, with the excetion of a few aers like Kadiyali et al. (000), most game-theoretic studies on channel interactions assume a standard equilibrium outcome (such as a Nash or a Stackelberg equilibrium) to the cometitive interactions. While such assumtions are based on sound economic theory and are generally adequate for many situations, in ractice, deviations from these standard outcomes may occur which are not catured in these s. To account for this ossibility, a more flexible of channel interactions that secifically catures such deviations (based on the observed data) would be needed. Along with the develoment of the literature on channel interactions, two other streams of literature have influenced the develoment of this aer. The first is the emirical literature on multi-market contact. Parker and Roller (997) used a structural of cometition to study the effects of multimarket contact and cross-ownershi in the mobile telehone industry, and their analysis suggested that a comany s cometitive behavior in one market may be a function of the characteristics of the other markets. Another examle is Shankar (999), who studied the effects of multi-market contact on a firm s new roduct introduction strategies and an incumbent firm s resonse strategies to a otential entrant to the market, and found that multi-market contact led to a lower sending on new roduct introduction as well as a milder resonse on the art of the incumbent firm. These aers suggest that multi-market contact between cometing firms may affect their strategic behavior in each market because marketing decisions within any one market may affect the firm s erformance in other related markets. Within the domain of channel interactions, it is thus reasonable to exect manufacturers to coordinate their marketing decisions across multile roduct markets or categories. The second stream of literature that has motivated the develoment of this aer is the consumer demand literature on household buying behavior across multile roduct categories. For examle, Ainslie and Rossi (998) studied the sensitivity of households to marketing mix variables by looking at correlations in buying behavior across different categories, and they found that significant correlations do exist, even for roducts that are not comlementary or related to each other. Manchanda et al. (999) further showed the existence of cross-category deendencies in consumer urchase decisions, esecially among comlementary roducts or roducts that are urchased within a similar urchase cycle. These studies suggest that consumers urchase decisions across different roduct categories are not 8 Journal of Alied Business and Economics vol. () 0

3 indeendent, which in turn would further influence the way firms coordinate their marketing decisions across these roduct categories. This aer attemts to integrate these streams of research and extend the literature on channel interactions in a unified framework. The existing literature on cometitive channel interactions and multimarket contact is combined by studying channel interactions across two different roduct categories, and the imact of consumer demand on firms strategic decisions is incororated into the framework by building an equilibrium of suly and demand that is flexible enough to accommodate a variety of channel interactions and cature emirical deviations from the Nash equilibrium outcome. Being an exloratory aer on cross-category channel cometition, the interactions among channel members have been confined to their rice-setting behavior. The study focuses on the ricing interactions between two national brand manufacturers of bathroom tissues and aer towels, P&G and Georgia-Pacific, and a local retailer in a major U.S. metroolitan area. In the next section, the mathematical for oerationalizing the cometitive ricing interactions between the channel members is resented. This is followed by a descrition of the data used to estimate the and a discussion of the estimation results and managerial imlications. The aer concludes by suggesting some areas for future research. MODEL The roosed is develoed within the context of an oligoolistic market consisting of two national brand manufacturers and a common retailer, cometing across two roduct categories. The retailer carries both national brands and also has its own rivate label in both roduct categories. To examine the imact of cross-category effects on channel interactions, two emirical s will be estimated. The basic is a single-category that assumes no cross-category effects and is estimated searately for each roduct category. The second is a that accounts for the ossibility of cross-category coordination of ricing decisions across the two roduct categories. Although only the manufacturers and retailers ricing decisions will be ed in this aer, the can also be extended to incororate other relevant marketing decisions such as advertising or distribution. Basic Model The basic in this aer is develoed using the aroach in Kadiyali et al. (000). By adoting an equilibrium ing aroach that takes into account both suly and demand considerations, both the manufacturers and retailer s ricing behavior, as well as consumer demand, can be ed and the relevant arameters estimated simultaneously. In order to obtain closed-form solutions to the manufacturers and retailer s ricing roblems, many studies on channel cometition have tyically had to restrict the interactions between the channel members to result in a articular form of equilibrium, most commonly a Nash equilibrium. In a Nash equilibrium, the channel members make their ricing decisions simultaneously under the assumtion that each member has made the best decision ossible in resonse to their exectations of the other layers strategies. Although intuitively and theoretically aealing, a Nash equilibrium may not always aly in ractice because channel members may have an incomlete understanding of their cometitors or the market and may thus under-react or over-react in their decisions. In this, no simlifying restrictions on the interactions between the channel members are imosed so that it is flexible enough to accommodate a variety of ricing interactions, measured in the form of a set of conduct arameters, which are estimated from the data and are used to determine if the nature of the interactions deviates from the basic Nash equilibrium outcome. The demand side of the consists of linear consumer demand functions, as traditionally ed in the consumer economics literature, aggregated across all the stores of the retail chain. On the suly-side, the manufacturers and retailers are assumed to maximize their rofits within each roduct category, and the cometitive ricing equations for the manufacturers and retailer are derived from the first-order conditions of their rofit-maximizing behavior. For each roduct category, three brands will be studied, one from each manufacturer (the brand with the highest market share for that manufacturer), and the retailer s own rivate label. For exository Journal of Alied Business and Economics vol. () 0 9

4 uroses, the two manufacturer brands will be designated as brand (P&G) and brand (Georgia- Pacific), while the retailer s rivate label will be designated as brand. Demand Secification The demand facing the retailer for each brand is a linear, semi-logarithmic function of the sales of brand i, denoted by q i, comrising of the rice of the focal brand under study, i, the rices of the other two cometing brands, a dummy demand shifter variable, ddshifter, that catures seasonal variations in demand, and a romotional variable for the brand, deal, that catures the in-store romotions occurring in any given week for the brand. The demand shifter and romotional variables are treated as exogenous variables in the. For each brand i, i =,,, the demand secification is: q a b *ln( ) c *ln( ) d *ln( ) g * ddshifter h * deal. i i i i i i i i i where a i, b i, c i, d i, g i, and h i are arameters to be estimated and i is the error term. There are other functional forms available for the demand secification (such as a linear or a log-log ) that can rovide comarable fit; the main reason that this secification was chosen was that it facilitated the identification of the conduct arameters used in analyzing the channel interactions. Another reason for the semi-log secification is that it does a good job of caturing the tyically non-linear relationshi between sales level and rices. Manufacturer Pricing Equations On the suly side, the rofit function for each manufacturer i, i =,, is given by:. ( m mc )* q i i i i Each manufacturer is assumed to maximize its category rofit for each roduct, i, with resect to the manufacturer s selling rice (i.e. the wholesale rice aid by the retailer), which is reresented by m i. The manufacturer s marginal cost of roduction, denoted by the arameter mc i, is estimated from the data. To derive the otimal ricing function for the manufacturer, consider the rofit function for P&G, the manufacturer of brand. Substituting equation into, the following equation for the rofit earned by brand is obtained: ( m mc ) * a b *ln( ) c *ln( ) d *ln( ) g * ddshifter h * deal. The manufacturer is assumed to maximize its rofit for brand with resect to its selling rice to the retailer. These first-order conditions, obtained by taking the artial derivative of equation with resect to m, are given by: b c d 4. ( m mc )*( * * * ) q 0 m m m Let the retail rice of each brand i be the sum of the retailer s margin on brand i, r i, and the manufacturer s selling rice to the retailer, m i, i.e., i = r i + m i. The artial derivative of the retail rice of brand,, with resect to m, is given by m r mand that of brand,, with resect to m is given by m m m r m. Each channel member s rice-setting behavior can thus be denoted by a vector of conduct arameters, which, in this case, is, m ),, m, m )}, where the arameter,, denotes the artial derivative of variable x with resect to variable y ( x y) that catures the change in x with resect to y. The first-order conditions in 0 Journal of Alied Business and Economics vol. () 0

5 equation 4, which reresents manufacturer s otimal ricing function for the wholesale rice, m, that maximizes brand s rofit, can thus be written as: 5. m mc q b c d *( ( r, m )) * (, m ) (, m ) The otimal ricing function for manufacturer, as written in equation 5, is an exression of its margin, (m - mc ), as a function of the retail demand for brand, the demand arameters, as well as a set of conduct arameters that describe the retailer s ricing behavior in resonse to manufacturer s setting of the wholesale rice, m. By looking at how the estimated arameter, m ), affect manufacturer s margin, the game that the retailer lays with the manufacturer can be analyzed. For examle, if the interaction between manufacturer and the retailer is a Nash equilibrium (i.e. manufacturer has resonded in the best ossible way given its exectations of the retailer s ricing behavior), all the conduct arameters would be equal to zero, and manufacturer s margin for this case can be calculated accordingly. If the estimated conduct arameters results in a manufacturer margin that is smaller than the Nash case, it means that the retailer is ricing more cometitively than Nash, because it is able to aroriate art of manufacturer s margin. Conversely, if the estimated conduct arameters results in a manufacturer margin that is larger than the Nash case, it means that the retailer is ricing less cometitively, or softer, than Nash. The latter does not imly cooerative behavior, as the manufacturer and retailer are not jointly maximizing channel rofits but are still maximizing their rofits individually. Pricing softer than Nash results from realizing the deendence of one s own rofits on those of the other firms. A similar otimal ricing function for m is obtained in a similar manner for manufacturer : q 6. m mc b c d *( ( r, m)) * (, m) (, m) The same analysis of the retailer s ricing behavior towards manufacturer can be erformed by looking at the arameter, m ). Retailer Pricing Equations The retailer is assumed to maximize its rofit across all the three brands that it is carrying with resect to each brand s retail margin (as determined by the retail rices that the retailer sets), and its rofit function can be written as follows: 7. retailer i i j r * q To derive the retailer s otimal ricing equation for each brand, consider the retailer s ricing behavior for brand. The first-order conditions for equation 7 with resect to the retailer s margin for brand, r, is given by: 8. b m c m q j j rj *( *( ) ( )) 0 j r r Journal of Alied Business and Economics vol. () 0

6 Rewriting equation 8 in conduct arameter terminology, the retailer s margin for brand can be written as: 9. r b c q r ( *( ( m, r)) * ( m, r)) j j j j b c *( ( m, r )) * ( m, r ) Equation 9 thus reresents the retailer s otimal ricing equation for brand, exressed as a function of brand s retail margin, r. The conduct arameters in this ricing equation, which are also estimated from the data, describe the corresonding ricing game that manufacturer lays with the retailer. In equation 9, the arameter,r ) reresents manufacturer s rice-setting behavior of its wholesale rice, m, in resonse to the retailer s retail rice-setting behavior and the resulting retail margin, r. Under a Nash equilibrium assumtion, r is calculated by setting,r ) = 0 (while keeing the other arameters at their estimated values). If the estimated value of,r ) results in a retail margin that is smaller than the Nash equilibrium margin, manufacturer is ricing more cometitively than Nash, and if the estimated value of,r ) results in a retail margin that is larger than the Nash margin, manufacturer is ricing less cometitively than Nash. Similar equations can be obtained for the otimal retailer ricing rules for brand and the retailer s own rivate label, brand, and a similar analysis of manufacturer s games with the retailer can be conducted. The resulting otimal retailer ricing equations for brands and are: 0.. r r q q j b j b j r j ( * ( ( m, r b j r j ( * ( m, r c )) c )) c * ( ( m, r )) b c * ( ( m, r )) j * ( ( m * ( ( m j * ( m * ( m, r )) d, r ), r ))) d, r ) j ) The ricing interactions between the manufacturers and retailers as reresented by the conduct arameters given in the otimal ricing equations can be reresented in a schematic diagram as shown in Figure. Arrows and are the horizontal interactions between the manufacturers, i.e. i,m j ). Arrow catures manufacturer s resonse to the retailer s ricing behavior for brands,, and, given by,r,r ), and,r ), and arrow 4 catures the retailer s resonse to manufacturer s rice-setting behavior of brand, given by,m,m ), and,m ). Arrows 5 and 6 describe the same interactions between manufacturer and the retailer as arrows and 4 do for manufacturer. Note that not all of the conduct arameters in the diagram are distinctly identifiable for estimation uroses. These include the horizontal interactions between the manufacturers, i,m j ), and the resonse of the retailer on the ricing of one brand in resonse to the manufacturer s rice-setting behavior for another brand, i,m j ) for i j, as both these arameters are subsumed within i,m j ). However, since the focus of the aer is to study manufacturer-retailer interactions, being able to estimate i,m j ) is sufficient for this urose. The estimation of the other arameters, however, will be a fruitful area for future research. Journal of Alied Business and Economics vol. () 0

7 FIGURE CONDUCT PARAMETERS REPRESENTING MANUFACTURER-RETAILER CHANNEL INTERACTIONS Manufacturer Retailer Manufacturer Arrow Conduct Parameters,m ),m ),r,r,r ) 4,m,m,m ) 5,m,m,m ) 6,r,r,r ) Two-Category Model The two-category builds uon the basic described in the revious section. If crosscategory effects exist, it is reasonable to ostulate that the conduct arameters describing the channel interactions in any one category may be a function of the market characteristics of the other categories. This idea is consistent with the multi-market study of the mobile telehone industry in Parker and Roller (997). A ertinent market characteristic that can be used to reresent cross-category effects is the market share, or a function of the market shares, of the roducts in each category because the relative size and market ower that a firm has relative to the cometition across different roduct categories can affect its ricing behavior in each category. This aroach results in an analogous set of conduct arameters which can be estimated from the data and which describe the same manufacturer-retailer interactions for the two-category case as the conduct arameters for the single-category case. Secifically, to cature the market outcomes of the firms marketing decisions in both roduct categories, the two-category is develoed with the conduct arameters as a function of the sum of the market shares of both roduct categories under study, as shown in equation. In this, the conduct arameters are denoted by x s (to reresent retailer interactions) and y s (to reresent manufacturer interactions) to differentiate them from the s used in the single-category case, MS i, cat and MS i, cat reresent the market shares of brand i in the two categories, while MS j, cat and MS j, cat denote the market shares of brand j in the two categories.. ( r, m ) x *( MS MS ) i i ii i, cat i, cat ( MSi, cat MSi, cat ) ( i, mj) xij * ( MS MS ) j, cat j, cat ( m, r ) y *( MS MS ) i i ii i, cat i, cat ( MSi, cat MSi, cat ) ( mi, rj) yij * ( MS MS ) j, cat j, cat With this secification, the estimation results for the two-category can be comared with the single-category to see if accounting for cross-category effects result in differences in the channel members ricing behavior in any one category. Journal of Alied Business and Economics vol. () 0

8 EMPIRICAL ANALYSIS Data and Estimation The is estimated using a data set consisting of weekly retail sales data of bathroom tissues and aer towels for Dominick s Finer Foods (DFF), a large retail chain in the Chicago area, aggregated across stores for aroximately a five-year eriod from 99 to 997. This data set is ublicly available at the website of the University of Chicago Booth School of Business. The two manufacturers, P&G and Georgia-Pacific, have the largest market shares in both the roduct categories of bathroom tissues and aer towels for the time eriod under consideration. Examle of bathroom tissue and aer towel brands sold by these manufacturers include Charmin and Bounty for P&G, and Quilted Northern and Brawny for Georgia-Pacific. For each category, the to-selling brand sold by each manufacturer was selected for analysis. The retailer also has its own rivate label in both categories. The variables obtained from the data set include the retail rice, the manufacturer s wholesale rice to the retailer, unit sales, as well as the deal variable that catures information about weekly in-store romotions for a brand. In addition to the DFF data, sulemental data from the Bureau of Labor Statistics have also been obtained, including data on consumer and roducer rice indices (used to correct the retail and manufacturer rices for inflation over the five-year eriod), inut costs, and the average weekly wages for the State of Illinois, which is used as the demand shifter variable in the demand functions. The estimation of the is carried out using the SLS (-Stage Least Squares) rocedure in the SAS rogramming language. The instrumental variables used for the estimation are a series of lagged deendent variables (such as rices, sales, and the deal variable), lagged values of the demand shifter variable, and rices of manufacturing inut variables such as the cost of labor and materials. The comlete set simultaneous equations for the single-category consists of the three demand functions (equation for i =,, ), the two manufacturer ricing equations 5 and 6, and the three retailer ricing equations 9 through. The same equations are used for the two-category, excet that the conduct arameters in the manufacturer and retailer ricing equations are relaced by the multi-category conduct arameters given in equation. Results and Discussion Looking at the estimation results for both the basic and two-category s, it is interesting to note that none of the channel members are ricing less cometitively than the Nash equilibrium, suggesting a high level of cometition. In addition, a channel member s ricing strategy vis-a-vis its cometitors can change when multi-category effects are included in the analysis. The results for the basic examine the channel interactions within a single roduct category are given in Table. For bathroom tissues, the own-rice coefficients in the demand functions for all three brands are negative and significant, as exected. The estimated manufacturer marginal costs are also statistically significant and verified to be less than the manufacturer s wholesale rices, which rovide face validity to the. The same results are observed for the aer towel category. The key results of interest, however, are the conduct arameters, which describe secific airs of manufacturer-retailer interactions. For examle,, m ) describes the retailer s cometitive ricing resonse to its exectation of manufacturer s (P&G) ricing decision, while,r ) describes P&G s cometitive ricing decision in resonse to its exectation of the retailer s rices. Between the retailer and Georgia-Pacific, the arameters, m ) and,r ) reresent similar ricing interactions. In articular, it would be interesting to see whether these arameters deviate from a Nash equilibrium, which is the usual equilibrium outcome assumed in much of the game theoretic literature when no secific information on the nature of the cometitive interactions are available. As oerationalized in this, a conduct arameter that is not significantly different from zero would imly a Nash equilibrium; otherwise, a level of cometition that is more cometitive or less cometitive than a Nash equilibrium is imlied. 4 Journal of Alied Business and Economics vol. () 0

9 TABLE RESULTS FOR THE BASIC MODEL Bathroom tissues Paer towels Parameter Estimate Prob > t Estimate Prob > t P&G Own rice coefficient (unit/$) (Brand ) Marginal cost ($) Manufacturer margin ($) Georgia-Pacific Own rice coefficient (unit/$) (Brand ) Marginal cost ($) Manufacturer margin ($) Private label Own rice coefficient (unit/$) (Brand ) (r,m ) (> Nash) (> Nash) Conduct (r,m ) (> Nash) (Nash) Parameters (m,r ) (> Nash) (> Nash) (m,r ) (> Nash) (Nash) Looking at the ositive and significant estimates for (r i, m i ) and (m i, r i,) for bathroom tissues in Table, both the retailer and the manufacturers are resectively ricing more cometitively than a Nash equilibrium in their interactions with one another (denoted by the term > Nash in arentheses in Table ). For the aer towel category, P&G and the retailer are ricing more cometitively than Nash against each other as shown by the ositive and significant estimates of (m,r ) of.6 and (r, m ) of.95, but the interactions between Georgia-Pacific and the retailer aear to be one-sided: while Georgia- Pacific is taking a more aggressive ricing stance against the retailer by ricing more cometitively than Nash as denoted by the ositive and significant estimate of (m, r ) of.8, the retailer is not doing the same and is in fact ricing at a Nash equilibrium ((r,m ) is non-significant for aer towels). As a whole, there aears to be a fair amount of manufacturer-retailer cometition going on, which could be the result of the retailer having a significant rivate label in both categories. This is further suorted by the ositive signs on all the conduct arameters, which suggest that the channel layers rice their roducts in cometitive tandem with each other (i.e. if one exects the other to lower rice, one is likely to lower one s own rices as well). The more cometitive interactions between P&G and the retailer in aer towels (as comared to Georgia-Pacific and the retailer) may be exlained by the fact that P&G is the market leader in this category; hence it has a greater incentive to exert greater ricing ressure on the retailer to maintain its market leadershi. Likewise, the retailer aears to view P&G as a greater threat to its rivate label brand for aer towels, hence its more cometitive ricing decisions against P&G relative to Georgia-Pacific. As for Georgia-Pacific, it may be ricing more cometitively against the retailer in aer towels but not in bathroom tissues because the retailer s aer towel label is more significant than its bathroom tissue label (about 0% of market share for aer towels vs. about 5% for bathroom tissues). Table resents the estimation results for the two-category, with the conduct arameters secified as a function of the sum of the focal category s market share as well as the other category s market share. As before, the estimated own-rice coefficients and marginal costs look reasonable and significant. However, there are a number of interesting differences in the estimates of the conduct arameters. Journal of Alied Business and Economics vol. () 0 5

10 TABLE RESULTS FOR THE TWO-CATEGORY MODEL Bathroom tissues Paer towels Parameter Estimate Prob > t Estimate Prob > t P&G Own rice coefficient (unit/$) (Brand ) Marginal cost ($) Manufacturer margin ($) Georgia-Pacific Own rice coefficient (unit/$) (Brand ) Marginal cost ($) Manufacturer margin ($) Private label Own rice coefficient (unit/$) (Brand ) x(r, m ) (> Nash) (> Nash) Conduct x(r,m ) (> Nash) (> Nash) Parameters y(m,r ) (> Nash) (> Nash) y(m,r ) (Nash) ( Nash) First, the ositive and significant estimates of x(r,m) of 5.04 (bathroom tissues) and 6.4 (aer towels) show that the retailer is ricing more cometitively than Nash against P&G. Similarly, the ositive and significant estimates of y(m r) of.7 (bathroom tissues) and.54 (aer towels) show that P&G is ricing more aggressively than the Nash equilibrium against the retailer. Although these results are directionally similar to those in the basic, the magnitude of the arameters are different. Relative to the basic (which examined ricing cometition searately within each roduct category), the retailer aears to be ricing more aggressively against P&G, while P&G actually aears to be ricing less cometitively against the retailer. This result is observed for both roduct categories. Second, Georgia-Pacific is observed to be ricing at a Nash equilibrium against the retailer for both the bathroom tissue and aer towel category, as shown by the two non-significant estimates of y(m,r ) of. and.9, suggesting a reduction in cometitive intensity in Georgia-Pacific s overall ricing strategy when cross-category effects are taken into account. Finally, in terms of the retailer s ricing decisions towards Georgia-Pacific, the larger and significant estimates of x(r, m ) of 4.9 (bathroom tissues) and. (aer towels) suggest that, like its ricing strategy towards P&G, the retailer is also ricing more aggressively against Georgia-Pacific in both roduct categories, as comared to its ricing strategy in the basic. The general message from these results seems to be that accounting for cross-category effects in the results affects the observed level of cometitive intensity in the channel, suggesting that channel members ricing decisions involve cross-category coordination. In addition, this crosscategory effect differs across manufacturers and retailer: while manufacturers tend to rice less cometitively across two related roduct categories, retailers tend to rice more aggressively when coordinating their decisions across the two categories. These findings can be due to a number of reasons and have a number of managerial imlications. For related roducts such as bathroom tissues and aer towels, it is reasonable to exect the manufacturer to derive roduction efficiencies (such as economies of scale or sharing of roduction resources) from roducing both roducts at the same time. These efficiencies may result in lower roduction costs and higher margins, resulting in a smaller ush for manufacturers to comete aggressively with the retailer. 6 Journal of Alied Business and Economics vol. () 0

11 The retailer, on the other hand, does not get to enjoy such roduction efficiencies and is rimarily cometing on volume. As a result, it maintains a relatively aggressive ricing stance across both manufacturers across both roduct categories. Another reason why manufacturers aear to rice their roducts less cometitively when considering their ricing behavior across multile roduct categories is that they may be coordinating their ricing strategies across the categories to fulfill a marketing objective and are hence less inclined to comete fiercely in any one category without considering its effects on the other roduct. For instance, if P&G bathroom tissues and aer towels are ositioned as remium, high quality roducts relative to rivate labels and are also riced at a remium, a minimum rice threshold is needed to maintain the roducts ositioning, and cutting rices excessively in one category may affect the roduct s brand image in the other category. Finally, the difference in the observed results between the basic and the two-category have imlications on the distribution of rofits between manufacturer and retailer in the channel. Table resents a comarison of the distribution of channel rofits between the manufacturers and the retailer for the two s. In the interaction between P&G and the retailer in the basic, 8.% of the channel rofits went to P&G for bathroom tissues, while the figure is at 67.% for aer towels. Between Georgia-Pacific and the retailer, 76.% of the channel rofits for bathroom tissues went to Georgia- Pacific while the figure is at 5.7% for aer towels. The results for the two-category show a similar attern in the distribution of rofits, excet that a larger share of the channel rofits are accrued to the manufacturers: 87.6% and 9% for bathroom tissues and aer towels resectively for P&G, and 78.% and 59.% for bathroom tissues and aer towels resectively for Georgia-Pacific. These rofit estimates aear reasonable given that P&G is the market leader in both roduct categories and the retailer has a fairly significant market share in the aer towel category relative to bathroom tissues, and are quite consistent with the ricing strategies observed from the conduct arameter estimates. They also suggest that coordinating ricing strategies across related roduct categories can lead to channel higher rofits for manufacturers, imlying that manufacturers should engage in such ricing coordination across their roducts to maximize their rofits. TABLE SHARE OF CHANNEL PROFITS Bathroom tissue Twocategory Basic Basic Twocategory P&G 8.% 87.6% Georgia- Pacific 76.% 78.% Retailer 8.7%.% Retailer.8%.9% Paer towels Basic Twocategory Basic Twocategory P&G 67.% 7.0% Georgia- Pacific 5.7% 59.% Retailer.9% 8.0% Retailer 47.% 40.9% Journal of Alied Business and Economics vol. () 0 7

12 CONCLUSION AND FUTURE RESEARCH This aer has conducted an exloratory study of the nature of channel interactions across multile roduct categories, which has received fairly little attention in the literature, and develoed a flexible of channel ricing cometition that allows for deviations from the standard Nash equilibrium assumed in most game-theoretic aers on channel interactions. The resented in the aer has formalized cross-category effects as a function of the market shares of the roduct categories under study. Initial estimation results suggest that cross-category effects result in decreased cometition in the channel, suggesting that channel interactions across roduct categories are deendent and ricing decisions may involve cross-category coordination. In addition, coordination of ricing behavior across multile roduct categories also affects the distribution of channel rofits among channel members, which has imlications for marketing managers. It is thus imortant for future studies on channel interactions to account for such cross-category effects, as studying the roduct categories indeendently of one another can result in results that do not truly reflect the true nature of the channel cometition. Further research on the toic can involve more detailed investigations of these effects. To begin with, the can be extended to include other marketing mix elements besides rice, such as advertising, distribution, and roduct design or ackaging. Next, more analytically comlex s can be develoed that are able to estimate the conduct arameters reresenting the horizontal manufacturer interactions and cross-brand interactions in Figure, as they will rovide further insights and a more comlete icture of the overall nature of the channel interactions. In addition, the cross-category effects may be formalized by other different functional forms of the market shares or may involve the use of other relevant variables in addition to market shares. On the suly side, the way these cross-category effects may affect roduction considerations such as cost can be further investigated, while on the demand side, other functional forms of demand, such as a discrete choice based on the random utility framework (McFadden, 974), may also be used. Other interesting issues to look into would be the role of category cataincy, loss leaders, as well as roduct line ricing issues involving multile brands in each roduct category, all of which may affect the nature of channel interactions and the manufacturers and retailers marketing strategies in the channel. REFERENCES Ainslie, A. and Rossi, P. E. (998). Similarities in Choice Behavior Across Product Categories. Marketing Science, 7, (), Besanko, D., Guta, S. and Jain, D. (998). Logit Demand Estimation Under Cometitive Pricing Behavior: An Equilibrium Framework. Management Science, 44, (), Part of, Choi, S. (99). Price Cometition in a Channel Structure With a Common Retailer. Marketing Science, 0, (4), Draganska, M., Klaer, D., Villas-Boas, S. B. (00). A Larger Slice or a Larger Pie? An Emirical Investigation of Bargaining Power in the Distribution Channel. Marketing Science, 9, (), Iyer, G. and Villas-Boas, J. M. (00). A Bargaining Theory of Distribution Channels. Journal of Marketing Research, 40, (), Jeuland, A. P. and Shugan, S. M. (98). Managing Channel Profits. Marketing Science,, (), 9-7. Kadiyali, V., Chintagunta, P. K. and Vilcassim, N. (000). Manufacturer-Retailer Channel Interactions and Imlications for Channel Power: An Emirical Investigation of Pricing in a Local Market. Marketing Science, 9, (), Journal of Alied Business and Economics vol. () 0

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