INTRODUCTION
Two strategies of market competition have been widely observed in SC systems. One strategy is price competition which is often defined as Bertrand competition in economics literature. The other is quantity competition which is typically defined as Cournot competition in economics. In price competition, prices are often compelled to marginal cost while in quantity competition positive price-cost margins are often achieved.
Distribution channel structure has been another major strategic concern for SC system. Many distribution channels have been observed ranging from traditional retail channel to the direct sales model and the clicks-and-mortar channel (Gap/Gap.com, Staples/Staples.com etc.). The contracting arrangement between a manufacturer and a retailer also varies from channel to channel. Some manufacturers use an exclusive arrangement with a retailer while others use multiple channels. The direct channel is a vertically integrated channel often controlled by a manufacturer (Dell, for example).
The efficiency of a decentralized SC system is defined as the ratio of its total equilibrium profit to the optimal profit of the centralized system. The objective of this paper is to study the disparity of SC efficiencies between price competition and quantity competition. To that end, consider two substitutable products, produced either by a single manufacturer or by two manufacturers. The products are sold through utmost two retailers. Within this framework, consider different SC arrangements ranging from a centralized configuration to several decentralized multi-channel ones. The decentralized configurations include the single retailer channel (two manufacturers, each producing one product; both sell their products through a single retailer), the single manufacturer channel (one manufacturer, two retailers), and the exclusive channel (two manufacturers and two retailers; each manufacturer sells through only one retailer and each retailer carry only one product). This paper is intended to answer the following questions. Does price competition result in the same efficiencies for SC configurations as quantity competition? Is one competition strategy always superior to the other one? How does product substitutability affect competition strategies?
Many of the channel arrangements described above are observed in practice. The factory outlets and the direct distribution channels are the typical examples of centralized SC between a manufacturer and a retailer. The exclusive channel is most often observed in manufacturer-distributor relationships in various industries ranging from chemicals and paper to appliances and Beer. For example, Hercules Inc. is the exclusive distributor for GE Specialty Materials' water treatment solutions to the paper industry (Challener, 2003); Diego Suarez is the exclusive distributor of Coors brand of beers in Puerto Rico (Allio & Allio, 2002). The Wall Street Journal (October 28, 2003) reports that Estee Lauder has created a new company division, called BeautyBank, to develop cosmetic products exclusively for Kohl's (Merrick & Beatty, 2003). Different auto makers often sell vehicles through a single dealer in smaller cities, giving rise to a distribution channel similar to the single retailer channel noted above. Wu et al. (2009 & 2010) have used similar SC configurations in their study.
This paper compares and contrasts price and quantity competition strategies in these decentralized SCs, and studies how the differences between the two strategies change with the degree of substitutability.
LITERATURE REVIEW
SC structure, conflict and coordination have been extensively studied in operations literature. The majority of the works assume a single manufacturer and a single retailer. The typical approach is to study the source of inefficiency (often related to double marginalization), and mechanisms for achieving coordination. Cachon (2001) provides a review of this stream of literature. The channel conflict literature typically considers the scenario where the manufacturer is simultaneously a supplier to and competitor of its retail partners(s). Chiang et al. (2003) consider whether a single manufacturer should sell exclusively through a retailer, direct over the Internet, or through a hybrid channel. Their key finding is that the manufacturer may use a direct channel as a way to combat double marginalization in the retail channel. Ahn et al. (2002) consider the competition between independent retailers and manufacturer-owned stores where parties compete in price. The manufacturer sells an identical product through two spatially separated markets. Tsay and Agarwal (2002) provide a review in modeling channel conflict and coordination. This stream of literature typically considers a single manufacturer selling identical products, whereas our work considers multiple manufacturers selling substitutable products.
Existing comparative work of price and quantity competitions is fruitful in the field of Economics and Supply Chain Management. Singh and Vives (1984) show that in a duopoly game with linear demand and constant marginal cost, firms should employ quantity competition strategy if products are substitutable and take price competition strategy if products are well differentiated. Cheng (1985) studies the equilibrium outcomes of price and quantity competitions with differentiated products and finds that quantity competition is superior to price competition under certain assumptions. There are other studies that show preference to price competition. For example, Amir and Jin (2001) provide support to the result that Bertrand equilibrium is intrinsically more competitive than Cournot equilibrium in an oligopoly model with linear demand, and a mixture of substitute and complementary products under some limitations. On the other hand, Miller and Pazgal (2001) demonstrate the equivalence result in a two-stage differentiated-products oligopoly model under certain assumptions.
The third stream of literature related to our work is product substitutability which has also been studied extensively in both Operations and Marketing literature. In Operations, for instance, Boyaci (2003) considers a multi-channel distribution system in presence of both vertical and horizontal competition. He concludes that there is a tendency for both manufacturer and retailer to overstock due to substitutability. In Marketing, Raju et al. (1995) consider the introduction and performance of store brands vis-a-vis a national brand. Mahajan and van Ryzin (1999) provide a comprehensive survey of research on demand substitutability. However, these studies take the SC structure as given and do not address the issue of SC efficiency. Our work differs from these studies by quantifying SC efficiency.
MODELS
Consider multi-channel distribution systems for two substitutable products, denoted by 1 and 2. The products reach the end consumer through a two-echelon SC involving manufacturer(s) and retailer(s). Multi-channel systems studied in this paper involve utmost two manufacturers and utmost two retailers. The manufacturers are denoted by [M.sup.1] and [M.sup.2] (or by M, if there is only one manufacturer), while the retailers will be denoted by [R.sup.1] and [R.sup.2] (or by R, if there is only one retailer) respectively. Vertical competition is introduced by considering decentralized decisions made within the channels; while, the horizontal competition is introduced by substitutable products. Several different multi-channel distribution systems are considered. Figures 1(a) and 1(b) schematically describe these configurations. The configurations in Figure 1(a) involve either one manufacturer or one retailer, while the configurations in Figure 1(b) involve two manufacturers and two retailers.
The centralized system (denoted as C) is a fully integrated system where a single manufacturer produces both products and sells them through an integrated channel. It yields the highest system profit and serves as a benchmark for the decentralized systems. Figure 1(a) describes three decentralized systems. The decentralized single manufacturer single retailer system (denoted as DS) involves one manufacturer producing both products and selling them through a single retailer. The retailer makes stocking decisions of the two products independent of the manufacturer. A single manufacturer system (denoted as SM) involves one manufacturer and two retailers. The sole manufacturer produces both products and sells each product exclusively through one independent retailer. Under a single retailer system (denoted as SR), there are two manufacturers, each producing one product. The manufacturers sell their products through a single retailer who makes the stocking decisions of each product in its own interest.
Figure 1(b) describes three decentralized multi-channel distribution systems, each involving two manufacturers and two retailers. Under a partially centralized system (denoted as PC), [M.sub.1] sells its product exclusively through [R.sub.1] while [M.sub.2] sells its products exclusively through [R.sub.2]. In addition, each of the two competing manufacturer-retailer pair is centralized (or vertically integrated) and the stocking decision within each pair is coordinated. However, there exists horizontal coordination between the two channels. Under a minimally coordinated system (denoted as MC) [M.sub.1] sells its product exclusively through [R.sub.1], and [M.sub.2] sells its products exclusively through [R.sub.2]. In addition, only one of the two vertical channels is coordinated. Assume, without loss of generality, that [M.sub.1] and [R.sub.1] are coordinated, while the other manufacturer-retailer pair is not. An exclusive system (denoted as E) is similar to the PC and MC systems except that none of the two manufacturer-retailer pairs is coordinated. Thus, under an exclusive system, [M.sub.1] sells its product exclusively through [R.sub.1], [M.sub.2] sells its products exclusively through [R.sub.2], and all parties make decisions in self-interest. It is easy to see that the degree of coordination goes down as moving from PC to MC to E.
[FIGURE 1(a) OMITTED]
[FIGURE 1(b) OMITTED]
Without loss of generality, we assume the common marginal production cost for each product is 0. No fixed cost of production is considered and the production and delivery are assumed to be instantaneous. The manufacturers produce as retailers' orders under a wholesale price contract. Let [w.sub.1] and [w.sub.2] be the wholesale prices and [q.sub.1] and [q.sub.2] be the demand of products 1 and 2 respectively. The retailer(s) set the retail prices, denoted by [p.sub.1] and [p.sub.2] respectively. We model the horizontal competition between two channels under both price and quantity competitions.
Price competition model:
[q.sub.i] = 1 - [p.sub.i] -[theta]([p.sub.j] - [p.sub.i]), i, j = 1,2, i [not equal to] j, (1) where 6 is a parameter.
The horizontal competition between the products is captured by making the demand of a product sensitive to the prices of both products. The products are perfectly differentiated when
[theta] = 0. The products are nearly identical as [theta] approaches infinity.
Quantity competition model:
[p.sub.i] = [alpha] - [beta][q.sub.i] - [gamma][q.sub.j], [alpha], [beta], [gamma] > 0, [gamma] [less than or equal to] [beta]; i, j = 1,2, i [not equal to] j, (1')
where [alpha], [beta], and [gamma] are parameters.
The horizontal competition between the products is captured by making the price of a product sensitive to the available quantities of both products. In particular, the products are perfectly substitutable when [gamma] = [beta]; and are perfectly differentiated when [gamma] = 0. The condition [gamma] [less than or equal to] [beta] implies that the demand of a product is more sensitive to its own price rather than the price of the competing product.
These types of demand functions are standard in economics and marketing literature modeling product substitutability (Gal-Or, 1991; Raju et al., 1995). Moreover, Lee and Staelin (2000) show that a linear demand function involving substitutable products is indeed consistent with reasonable buyer behavior and market characteristics.
[pi], with subscripts and superscripts, is used to denote profit. A subscript of "M" or "R" is used to refer to a manufacturer or a retailer respectively. Superscripts are used to denote a specific SC configuration. Thus, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the profit of retailer i under an exclusive system.
The notation j denotes an index on the SC configurations under consideration. Clearly, j = C, DS, SM, SR, PC, MC, E. The total SC profit (i.e. the sum of the profits of retailer(s) and manufacturer(s)) under configuration j will be denoted as [[pi].sup.j] (no subscripts).
The centralized system yields the highest profit and serves as a benchmark for the decentralized systems noted earlier. The profit maximization problem of a centralized system is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
The solution of the above optimization problem yields the following results. Price competition model:
Inserting equation (1) into (2) and the 1st order conditions (the 2nd order conditions are satisfied) yields
[p.sup.*.sub.1] = [p.sup.*.sub.2] = [p.sup.c*] = 1/2; [q.sup.*.sub.1] = [q.sup.*.sub.2] = [q.sup.c*] = 1/2; and [[pi].sup.c*] = 1/2. (3)
Quantity competition model:
Similarly, insert equation (1') into (2) and we get
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3')
For the reasons of brevity, among the decentralized SC configurations only the single retailer (SR) system is described here. The rest will have similar formulations. Under a single retailer system, both manufacturers sell their products through a single retailer. The profit maximization problem of the retailer is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)
Price competition model:
The 1st-order conditions (it is easy to verify that the second order conditions are satisfied) yield:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
Quantity competition model:
[q.sup.SR*.sub.i]([w.sub.1], [w.sub.2]) = [[alpha]([beta] - [gamma]) - [beta]([w.sub.i] + c) + [gamma]([w.sub.j] + c)]/[2([[beta].sup.2] - [[gamma].sup.2])], i, j = 1,2, i [not equal to] j. (5')
The two manufacturers select their wholesale prices by solving the following problems.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)
The equilibrium wholesale prices [w.sup.*.sub.1] and [w.sup.*.sub.2] can be found by solving the 1st-order conditions given by (6). Once [w.sup.*.sub.1] and [w.sup.*.sub.2] are known, the equilibrium prices, quantities, and profits as well as the total profit can be calculated accordingly under both price and quantity competitions. Similarly, we can solve for the equilibrium prices, quantities, and profits for the other decentralized SC configurations.
Since our focus is efficiencies of SC configurations, only the equilibrium profits are summarized in Table 1.
RESULTS AND ANALYSIS
This section compares and contrasts the efficiencies of SC configurations under price competition with those under quantity competition and also examines the effects of product substitutability on the comparison. Under quantity competition, the relative magnitudes of the parameters [beta] and [gamma] determine the degree of substitutability between the two products. The product substitutability can be parameterized by defining [lambda] = [gamma] / [beta]. Since [beta] [greater than or equal to] [gamma], 0 [less than or equal to] [lambda] [less than or equal to] 1. Recall that the efficiency of decentralized SC j is defined as the ratio of equilibrium total SC profit under configuration j to that of the centralized SC; i.e., [R.sup.j] = [[pi].sup.j*] / [[pi].sup.c*], [for all]j. Given that the centralized system yields the highest system profit, 0 [less than or equal to] [R.sup.j] [less than or equal to] 1, [for all]j.
Table 2 summarizes the efficiency for each SC configuration under different horizontal competition.
Let [lambda]' = 1 - [e.sup.-[theta]]. Hence [lambda]'[member of] [0,1] and [theta] = -ln(l - [lambda]'). Now product substitutability under price competition is rescaled from [0, [infinity]] to [0, 1] and captured by [lambda]'.
Among all SC configurations, C and DS have the same efficiencies. Figure 2 (a)-(e) compare the efficiencies of other configurations under price and quantity competitions.
Theorem.
(i) Price and quantity competitions are equivalent only if the two products are perfectly differentiated.
(ii) Neither price competition nor quantity competition is a dominant strategy.
(iii) As the product substitutability increases, a large difference of the efficiencies between price and quantity competition is observed (except when the two products are almost identical).
Comparing price with quantity competition analytically, we find the same efficiency is achieved for each configuration only when [lambda] = [lambda]' = 0. So the two competitions are never equivalent if the two products are not perfectly differentiated.
It is easy to see that quantity competition is not always better in terms of higher efficiency for SC configurations. Neither is price competition. Actually in SM and E SC configurations, price competition almost always yields higher efficiency (except when the two products are almost identical in E SC configuration) while in SR, PC, and MC configurations, quantity competition always yields higher efficiency.
It is also interesting to notice that as the product substitutability increases, the difference between quantity and price competitions increases too (except when the two products are almost identical in SR and E SC configurations).
[FIGURE 2(a) OMITTED]
[FIGURE 2(b) OMITTED]
[FIGURE 2(c) OMITTED]
[FIGURE 2(d) OMITTED]
[FIGURE 2(e) OMITTED]
SUMMARY AND CONCLUSION
Multi-channel distribution systems with differing channel configurations are widely observed in practice. This paper studies price and quantity competitions of dual-channel-dualechelon SC systems. Six decentralized SC configurations with different degree of horizontal and vertical integration were discussed. We compare and contrast the equilibrium SC efficiencies of different SC structures under price with those under quantity competition.
The most important contributions of this paper are that price competition and quantity competition are not equivalent, and that neither of them is a dominant strategy for the SC configuration systems discussed in this paper.
Another important finding is that for each dual-channel (either two retailers or two manufacturers or both) SC configuration the difference of efficiencies under price and quantity competitions increases with increased product substitutability.
The metrics used in this paper for comparison is the efficiency of SC configurations. It will be interesting to examine what will be the results if other metrics are used, such as price. It will also be interesting, although difficult, to investigate the comparison using more complex SC configurations, such as SC systems with more than two echelons or with more than two manufacturers/retailers. If SC systems of three or more echelons are considered, the tractability of the resulting analytic models significantly decreases. Another extension we consider pursuing is to relax the assumption in this paper that the demand functions of two retailers are symmetric. It will be very intriguing to see how sensitive the results in this article are to the changes in the demand function structures.
REFERENCES
Ahn, H., I. Duenyas, and R. Zhang (2002), "Price Competition between Retailers and Manufacturer-Owned Stores," Working Paper, University of California at Berkeley.
Amir, R. and J.Y. Jin (2001), "Cournot and Bertrand Equilibria Compared: Substitutability, Complementarity and Concavity," International Journal of Industrial Organization, 19(3), 303-317.
Allio, D. J. and R. J. Allio (2002), "Coors Light in Puerto Rico: Battling for Local Dominance in a Global Market," Strategy & Leadership, 30(6), 13-17.
Bell, D. R., Y. Wang, and V. Padmanabhan (2006), "An Explanation for Partial Forward Integration: Why Manufacturers Become Marketers," Working Paper, The Wharton School, University of Pennsylvania.
Boyaci, T. (2005), "Competitive Stocking and Coordination in a Multiple-Channel Distribution System," IIE Transactions, 37(5), 407-427.
Challener, C. (2003), "Specialty Paper Chemicals Plagued by Price Pressures," Chemical Market Reporter, 263(18), FR8-FR9.
Cheng, L. (1985), "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, 16(1), 146-152.
Chiang, W. K., D. Chhajed, and J. D. Hess (2003), "Direct Marketing, Indirect Profits: A Strategic Analysis of Dual-Channel Supply-Chain Design," Management Science, 49(1), 1-20.
Davis, J. (2001), "Manufacturers Are Testing the Web for Direct Sales; Some Are Finding Success," InfoWorld, 23(5), 102-103.
Ernst, R. and P. Kouvelis (1999), "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, 45(8), 1142-1155.
Gal-Or, E. (1991), "Duopolistic Vertical Restraints," European Economic Review, 35(6), 1237-1253.
Lee, E. and R. Staelin (2000), "A General Theory of Demand in a Multi-Product Multi-Outlet Market," Working Paper, Fuqua School of Business, Duke University.
Mahajan, S. and G. van Ryzin (1999), "Retail Inventories and Consumer Choice," In Quantitative Models for Supply Chain Management, Tayur et al. (eds.), Kluwer, Dordrecht, The Netherlands.
McWilliams, G. (2002), "In an About-Face Dell Plans to Sell PCs through Dealers," The Wall Street Journal, August 20.
Merrick, A. and S. Beatty (2003), "Kohl's Plans Estee Lauder Counters," The Wall Street Journal, October 23.
Miller, N. H. and A. I. Pazgal (2001), "The Equivalence of Price and Quantity Competition with Delegation," RAND Journal of Economics, 32(2), 284-301.
Netessine, S. and N. Rudi (2006), "Supply Chain Choice on the Internet," Management Science, 52(6), 844-864.
Raju, J. S., R. Sethuraman, and S. K. Dhar (1995), "The Introduction and Performance of Store Brands," Management Science, 41(6), 957-978.
Rhee, B. (2001), "A Hybrid Channel System in Competition with Net-Only Direct Marketers," Working Paper, Hong Kong University of Science & Technology.
Singh, N. and X. Vives (1984), "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, 15(4), 546-554.
Smith, S. A. and N. Agrawal (2000), "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, 48(1), 50-64.
Tsay, A. A. and N. Agrawal (2001), "Manufacturer and Reseller Perspectives on Channel Conflict and Coordination in Multiple-Channel Distribution," Working Paper, Leavey School of Business, Santa Clara University.
Tsay, A. A., and N. Agrawal (2004), "Modeling Conflict and Coordination in Multi-Channel Distribution Systems," Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era, Simchi-Levi et al. (eds.), Springer, 557-606.
van Ryzin, G. and S. Mahajan (2000), "Supply Chain Coordination under Horizontal Competition," Working Paper, Columbia University.
Wu, C., B. Shao, and H. Du (2010), "Efficiency of Competing Supply Chains Under Price Competition,"
California Journal of Operations Management, 8 (1), 1-10
Wu, C., B. Shao, and S. Peng (2009), "Impact of Integration Cost and Product Substitutability on Equilibrium Structure of Competing Supply Chains," Review of Business Research, 9 (5), 171-178
Bin Shao, West Texas A&M University
Chongqi Wu, California State University, East Bay
Kunpeng Li, Sam Houston State University
TABLE 1: EQUILIBRIUM PROFITS OF SC CONFIGURATIONS.Configuration [[pi].sub.j] under [[pi].sub.j] under(j) Price Competition Quantity CompetitionC [MATHEMATICAL EXPRESSION [[alpha].sup.2]/ NOT REPRODUCIBLE IN 2([beta] + [gamma]) ASCII]DS 3/8 [[alpha].sup.2]/ 8[([beta] + [gamma]).sup.2]SM ([theta] + 3) [[alpha].sup.2] ([theta] + 1)/ (3[beta] + [gamma])/ 2[([theta] + 2).sup.2] 2[(2[beta] + [gamma]).sup.2]SR ([theta] + 1) [[alpha].sup.2][beta] ([theta] + 3)/2[([theta] (3[beta] - 2[gamma])/ + 2).sup.2] 2([beta] + [gamma]) (2[beta] - [gamma]).sup.2]PC 2([theta] + 1)/ 2[[alpha].sup.2][beta]/ [([theta] + 2).sup.2] [(2[beta] + [gamma]).sup.2]MC ([theta] + 1) [[alpha].sup.2] (13[[theta].sup.4] + (28[[beta].sup.2] + 82[[theta].sup.3] + 8[beta][gamma] - 167[[theta].sup.2] + [[gamma].sup.2])/ 12[[theta].sup.6] + 28)/ 16[beta][(2[beta] + 4[([theta] + 2).sup.2] [gamma]).sup.2] [([[theta].sup.2] + 4[theta] + 2).sup.2]E 4([theta] + 1) 4[[alpha].sup.2][beta] ([[theta].sup.2] + (6[[beta].sup.2] - 4[theta] + 2) [[gamma].sup.2])/ (2[[theta].sup.2] + [(2[beta] + 6[theta] + 3)/ [gamma]).sup.2] [([theta] + 2).sup.2] (4[beta] - ([[theta].sup.2] + [gamma]).sup.2] 7[theta] + 4).sup.2]TABLE 2: EFFICIENCIES OF SC CONFIGURATIONSConfiguration [R.sup.j] under [R.sup.j] under(j) Price Competition Quantity CompetitionC 1.0 1.0DS 0.75 0.75SM ([theta] + 3) 1 - 1/2 (2 + ([theta] + 1)/ [lambda]).sup.2] [([theta] + 2).sup.2]SR ([theta] + 3) (3 - 2[lambda])/ ([theta] + 1)/ (2 - [lambda]).sup.2] [([theta] + 2).sup.2]PC 4([theta] +1)/ 4(1 + [lambda])/ [([theta] + 2).sup.2] [(2 + [lambda]).sup.2]MC ([theta] +1) (1 + [lambda])(28 + (13[[theta].sup.4] + 8[lambda] - 82[[theta].sup.3] + [lambda].sup.2])/ 167[[theta].sup.2] + 120[theta] + 28)/ 2[([theta] + 2).sup.2] 8(2 + [lambda]).sup.2] ([[theta].sup.2] + 4[theta] + 2).sup.2]E 8([theta] +1) 8(1 + [lambda])([theta] - ([[theta].sup.2] + [[lambda].sup.2])/ 4[theta] + 2) [(4 - [lambda]).sup.2] (2[[theta].sup.2] + [(2 + [lambda]).sup.2] 6[theta] + 3)/ [([theta] + 2).sup.2] [([[theta].sup.2] + 7[theta] + 4).sup.2]
