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doi: 10.3934/jimo.2021194
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Retail outsourcing strategy in Cournot & Bertrand retail competitions with economies of scale

1. 

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211100, China

2. 

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211100, China

3. 

School of Business, The College of New Jersey, Ewing, NJ 08618, USA

* Corresponding author: Kebing Chen

Received  April 2021 Revised  August 2021 Early access November 2021

This paper investigates a manufacturer's retail outsourcing strategies under different competition modes with economies of scale. We focus on the effects of market competition modes, economies of scale and competitor's behavior on manufacturer's retail outsourcing decisions, and then we develop four game models under three competition modes. Firstly, we find the channel structure where both manufacturers choose retail outsourcing cannot be an equilibrium structure under the Cournot competition. The Cournot competition mode is less profitable to the firm than the Bertrand competition when the products are complements. Secondly, under the hybrid Cournot-Bertrand competition mode, there is only one equilibrium supply chain structure where neither manufacturer chooses retail outsourcing, when the substitutability and complementarity levels are not sufficiently high. In addition, setting price (quantity) contracts as the strategic variables is the dominant strategy for the direct-sale manufacturer who provides complementary (substitutable) products. Thirdly, both competitive firms will benefit from the situation where they choose the same competition mode. When the products are substitutes (complements), both of them choose the Cournot (Bertrand) competition mode. Finally, we show that the economies of scale have little impact on the equilibrium of the outsourcing structure but a great impact on the competition mode equilibrium.

Citation: Mingxia Li, Kebing Chen, Shengbin Wang. Retail outsourcing strategy in Cournot & Bertrand retail competitions with economies of scale. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021194
References:
[1]

S. M. AliM. H. RahmanT. J. TumpaA. A. M. Rifat and S. K. Paul, Examining price and service competition among retailers in a supply chain under potential demand disruption, Journal of Retailing and Consumer Services, 40 (2018), 40-47.  doi: 10.1016/j.jretconser.2017.08.025.  Google Scholar

[2]

A. AryaB. Mittendorf and D. E. M. Sappington, Outsourcing, vertical integration, and price vs. quantity competition, International Journal of Industrial Organization, 26 (2008), 1-16.  doi: 10.1016/j.ijindorg.2006.10.006.  Google Scholar

[3]

A. AryaB. Mittendorf and D. E. M. Sappington, The make-or-buy decision in the presence of a rival: Strategic outsourcing to a common supplier, Management Science, 54 (2008), 1747-1758.  doi: 10.1287/mnsc.1080.0896.  Google Scholar

[4]

D. Atkins and L. Liang, A note on competitive supply chains with generalized supply costs, European Journal of Operational Research, 207 (2010), 1316-1320.  doi: 10.1016/j.ejor.2010.07.012.  Google Scholar

[5]

P. Bajec and M. Zanne, The current status of the Slovenian logistics outsourcing market, its ability and potential measures to improve the pursuit of global trends, International Journal of Logistics Systems & Management, 18 (2014), 436-448.  doi: 10.1504/IJLSM.2014.063979.  Google Scholar

[6]

J. BianK. K. LaiZ. HuaX. Zhao and G. Zhou, Bertrand vs. Cournot competition in distribution channels with upstream collusion, International Journal of Production Economics, 204 (2018), 278-289.  doi: 10.1016/j.ijpe.2018.08.007.  Google Scholar

[7]

G. P. Cachon and P. T. Harker, Competition and outsourcing with scale economies, Management Science, 48 (2002), 1314-1333.  doi: 10.1287/mnsc.48.10.1314.271.  Google Scholar

[8]

K. Chen and T. Xiao, Outsourcing strategy and production disruption of supply chain with demand and capacity allocation uncertainties, International Journal of Production Economics, 170 (2015), 243-257.  doi: 10.1016/j.ijpe.2015.09.028.  Google Scholar

[9]

K. Chen, R. Xu and H. Fang, Information disclosure model under supply chain competition with asymmetric demand disruption, Asia-Pacific Journal of Operational Research, 33 (2016), 1650043, 35 pp. doi: 10.1142/S0217595916500433.  Google Scholar

[10]

J. Chen and S.-H. Lee., Cournot-bertrand comparison under R & D competition: Output versus R & D subsidies, Cogent Business & Management, (2021), https://mpra.ub.uni-muenchen.de/107949/. Google Scholar

[11]

L. K. Cheng, Comparing Bertrand and Cournot equilibria: A geometric approach, The Rand Journal of Economics, 16 (1985), 146-152.  doi: 10.2307/2555596.  Google Scholar

[12]

H.-R. Din and C.-H. Sun, Welfare improving licensing with endogenous choice of prices versus quantities, The North American Journal of Economics & Finance, 51 (2020), 100859.  doi: 10.1016/j.najef.2018.10.007.  Google Scholar

[13]

Y. Fang and B. Shou, Managing supply uncertainty under supply chain Cournot competition, European Journal of Operational Research, 243 (2015), 156-176.  doi: 10.1016/j.ejor.2014.11.038.  Google Scholar

[14]

L. Fanti and M. Scrimitore, How to competer Cournot versus Bertrand in a vertical structure with an integrated input supplier, Southern Economic Journal, 85 (2019), 796-820.  doi: 10.1002/soej.12324.  Google Scholar

[15]

A. Farahat and G. Perakis, A comparison of Bertrand and Cournot profits in oligopolies with differentiated products, Operations Research, 59 (2011), 507-513.  doi: 10.1287/opre.1100.0900.  Google Scholar

[16]

E. Garaventa and T. Tellefsen, Outsourcing: The hidden costs, Review of Business, 22 (2001), 28-31.   Google Scholar

[17]

A. Ghosh and M. Mitra, Comparing Bertrand and Cournot in mixed markets, Economics Letters, 109 (2010), 72-74.  doi: 10.1016/j.econlet.2010.08.021.  Google Scholar

[18]

B. C. Giri and B. R. Sarker, Improving performance by coordinating a supply chain with third party logistics outsourcing under production disruption, Computers & Industrial Engineering, 103 (2017), 168-177.  doi: 10.1016/j.cie.2016.11.022.  Google Scholar

[19]

A. Goli and B. Malmir, A covering tour approach for disaster relief locating and routing with fuzzy demand, International Journal of Intelligent Transportation Systems Research, 18 (2020), 140-152.  doi: 10.1007/s13177-019-00185-2.  Google Scholar

[20]

A. Goli, E. B. Tirkolaee and N. S. Aydin, Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors, IEEE Transactions on Fuzzy Systems, (2021). doi: 10.1109/TFUZZ.2021.3053838.  Google Scholar

[21]

A. GoliH. K. ZareR. T. Moghaddam and A. Sadeghieh, A comprehensive model of demand prediction based on hybrid artificial intelligence and metaheuristic algorithms: A case study in dairy industry, Journal of Industrial and Systems Engineering, 11 (2018), 190-203.   Google Scholar

[22]

J. Haraguchi and T. Matsumura, Cournot-Bertrand comparison in a mixed oligopoly, Journal of Economics, 117 (2016), 117-136.  doi: 10.1007/s00712-015-0452-6.  Google Scholar

[23]

M. HuangJ. TuX. Chao and D. Jin, Quality risk in logistics outsourcing: A fourth party logistics perspective, European Journal of Operational Research, 276 (2019), 855-879.  doi: 10.1016/j.ejor.2019.01.049.  Google Scholar

[24]

B. JiangJ. A. Belohlav and S. T. Young, Outsourcing impact on manufacturing firms' value: Evidence from Japan, Journal of Operations Management, 25 (2007), 885-900.  doi: 10.1016/j.jom.2006.12.002.  Google Scholar

[25]

M. Kaya and Ö. Özer, Quality risk in outsourcing: Noncontractible product quality and private quality cost information, Naval Research Logistics, 56 (2009), 669-685.  doi: 10.1002/nav.20372.  Google Scholar

[26]

T. KremicO. I. Tukel and W. O. Rom, Outsourcing decision support: A survey of benefits, risks, and decision factors, Supply Chain Management, 11 (2006), 467-482.  doi: 10.1108/13598540610703864.  Google Scholar

[27]

J. R. Kroes and S. Ghosh, Outsourcing congruence with competitive priorities: Impact on supply chain and firm performance, Journal of Operations Management, 28 (2010), 124-143.  doi: 10.1016/j.jom.2009.09.004.  Google Scholar

[28]

Y. J. Lin, Oligopoly and vertical integration: Note, The American Economic Review, 78 (1988), 251-254.   Google Scholar

[29]

Z. Liu and A. Nagurney, Supply chain outsourcing under exchange rate risk and competition, Omega: International Journal of Management Science, 39 (2011), 539-549.  doi: 10.1016/j.omega.2010.11.003.  Google Scholar

[30]

T. Matsumura and A. Ogawa, Price versus quantity in a mixed duopoly, Economics Letters, 116 (2012), 174-177.  doi: 10.1016/j.econlet.2012.02.012.  Google Scholar

[31]

T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-191.  doi: 10.1287/mksc.2.2.161.  Google Scholar

[32]

M. MorrisM. Schindehutte and J. Allen, The entrepreneur's business model: Toward a unified perspective, Journal of Business Research, 58 (2005), 726-735.  doi: 10.1016/j.jbusres.2003.11.001.  Google Scholar

[33]

T. NariuD. Flath and M. Okamura, A vertical oligopoly in which entry increases every firm's profit, Journal of Economics & Management Strategy, 30 (2021), 684-694.  doi: 10.1111/jems.12426.  Google Scholar

[34]

S. M. Pahlevan, S. Hosseini and A. Goli, Sustainable supply chain network design using products' life cycle in the aluminum industry, Environmental Science and Pollution Research, (2021). doi: 10.1007/s11356-020-12150-8.  Google Scholar

[35]

N. Singh and X. Vives, Price and quantity competition in a differentiated duopoly, The Rand Journal of Economics, 15 (1984), 546-554.  doi: 10.2307/2555525.  Google Scholar

[36]

S. Sinha and S. P. Sarmah, Supply chain coordination model with insufficient production capacity and option for outsourcing, Mathematical and Computer Modelling, 46 (2007), 1442-1452.  doi: 10.1016/j.mcm.2007.03.014.  Google Scholar

[37]

H. SunY. WanY. LiL. L. Zhang and Z. Zhou, Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours, Journal of Industrial & Management Optimization, 17 (2021), 601-631.  doi: 10.3934/jimo.2019125.  Google Scholar

[38]

V. J. TremblayC. H. Tremblay and K. Isariyawongse, Cournot and Bertrand competition when advertising rotates demand: The case of Honda and Scion, International Journal of the Economics of Business, 20 (2013), 125-141.  doi: 10.1080/13571516.2012.750045.  Google Scholar

[39]

L. WangH. SongD. Zhang and H. Yang, Pricing decisions for complementary products in a fuzzy dual-channel supply chain, Journal of Industrial & Management Optimization, 15 (2019), 343-364.  doi: 10.3934/jimo.2018046.  Google Scholar

[40]

C. Y. Wong and N. Karia, Explaining the competitive advantage of logistics service providers: A resource-based view approach, International Journal of Production Economics, 128 (2010), 51-67.  doi: 10.1016/j.ijpe.2009.08.026.  Google Scholar

[41]

T. XiaoY. Xia and G. P. Zhang, Strategic outsourcing decisions for manufacturers competing on product quality, IIE Transactions, 46 (2014), 313-329.  doi: 10.1080/0740817X.2012.761368.  Google Scholar

[42]

T. XiaoY. Xia and G. P. Zhang, Strategic outsourcing decisions for manufacturers that produce partially substitutable products in a quantity-setting duopoly situation, Decision Sciences, 38 (2007), 81-106.  doi: 10.1111/j.1540-5915.2007.00149.x.  Google Scholar

[43]

Q. YangX. ZhaoH. Y. J. Yeung and Y. Liu, Improving logistics outsourcing performance through transactional and relational mechanisms under transaction uncertainties: Evidence from China, International Journal of Production Economics, 175 (2016), 12-23.  doi: 10.1016/j.ijpe.2016.01.022.  Google Scholar

[44]

J. ZhaoX. HouY. Guo and J. Wei, Pricing policies for complementary products in a dual-channel supply chain, Applied Mathematical Modelling, 49 (2017), 437-451.  doi: 10.1016/j.apm.2017.04.023.  Google Scholar

[45]

W. ZhuS. C. H. NgZ. Wang and X. Zhao, The role of outsourcing management process in improving the effectiveness of logistics outsourcing, International Journal of Production Economics, 188 (2017), 29-40.  doi: 10.1016/j.ijpe.2017.03.004.  Google Scholar

show all references

References:
[1]

S. M. AliM. H. RahmanT. J. TumpaA. A. M. Rifat and S. K. Paul, Examining price and service competition among retailers in a supply chain under potential demand disruption, Journal of Retailing and Consumer Services, 40 (2018), 40-47.  doi: 10.1016/j.jretconser.2017.08.025.  Google Scholar

[2]

A. AryaB. Mittendorf and D. E. M. Sappington, Outsourcing, vertical integration, and price vs. quantity competition, International Journal of Industrial Organization, 26 (2008), 1-16.  doi: 10.1016/j.ijindorg.2006.10.006.  Google Scholar

[3]

A. AryaB. Mittendorf and D. E. M. Sappington, The make-or-buy decision in the presence of a rival: Strategic outsourcing to a common supplier, Management Science, 54 (2008), 1747-1758.  doi: 10.1287/mnsc.1080.0896.  Google Scholar

[4]

D. Atkins and L. Liang, A note on competitive supply chains with generalized supply costs, European Journal of Operational Research, 207 (2010), 1316-1320.  doi: 10.1016/j.ejor.2010.07.012.  Google Scholar

[5]

P. Bajec and M. Zanne, The current status of the Slovenian logistics outsourcing market, its ability and potential measures to improve the pursuit of global trends, International Journal of Logistics Systems & Management, 18 (2014), 436-448.  doi: 10.1504/IJLSM.2014.063979.  Google Scholar

[6]

J. BianK. K. LaiZ. HuaX. Zhao and G. Zhou, Bertrand vs. Cournot competition in distribution channels with upstream collusion, International Journal of Production Economics, 204 (2018), 278-289.  doi: 10.1016/j.ijpe.2018.08.007.  Google Scholar

[7]

G. P. Cachon and P. T. Harker, Competition and outsourcing with scale economies, Management Science, 48 (2002), 1314-1333.  doi: 10.1287/mnsc.48.10.1314.271.  Google Scholar

[8]

K. Chen and T. Xiao, Outsourcing strategy and production disruption of supply chain with demand and capacity allocation uncertainties, International Journal of Production Economics, 170 (2015), 243-257.  doi: 10.1016/j.ijpe.2015.09.028.  Google Scholar

[9]

K. Chen, R. Xu and H. Fang, Information disclosure model under supply chain competition with asymmetric demand disruption, Asia-Pacific Journal of Operational Research, 33 (2016), 1650043, 35 pp. doi: 10.1142/S0217595916500433.  Google Scholar

[10]

J. Chen and S.-H. Lee., Cournot-bertrand comparison under R & D competition: Output versus R & D subsidies, Cogent Business & Management, (2021), https://mpra.ub.uni-muenchen.de/107949/. Google Scholar

[11]

L. K. Cheng, Comparing Bertrand and Cournot equilibria: A geometric approach, The Rand Journal of Economics, 16 (1985), 146-152.  doi: 10.2307/2555596.  Google Scholar

[12]

H.-R. Din and C.-H. Sun, Welfare improving licensing with endogenous choice of prices versus quantities, The North American Journal of Economics & Finance, 51 (2020), 100859.  doi: 10.1016/j.najef.2018.10.007.  Google Scholar

[13]

Y. Fang and B. Shou, Managing supply uncertainty under supply chain Cournot competition, European Journal of Operational Research, 243 (2015), 156-176.  doi: 10.1016/j.ejor.2014.11.038.  Google Scholar

[14]

L. Fanti and M. Scrimitore, How to competer Cournot versus Bertrand in a vertical structure with an integrated input supplier, Southern Economic Journal, 85 (2019), 796-820.  doi: 10.1002/soej.12324.  Google Scholar

[15]

A. Farahat and G. Perakis, A comparison of Bertrand and Cournot profits in oligopolies with differentiated products, Operations Research, 59 (2011), 507-513.  doi: 10.1287/opre.1100.0900.  Google Scholar

[16]

E. Garaventa and T. Tellefsen, Outsourcing: The hidden costs, Review of Business, 22 (2001), 28-31.   Google Scholar

[17]

A. Ghosh and M. Mitra, Comparing Bertrand and Cournot in mixed markets, Economics Letters, 109 (2010), 72-74.  doi: 10.1016/j.econlet.2010.08.021.  Google Scholar

[18]

B. C. Giri and B. R. Sarker, Improving performance by coordinating a supply chain with third party logistics outsourcing under production disruption, Computers & Industrial Engineering, 103 (2017), 168-177.  doi: 10.1016/j.cie.2016.11.022.  Google Scholar

[19]

A. Goli and B. Malmir, A covering tour approach for disaster relief locating and routing with fuzzy demand, International Journal of Intelligent Transportation Systems Research, 18 (2020), 140-152.  doi: 10.1007/s13177-019-00185-2.  Google Scholar

[20]

A. Goli, E. B. Tirkolaee and N. S. Aydin, Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors, IEEE Transactions on Fuzzy Systems, (2021). doi: 10.1109/TFUZZ.2021.3053838.  Google Scholar

[21]

A. GoliH. K. ZareR. T. Moghaddam and A. Sadeghieh, A comprehensive model of demand prediction based on hybrid artificial intelligence and metaheuristic algorithms: A case study in dairy industry, Journal of Industrial and Systems Engineering, 11 (2018), 190-203.   Google Scholar

[22]

J. Haraguchi and T. Matsumura, Cournot-Bertrand comparison in a mixed oligopoly, Journal of Economics, 117 (2016), 117-136.  doi: 10.1007/s00712-015-0452-6.  Google Scholar

[23]

M. HuangJ. TuX. Chao and D. Jin, Quality risk in logistics outsourcing: A fourth party logistics perspective, European Journal of Operational Research, 276 (2019), 855-879.  doi: 10.1016/j.ejor.2019.01.049.  Google Scholar

[24]

B. JiangJ. A. Belohlav and S. T. Young, Outsourcing impact on manufacturing firms' value: Evidence from Japan, Journal of Operations Management, 25 (2007), 885-900.  doi: 10.1016/j.jom.2006.12.002.  Google Scholar

[25]

M. Kaya and Ö. Özer, Quality risk in outsourcing: Noncontractible product quality and private quality cost information, Naval Research Logistics, 56 (2009), 669-685.  doi: 10.1002/nav.20372.  Google Scholar

[26]

T. KremicO. I. Tukel and W. O. Rom, Outsourcing decision support: A survey of benefits, risks, and decision factors, Supply Chain Management, 11 (2006), 467-482.  doi: 10.1108/13598540610703864.  Google Scholar

[27]

J. R. Kroes and S. Ghosh, Outsourcing congruence with competitive priorities: Impact on supply chain and firm performance, Journal of Operations Management, 28 (2010), 124-143.  doi: 10.1016/j.jom.2009.09.004.  Google Scholar

[28]

Y. J. Lin, Oligopoly and vertical integration: Note, The American Economic Review, 78 (1988), 251-254.   Google Scholar

[29]

Z. Liu and A. Nagurney, Supply chain outsourcing under exchange rate risk and competition, Omega: International Journal of Management Science, 39 (2011), 539-549.  doi: 10.1016/j.omega.2010.11.003.  Google Scholar

[30]

T. Matsumura and A. Ogawa, Price versus quantity in a mixed duopoly, Economics Letters, 116 (2012), 174-177.  doi: 10.1016/j.econlet.2012.02.012.  Google Scholar

[31]

T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-191.  doi: 10.1287/mksc.2.2.161.  Google Scholar

[32]

M. MorrisM. Schindehutte and J. Allen, The entrepreneur's business model: Toward a unified perspective, Journal of Business Research, 58 (2005), 726-735.  doi: 10.1016/j.jbusres.2003.11.001.  Google Scholar

[33]

T. NariuD. Flath and M. Okamura, A vertical oligopoly in which entry increases every firm's profit, Journal of Economics & Management Strategy, 30 (2021), 684-694.  doi: 10.1111/jems.12426.  Google Scholar

[34]

S. M. Pahlevan, S. Hosseini and A. Goli, Sustainable supply chain network design using products' life cycle in the aluminum industry, Environmental Science and Pollution Research, (2021). doi: 10.1007/s11356-020-12150-8.  Google Scholar

[35]

N. Singh and X. Vives, Price and quantity competition in a differentiated duopoly, The Rand Journal of Economics, 15 (1984), 546-554.  doi: 10.2307/2555525.  Google Scholar

[36]

S. Sinha and S. P. Sarmah, Supply chain coordination model with insufficient production capacity and option for outsourcing, Mathematical and Computer Modelling, 46 (2007), 1442-1452.  doi: 10.1016/j.mcm.2007.03.014.  Google Scholar

[37]

H. SunY. WanY. LiL. L. Zhang and Z. Zhou, Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours, Journal of Industrial & Management Optimization, 17 (2021), 601-631.  doi: 10.3934/jimo.2019125.  Google Scholar

[38]

V. J. TremblayC. H. Tremblay and K. Isariyawongse, Cournot and Bertrand competition when advertising rotates demand: The case of Honda and Scion, International Journal of the Economics of Business, 20 (2013), 125-141.  doi: 10.1080/13571516.2012.750045.  Google Scholar

[39]

L. WangH. SongD. Zhang and H. Yang, Pricing decisions for complementary products in a fuzzy dual-channel supply chain, Journal of Industrial & Management Optimization, 15 (2019), 343-364.  doi: 10.3934/jimo.2018046.  Google Scholar

[40]

C. Y. Wong and N. Karia, Explaining the competitive advantage of logistics service providers: A resource-based view approach, International Journal of Production Economics, 128 (2010), 51-67.  doi: 10.1016/j.ijpe.2009.08.026.  Google Scholar

[41]

T. XiaoY. Xia and G. P. Zhang, Strategic outsourcing decisions for manufacturers competing on product quality, IIE Transactions, 46 (2014), 313-329.  doi: 10.1080/0740817X.2012.761368.  Google Scholar

[42]

T. XiaoY. Xia and G. P. Zhang, Strategic outsourcing decisions for manufacturers that produce partially substitutable products in a quantity-setting duopoly situation, Decision Sciences, 38 (2007), 81-106.  doi: 10.1111/j.1540-5915.2007.00149.x.  Google Scholar

[43]

Q. YangX. ZhaoH. Y. J. Yeung and Y. Liu, Improving logistics outsourcing performance through transactional and relational mechanisms under transaction uncertainties: Evidence from China, International Journal of Production Economics, 175 (2016), 12-23.  doi: 10.1016/j.ijpe.2016.01.022.  Google Scholar

[44]

J. ZhaoX. HouY. Guo and J. Wei, Pricing policies for complementary products in a dual-channel supply chain, Applied Mathematical Modelling, 49 (2017), 437-451.  doi: 10.1016/j.apm.2017.04.023.  Google Scholar

[45]

W. ZhuS. C. H. NgZ. Wang and X. Zhao, The role of outsourcing management process in improving the effectiveness of logistics outsourcing, International Journal of Production Economics, 188 (2017), 29-40.  doi: 10.1016/j.ijpe.2017.03.004.  Google Scholar

Figure 1.  Possible regions for equilibrium structures in the pure Cournot competition
Figure 2.  Possible regions for the more profitable competition mode
Figure 3.  Possible regions for equilibrium structure in pure Bertrand competition
Figure 4.  Possible regions for equilibrium structures in the Cournot-Bertrand competition
Figure 5.  Possible regions for the equilibrium competition mode
Figure 6.  The effect of the retail outsourcing strategy on $ M_{1} $'s profit when $ M_{2} $ uses direct sales
Figure 7.  The effect of the retail outsourcing strategy on $ M_{1} $'s profit when $ M_{2} $ uses retail outsourcing
Figure 8.  The effect of the retail outsourcing strategy on $ M_{1} $'s profit when $ M_{2} $ uses direct sales
Figure 9.  The effect of the retail outsourcing strategy on $ M_{1} $'s profit when $ M_{2} $ uses retail outsourcing
Table 1.  Compare and contrast our model with the extant literature
Article Model Market competition mode Economies of scale Product complementation Outsourcing decision Structure equilbrium Competition mode equilbrium
Bertrand Cournot
Chen & Lee [10] Price vs. quantity under R&D competition
Nariu et al [33] Product-differentiated Cournot competition
Arya et al [2] Price vs. quantity competition
Farahat & Perakis [15] Equilibrium profits of price & quantity competition
Matsumura & Ogawa [30] Choice of a price or a quantity contract in a mixed duopoly
Fang & Shou [13] Cournot competition between two supply chains
Zhao et al [44] Pricing of complementary products in dual channel chain
Atkins & Liang [4] Competitive supply chains with generalised supply costs
Haraguchi & Matsumura [22] Comparing price and quantity competition
Din & Sun [12] Choice of prices versusquantities with patent licensing
Wang et al [39] pricing problem of complementary products
Our paper Equilibrium analysis under the supply chain competition
Article Model Market competition mode Economies of scale Product complementation Outsourcing decision Structure equilbrium Competition mode equilbrium
Bertrand Cournot
Chen & Lee [10] Price vs. quantity under R&D competition
Nariu et al [33] Product-differentiated Cournot competition
Arya et al [2] Price vs. quantity competition
Farahat & Perakis [15] Equilibrium profits of price & quantity competition
Matsumura & Ogawa [30] Choice of a price or a quantity contract in a mixed duopoly
Fang & Shou [13] Cournot competition between two supply chains
Zhao et al [44] Pricing of complementary products in dual channel chain
Atkins & Liang [4] Competitive supply chains with generalised supply costs
Haraguchi & Matsumura [22] Comparing price and quantity competition
Din & Sun [12] Choice of prices versusquantities with patent licensing
Wang et al [39] pricing problem of complementary products
Our paper Equilibrium analysis under the supply chain competition
Table 2.  Equilibrium solutions for the four different structures
X= CC CD(DC) DD
Chain i Chain 1(2) Chain 2(1) Chain i
$ q_{{X_i}}^{*QQ} $ $ \frac{{a - {c_0}}}{{A + b}} $ $ \frac{{({A^2} + 2A - {b^2} - Ab)(a - {c_0})}}{{A({A^2} + 2A - 2{b^2})}} $ $ \frac{{(A - b)(a - {c_0})}}{{{A^2} + 2A - 2{b^2}}} $ $ \frac{{2({c_0} - a)}}{{(b - 4)(b + 2) + 4\theta }} $
$ \pi _{{X_{Mi}}}^{*QQ} $ $ (1 - \theta ){(q_{C{C_i}}^{QQ})^2} $ $ (1 - \theta ){(q_{C{D_1}}^{QQ})^2} $ $ \frac{{(2 - \theta )A - {b^2}}}{A}{(q_{C{D_2}}^{QQ})^2} $ $ \frac{{(4 - 2\theta - {b^2})}}{2}{(q_{D{D_i}}^{QQ})^2} $
X= CC CD(DC) DD
Chain i Chain 1(2) Chain 2(1) Chain i
$ q_{{X_i}}^{*QQ} $ $ \frac{{a - {c_0}}}{{A + b}} $ $ \frac{{({A^2} + 2A - {b^2} - Ab)(a - {c_0})}}{{A({A^2} + 2A - 2{b^2})}} $ $ \frac{{(A - b)(a - {c_0})}}{{{A^2} + 2A - 2{b^2}}} $ $ \frac{{2({c_0} - a)}}{{(b - 4)(b + 2) + 4\theta }} $
$ \pi _{{X_{Mi}}}^{*QQ} $ $ (1 - \theta ){(q_{C{C_i}}^{QQ})^2} $ $ (1 - \theta ){(q_{C{D_1}}^{QQ})^2} $ $ \frac{{(2 - \theta )A - {b^2}}}{A}{(q_{C{D_2}}^{QQ})^2} $ $ \frac{{(4 - 2\theta - {b^2})}}{2}{(q_{D{D_i}}^{QQ})^2} $
Table 3.  Equilibrium solutions for the four different structures
X chain $ w_{{X_i}}^{*PP} $ $ q_{{X_i}}^{*PP} $ $ \pi _{{X_{Mi}}}^{*PP} $
CC i NA $ \frac{{a - {c_0}}}{{(2 - b)(1 + b) - 2\theta }} $ $ (1 - {b^2} - \theta ){(q_{C{C_i}}^{*PP})^2} $
CD 1(2) NA $ \frac{{(1 - b)(2 + b)a + ({b^2} - 2){c_0} + bw_{C{D_2}}^{*PP}}}{S} $ $ (1 - {b^2} - \theta ){(q_{C{D_1}}^{*PP})^2} $
(DC) 2(1) $ \frac{{(S + 2\theta T)(T + b)a + (ST - Sb - 2\theta Tb){c_0}}}{{2T(S + \theta T)}} $ $ \frac{{ - (T + b)a + b{c_0} + Tw_{C{D_2}}^{*PP}}}{S} $ $ \frac{{(4 - {b^2})(1 - {b^2})}}{{2 - {b^2}}}{(q_{C{D_2}}^{*PP})^2} $
DD i $ \frac{{Sa - (1 + b)(2 - b)({b^2} - 2){c_0}}}{{S - (1 + b)(2 - b)({b^2} - 2)}} $ $ \frac{{a - w_{D{D_i}}^{*PP}}}{{(1 + b)(2 - b)}} $ $ [\frac{{(4 - {b^2})(1 - {b^2})}}{{2 - {b^2}}} - \theta ]{(q_{D{D_i}}^{*PP})^2} $
X chain $ w_{{X_i}}^{*PP} $ $ q_{{X_i}}^{*PP} $ $ \pi _{{X_{Mi}}}^{*PP} $
CC i NA $ \frac{{a - {c_0}}}{{(2 - b)(1 + b) - 2\theta }} $ $ (1 - {b^2} - \theta ){(q_{C{C_i}}^{*PP})^2} $
CD 1(2) NA $ \frac{{(1 - b)(2 + b)a + ({b^2} - 2){c_0} + bw_{C{D_2}}^{*PP}}}{S} $ $ (1 - {b^2} - \theta ){(q_{C{D_1}}^{*PP})^2} $
(DC) 2(1) $ \frac{{(S + 2\theta T)(T + b)a + (ST - Sb - 2\theta Tb){c_0}}}{{2T(S + \theta T)}} $ $ \frac{{ - (T + b)a + b{c_0} + Tw_{C{D_2}}^{*PP}}}{S} $ $ \frac{{(4 - {b^2})(1 - {b^2})}}{{2 - {b^2}}}{(q_{C{D_2}}^{*PP})^2} $
DD i $ \frac{{Sa - (1 + b)(2 - b)({b^2} - 2){c_0}}}{{S - (1 + b)(2 - b)({b^2} - 2)}} $ $ \frac{{a - w_{D{D_i}}^{*PP}}}{{(1 + b)(2 - b)}} $ $ [\frac{{(4 - {b^2})(1 - {b^2})}}{{2 - {b^2}}} - \theta ]{(q_{D{D_i}}^{*PP})^2} $
Table 4.  Equilibrium solutions for the four supply chain structures
Chain i $ w_{{X_i}}^{*QP} $ $ p_{{X_i}}^{*QP} $ $ q_{{X_i}}^{*QP} $ $ \pi _{{X_{Mi}}}^{*QP} $ $ \pi _{{X_{Ri}}}^{*QP} $
CC 1 NA $ \frac{{({b^2} - b - 2)(1 - b)(a - {c_0}) + (3{b^2} - 4){c_0}}}{{3{b^2} - 4}} $ $ \frac{{(b - 2)(a - {c_0})}}{{3{b^2} - 4}} $ $ (1 - {b^2}){(q_{C{C_1}}^{*QP})^2} $ NA
2 NA $ \frac{{({b^2} + b - 2)(a - {c_0}) + (3{b^2} - 4){c_0}}}{{3{b^2} - 4}} $ $ \frac{{({b^2} + b - 2)(a - {c_0})}}{{3{b^2} - 4}} $ $ {(q_{C{C_2}}^{*QP})^2} $ NA
CD 1 NA $ \frac{{(1 - {b^2})(2 - b)a + (2 - {b^2}){c_0} + b(1 - {b^2})w_{C{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(2 - b)a - 2{c_0} + bw_{C{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ (1 - {b^2}){(q_{C{D_1}}^{*QP})^2} $ NA
2 $ \frac{{(1 - b)(2 + b)a - (1 + b)(b - 2){c_0}}}{{2(2 - {b^2})}} $ $ \frac{{(1 - b)(2 + b)a + b{c_0} + 2(1 - {b^2})w_ {C{D_2}}^ {*QP} }}{{4 - 3{b^2}}} $ $ \frac{{(2 - {b^2} - b)a + b{c_0} + ({b^2} - 2)w_{C{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{4 - 3{b^2}}}{{2 - {b^2} }} {(q_{C{D_2}}^{*QP})^2} $ $ {(q_{C{D_2}}^{*QP})^2} $
DC 1 $ \frac{{(2 - b)a + (2 + b){c_0}}}{4} $ $ \frac{{(1 - {b^2})(2 - b)a + b(1 - {b^2}){c_0} + (2 - {b^2})w_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(2 - b)a + b{c_0} - 2w_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{4 - 3{b^2}}}{2}{(q_{D{C_1}}^{*QP})^2} $ $ (1 - {b^2}){(q_{D{C_1}}^{*QP})^2} $
2 NA $ \frac{{(1 - b)(2 + b)a + 2(1 - {b^2}){c_0} + bw_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(2 - {b^2} - b)a + ({b^2} - 2){c_0} + bw_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ {(q_{D{C_2}}^{*QP})^2} $ NA
DD 1 $ \frac{{({b^3} - 5{b^2} - 2b + 8)a - ({b^3} + 4{b^2} - 2b - 8){c_0}}}{{16 - 9{b^2}}} $ $ \frac{{(1 - {b^2})(2 - b)a + (2 - {b^2})w_{D{D_1}}^{*QP} + b(1 - {b^2})w_{D{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{2({b^3} - 5{b^2} - 2b + 8)(a - {c_0})}}{{(4 - 3{b^2})(16 - 9{b^2})}} $ $ \frac{{4 - 3{b^2}}}{2}{(q_{D{D_1}}^{*QP})^2} $ $ (1 - {b^2}){(q_{D{D_1}}^{*QP})^2} $
2 $ \frac{{(8 - 5{b^2} - 2b)a - (4{b^2} - 2b - 8){c_0}}}{{16 - 9{b^2}}} $ $ \frac{{(1 - b)(2 + b)a + 2(1 - {b^2})w_{D{D_2}}^{*QP} + bw_{D{D_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(5{b^2} + 2b - 8)({b^2} - 2)(a - {c_0})}}{{(4 - 3{b^2})(16 - 9{b^2})}} $ $ \frac{{4 - 3{b^2}}}{{2 - {b^2}}}{(q_{D{D_2}}^{*QP})^2} $ $ {(q_{D{D_2}}^{*QP})^2} $
Chain i $ w_{{X_i}}^{*QP} $ $ p_{{X_i}}^{*QP} $ $ q_{{X_i}}^{*QP} $ $ \pi _{{X_{Mi}}}^{*QP} $ $ \pi _{{X_{Ri}}}^{*QP} $
CC 1 NA $ \frac{{({b^2} - b - 2)(1 - b)(a - {c_0}) + (3{b^2} - 4){c_0}}}{{3{b^2} - 4}} $ $ \frac{{(b - 2)(a - {c_0})}}{{3{b^2} - 4}} $ $ (1 - {b^2}){(q_{C{C_1}}^{*QP})^2} $ NA
2 NA $ \frac{{({b^2} + b - 2)(a - {c_0}) + (3{b^2} - 4){c_0}}}{{3{b^2} - 4}} $ $ \frac{{({b^2} + b - 2)(a - {c_0})}}{{3{b^2} - 4}} $ $ {(q_{C{C_2}}^{*QP})^2} $ NA
CD 1 NA $ \frac{{(1 - {b^2})(2 - b)a + (2 - {b^2}){c_0} + b(1 - {b^2})w_{C{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(2 - b)a - 2{c_0} + bw_{C{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ (1 - {b^2}){(q_{C{D_1}}^{*QP})^2} $ NA
2 $ \frac{{(1 - b)(2 + b)a - (1 + b)(b - 2){c_0}}}{{2(2 - {b^2})}} $ $ \frac{{(1 - b)(2 + b)a + b{c_0} + 2(1 - {b^2})w_ {C{D_2}}^ {*QP} }}{{4 - 3{b^2}}} $ $ \frac{{(2 - {b^2} - b)a + b{c_0} + ({b^2} - 2)w_{C{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{4 - 3{b^2}}}{{2 - {b^2} }} {(q_{C{D_2}}^{*QP})^2} $ $ {(q_{C{D_2}}^{*QP})^2} $
DC 1 $ \frac{{(2 - b)a + (2 + b){c_0}}}{4} $ $ \frac{{(1 - {b^2})(2 - b)a + b(1 - {b^2}){c_0} + (2 - {b^2})w_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(2 - b)a + b{c_0} - 2w_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{4 - 3{b^2}}}{2}{(q_{D{C_1}}^{*QP})^2} $ $ (1 - {b^2}){(q_{D{C_1}}^{*QP})^2} $
2 NA $ \frac{{(1 - b)(2 + b)a + 2(1 - {b^2}){c_0} + bw_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(2 - {b^2} - b)a + ({b^2} - 2){c_0} + bw_{D{C_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ {(q_{D{C_2}}^{*QP})^2} $ NA
DD 1 $ \frac{{({b^3} - 5{b^2} - 2b + 8)a - ({b^3} + 4{b^2} - 2b - 8){c_0}}}{{16 - 9{b^2}}} $ $ \frac{{(1 - {b^2})(2 - b)a + (2 - {b^2})w_{D{D_1}}^{*QP} + b(1 - {b^2})w_{D{D_2}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{2({b^3} - 5{b^2} - 2b + 8)(a - {c_0})}}{{(4 - 3{b^2})(16 - 9{b^2})}} $ $ \frac{{4 - 3{b^2}}}{2}{(q_{D{D_1}}^{*QP})^2} $ $ (1 - {b^2}){(q_{D{D_1}}^{*QP})^2} $
2 $ \frac{{(8 - 5{b^2} - 2b)a - (4{b^2} - 2b - 8){c_0}}}{{16 - 9{b^2}}} $ $ \frac{{(1 - b)(2 + b)a + 2(1 - {b^2})w_{D{D_2}}^{*QP} + bw_{D{D_1}}^{*QP}}}{{4 - 3{b^2}}} $ $ \frac{{(5{b^2} + 2b - 8)({b^2} - 2)(a - {c_0})}}{{(4 - 3{b^2})(16 - 9{b^2})}} $ $ \frac{{4 - 3{b^2}}}{{2 - {b^2}}}{(q_{D{D_2}}^{*QP})^2} $ $ {(q_{D{D_2}}^{*QP})^2} $
Table 5.  Payoff table for the strategic competition choice of the X supply chain structure
Supply chain 2
Cournot Bertrand
Supply chain 1 Cournot $ (\pi _{{X_{M1}}}^{*QQ},\pi _{{X_{M2}}}^{*QQ}) $ $ (\pi _{{X_{M1}}}^{*QP},\pi _{{X_{M2}}}^{*QP}) $
Bertrand $ (\pi _{{X_{M1}}}^{*PQ},\pi _{{X_{M2}}}^{*PQ}) $ $ (\pi _{{X_{M1}}}^{*PP},\pi _{{X_{M2}}}^{*PP}) $
Supply chain 2
Cournot Bertrand
Supply chain 1 Cournot $ (\pi _{{X_{M1}}}^{*QQ},\pi _{{X_{M2}}}^{*QQ}) $ $ (\pi _{{X_{M1}}}^{*QP},\pi _{{X_{M2}}}^{*QP}) $
Bertrand $ (\pi _{{X_{M1}}}^{*PQ},\pi _{{X_{M2}}}^{*PQ}) $ $ (\pi _{{X_{M1}}}^{*PP},\pi _{{X_{M2}}}^{*PP}) $
Table 6.  Equilibrium solutions for the four structures with economies of scale
Chain i $ \tilde w_{{X_i}}^{*QP} $ $ \tilde q_{{X_i}}^{*QP} $ $ \tilde \pi _{{X_{Mi}}}^{*QP} $
CC 1 NA $ \frac{{(T + b - {b^2})(a - {c_0})}}{{AT + {b^2}}} $ $ (1 - {b^2} - \theta ){(\tilde q_{C{C_1}}^{*QP})^2} $
2 NA $ \frac{{(T + b)(a - {c_0})}}{{AT + {b^2}}} $ $ (1 - \theta ){(\tilde q_{C{C_2}}^{*QP})^2} $
CD 1 NA $ \frac{{(2 - b)a - 2{c_0} + b\tilde w_{C{D_2}}^{*QP}}}{{ - U}} $ $ (1 - {b^2} - \theta ){(\tilde q_{C{D_1}}^{*QP})^2} $
2 $ \frac{{(U - 2\theta T)(T + b)a + [U(T - b) + 2\theta bT]{c_0}}}{{2T(U - \theta T)}} $ $ \frac{{( - T - b)a + b{c_0} + T\tilde w_{C{D_2}}^{*QP}}}{{ - U}} $ $ (\frac{U}{T} - \theta ){(\tilde q_{C{D_2}}^{*QP})^2} $
DC 1 $ \frac{{(U - 2\theta T)(A - b)a + [U(b + A) - 2\theta b(T + Ab)]{c_0}}}{{2A[U + 2\theta (1 - {b^2} - \theta )]}} $ $ \frac{{(A - b)a + b{c_0} - A\tilde w_{D{C_1}}^{*QP}}}{{2\theta {b^2} - U}} $ $ \frac{{U + 2\theta (1 - {b^2} - \theta )}}{{ - A}}{(\tilde q_{D{C_1}}^{*QP})^2} $
2 NA $ \frac{{(2 + b)(1 - b)a + ({b^2} - 2){c_0} + b\tilde w_{D{C_1}}^{*QP}}}{{2\theta {b^2} - U}} $ $ (1 - \theta ){(\tilde q_{D{C_2}}^{*QP})^2} $
DD 1 $ \frac{{U[ - {b^3} + 5{b^2} + 2b - 8 + 2\theta (2 - {b^2})]a - (2 - {b^2})[5U + 4\theta (b - {b^2} - 3)]{c_0}}}{{(3{b^2} - 4)(9{b^2} - 16) + 2\theta (4 - {b^2})(5{b^2} - 8) + 8{\theta ^2}(2 - {b^2})}} $ $ \frac{{2(\tilde w_{D{D_1}}^{*QP} - {c_0})}}{{ - U}} $ $ (\frac{{4 - 3{b^2}}}{2} - \theta ){(\tilde q_{D{D_1}}^{*QP})^2} $
2 $ \frac{{U(b - 2)a - 2(U - 4\theta ){c_0} + 4(U - 2\theta )\tilde w_{D{D_1}}^{*QP}}}{{Ub}} $ $ \frac{{(2 - {b^2})(\tilde w_{D{D_2}}^{*QP} - {c_0})}}{{2\theta {b^2} - U}} $ $ (\frac{{4 - 3{b^2}}}{{2 - {b^2}}} - \theta ){(\tilde q_{D{D_2}}^{*QP})^2} $
Chain i $ \tilde w_{{X_i}}^{*QP} $ $ \tilde q_{{X_i}}^{*QP} $ $ \tilde \pi _{{X_{Mi}}}^{*QP} $
CC 1 NA $ \frac{{(T + b - {b^2})(a - {c_0})}}{{AT + {b^2}}} $ $ (1 - {b^2} - \theta ){(\tilde q_{C{C_1}}^{*QP})^2} $
2 NA $ \frac{{(T + b)(a - {c_0})}}{{AT + {b^2}}} $ $ (1 - \theta ){(\tilde q_{C{C_2}}^{*QP})^2} $
CD 1 NA $ \frac{{(2 - b)a - 2{c_0} + b\tilde w_{C{D_2}}^{*QP}}}{{ - U}} $ $ (1 - {b^2} - \theta ){(\tilde q_{C{D_1}}^{*QP})^2} $
2 $ \frac{{(U - 2\theta T)(T + b)a + [U(T - b) + 2\theta bT]{c_0}}}{{2T(U - \theta T)}} $ $ \frac{{( - T - b)a + b{c_0} + T\tilde w_{C{D_2}}^{*QP}}}{{ - U}} $ $ (\frac{U}{T} - \theta ){(\tilde q_{C{D_2}}^{*QP})^2} $
DC 1 $ \frac{{(U - 2\theta T)(A - b)a + [U(b + A) - 2\theta b(T + Ab)]{c_0}}}{{2A[U + 2\theta (1 - {b^2} - \theta )]}} $ $ \frac{{(A - b)a + b{c_0} - A\tilde w_{D{C_1}}^{*QP}}}{{2\theta {b^2} - U}} $ $ \frac{{U + 2\theta (1 - {b^2} - \theta )}}{{ - A}}{(\tilde q_{D{C_1}}^{*QP})^2} $
2 NA $ \frac{{(2 + b)(1 - b)a + ({b^2} - 2){c_0} + b\tilde w_{D{C_1}}^{*QP}}}{{2\theta {b^2} - U}} $ $ (1 - \theta ){(\tilde q_{D{C_2}}^{*QP})^2} $
DD 1 $ \frac{{U[ - {b^3} + 5{b^2} + 2b - 8 + 2\theta (2 - {b^2})]a - (2 - {b^2})[5U + 4\theta (b - {b^2} - 3)]{c_0}}}{{(3{b^2} - 4)(9{b^2} - 16) + 2\theta (4 - {b^2})(5{b^2} - 8) + 8{\theta ^2}(2 - {b^2})}} $ $ \frac{{2(\tilde w_{D{D_1}}^{*QP} - {c_0})}}{{ - U}} $ $ (\frac{{4 - 3{b^2}}}{2} - \theta ){(\tilde q_{D{D_1}}^{*QP})^2} $
2 $ \frac{{U(b - 2)a - 2(U - 4\theta ){c_0} + 4(U - 2\theta )\tilde w_{D{D_1}}^{*QP}}}{{Ub}} $ $ \frac{{(2 - {b^2})(\tilde w_{D{D_2}}^{*QP} - {c_0})}}{{2\theta {b^2} - U}} $ $ (\frac{{4 - 3{b^2}}}{{2 - {b^2}}} - \theta ){(\tilde q_{D{D_2}}^{*QP})^2} $
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