American Institute of Mathematical Sciences

Advanced
July  2022, 18(4): 3001-3027. doi: 10.3934/jimo.2021100

Managing piracy: Dual-channel strategy for digital contents

Yan-Xin Chai 1, , Steven Ji-Fan Ren 1,, and  Jian-Qiang Zhang 2,,

1. 

School of Economics and Management, Harbin Institute of Technology, Shenzhen, Shenzhen, 518055, China
2. 

School of Business, Jiangsu Normal University, Xuzhou, 221116, China

* Corresponding authors: renjifan@hit.edu.cn; jqzhang@jsnu.edu.cn

Received  August 2020 Revised  March 2021 Published  July 2022 Early access  May 2021

The Internet offers digital content disc producers the opportunities to design dual channels by introducing an online-direct store alongside traditional retail stores, but also leads related firms to suffer significant piracy problems. Using a game-theoretic framework, we explore dual-channel marketing optimality as a piracy-mitigating strategy for digital content sold in the physical disc format. We construct a price-setting game between a digital content producer and its independent retailer(s) in a pirated market by endogenizing the producer's copyright protection investments. We show that dual-channel marketing, a complement or a substitute for conventional copyright protection, can strategically mitigate the piracy level by increasing the equal-size retail sales volume. We also investigate how firms' pricing strategies and profits are influenced by the endogenous interaction of dual-channel marketing and copyright protection. We unexpectedly find that in a pirated market with insufficient copyright protection, dual-channel marketing can simultaneously raise firm pricing and sales volumes when the producer sells through a monopolistic retailer. We also identify the conditions under which dual-channel marketing can mitigate profit losses caused by piracy for the producer and the retailer(s). Unlike previous research which shows that dual-channel marketing benefits the producer and the monopolistic retailer because it mitigates double marginalization, in the pirated market, this win-win outcome occurs even if accompanied by aggravated double marginalization. Moreover, dual-channel marketing can mitigate all the firms' profit losses caused by piracy only when it can complement conventional copyright protection, i.e., when the producer sells through a monopolistic retailer or duopolistic retailers. In each situation, counter-intuitively, as copyright protection becomes increasingly costly, although the retailer(s) is (are) more willing to accept dual-channel marketing, the producer has a decreased incentive to design such sales channels.

Keywords: Digital content, discs, piracy, dual-channel marketing, double marginalization.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Yan-Xin Chai, Steven Ji-Fan Ren, Jian-Qiang Zhang. Managing piracy: Dual-channel strategy for digital contents. Journal of Industrial and Management Optimization, 2022, 18 (4) : 3001-3027. doi: 10.3934/jimo.2021100
References:
[1]

I. Ahn and I. Shin, On the optimal level of protection in DRM, Information Economics and Policy, 22 (2010), 341-353.  doi: 10.1016/j.infoecopol.2010.09.003.

[2]

A. Arya, B. Mittendorf and D. E. M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659.  doi: 10.1287/mksc.1070.0280.

[3]

T. Avinadav, T. Chernonog and Y. Perlman, Analysis of protection and pricing strategies for digital productsunder uncertain demand, International Journal of Production Economics, 158 (2014), 54-64.  doi: 10.1016/j.ijpe.2014.07.021.

[4]

S. H. Bae and J. P. Choi, A model of piracy, Information Economics and Policy, 18 (2006), 303-320.  doi: 10.1016/j.infoecopol.2006.02.002.

[5]

K. Cattani, W. Gilland, H. S. Heese and J. Swaminathan, Boiling frogs: Pricing strategies for a manufacturer adding a directchannel that competes with the traditional channel, Production and Operations Management, 15 (2006), 40-56.  doi: 10.1111/j.1937-5956.2006.tb00002.x.

[6]

R. K. Chellappa and S. Shivendu, Managing piracy: Pricing and sampling strategies for digital experience goods in vertically segmented markets, Information Systems Research, 16 (2005), 400-417.  doi: 10.1287/isre.1050.0069.

[7]

W.-Y. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Science, 49 (2003), 1-20.  doi: 10.1287/mnsc.49.1.1.12749.

[8]

P. Choi, S. H. Bae and J. Jun, Digital piracy and firms' strategic interactions: The effects ofpublic copy protection and DRM similarity, Information Economics and Policy, 22 (2010), 354-364.  doi: 10.1016/j.infoecopol.2010.10.001.

[9]

B. Fritz, Sales of digital movies surge, 2014. Available from: https://www.wsj.com/articles/SB10001424052702304887104579306440621142958.

[10]

R. D. Gopal and A. Gupta, Trading higher software piracy for higher profits: The case ofphantom piracy, Management Science, 56 (2010), 1946-1962.  doi: 10.1109/HICSS.2002.994188.

[11]

L. Guo and X. Meng, Digital content provision and optimal copyright protection, Management Science, 61 (2015), 1183-1196.  doi: 10.1287/mnsc.2014.1972.

[12]

D. Hayes, Six reasons why dvds still make money – and won't die anytime soon, 2014. Available from: https://www.forbes.com/sites/dadehayes/2013/07/08/six-reasons-why-dvds-still-make-money-and-wont-die-anytime-soon/.

[13]

Y.-S. Huang, S.-H. Lin and C.-C. Fang, Pricing and coordination with consideration of piracy for digitalgoods in supply chains, Journal of Business Research, 77 (2017), 30-40.  doi: 10.1016/j.jbusres.2017.03.023.

[14]

J. Jaisingh, Piracy on file-sharing networks: Strategies for recording companies, Journal of Organizational Computing and Electronic Commerce, 17 (2007), 329-348.  doi: 10.1080/10919390701636239.

[15]

J. J. Kacen, J. D. Hess and W.-Y. K. Chiang, Bricks or clicks? Consumer attitudes toward traditional stores andonline stores, Global Economics and Management Review, 18 (2013), 12-21.  doi: 10.1016/s2340-1540(13)70003-3.

[16]

A. Kim, A. Lahiri and D. Dey, The 'invisible hand' of piracy: An economic analysis of the information-goods supply chain, MIS Quarterly, 42 (2018), 1117–1141. doi: 10.2139/ssrn.2426577.

[17]

D. M. Kreps and J. A. Scheinkman, Quantity precommitment and bertrand competition yield cournot outcomes, The Bell Journal of Economics, 14 (1983), 326-337.  doi: 10.2307/3003636.

[18]

A. Lahiri and D. Dey, Effects of piracy on quality of information goods, Management Science, 59 (2013), 245-264.  doi: 10.1287/mnsc.1120.1578.

[19]

T.-P. Liang and J.-S. Huang, An empirical study on consumer acceptance of products in electronic markets: A transaction cost model, Decision Support Systems, 24 (1998), 29-43.  doi: 10.1016/S0167-9236(98)00061-X.

[20]

E. Priest, The future of music and film piracy in china, Berkeley Technology Law Journal, 21 (2006), 795.

[21]

RIAA, 2008 Year-End Shipment Statistics, 2009. Retrieved September 9, 2011.

[22]

M. D. Smith and R. Telang, Piracy or promotion? The impact of broadband internet penetration on DVD sales, Information Economics and Policy, 22 (2010), 289-298.  doi: 10.1016/j.infoecopol.2010.02.001.

[23]

A. Sundararajan, Managing digital piracy: Pricing and protection, Information Systems Research, 15 (2004), 287-308.  doi: 10.1287/isre.1040.0030.

[24]

A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2009), 93-110.  doi: 10.1111/j.1937-5956.2004.tb00147.x.

[25]

H. R. Varian, Versioning Information Goods, Working paper, University of California in Berkeley, 1997.

[26]

D. A. Vernik, D. Purohit and P. S. Desai, Music downloads and the flip side of digital rights management, Marketing Science, 30 (2011), 1011-1027.  doi: 10.1287/mksc.1110.0668.

[27]

S.-Y. Wu and P.-Y. Chen, Versioning and piracy control for digital information goods, Operations Research, 56 (2008), 157-172.  doi: 10.1287/opre.1070.0414.

show all references

References:
[1]

I. Ahn and I. Shin, On the optimal level of protection in DRM, Information Economics and Policy, 22 (2010), 341-353.  doi: 10.1016/j.infoecopol.2010.09.003.

[2]

A. Arya, B. Mittendorf and D. E. M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659.  doi: 10.1287/mksc.1070.0280.

[3]

T. Avinadav, T. Chernonog and Y. Perlman, Analysis of protection and pricing strategies for digital productsunder uncertain demand, International Journal of Production Economics, 158 (2014), 54-64.  doi: 10.1016/j.ijpe.2014.07.021.

[4]

S. H. Bae and J. P. Choi, A model of piracy, Information Economics and Policy, 18 (2006), 303-320.  doi: 10.1016/j.infoecopol.2006.02.002.

[5]

K. Cattani, W. Gilland, H. S. Heese and J. Swaminathan, Boiling frogs: Pricing strategies for a manufacturer adding a directchannel that competes with the traditional channel, Production and Operations Management, 15 (2006), 40-56.  doi: 10.1111/j.1937-5956.2006.tb00002.x.

[6]

R. K. Chellappa and S. Shivendu, Managing piracy: Pricing and sampling strategies for digital experience goods in vertically segmented markets, Information Systems Research, 16 (2005), 400-417.  doi: 10.1287/isre.1050.0069.

[7]

W.-Y. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Science, 49 (2003), 1-20.  doi: 10.1287/mnsc.49.1.1.12749.

[8]

P. Choi, S. H. Bae and J. Jun, Digital piracy and firms' strategic interactions: The effects ofpublic copy protection and DRM similarity, Information Economics and Policy, 22 (2010), 354-364.  doi: 10.1016/j.infoecopol.2010.10.001.

[9]

B. Fritz, Sales of digital movies surge, 2014. Available from: https://www.wsj.com/articles/SB10001424052702304887104579306440621142958.

[10]

R. D. Gopal and A. Gupta, Trading higher software piracy for higher profits: The case ofphantom piracy, Management Science, 56 (2010), 1946-1962.  doi: 10.1109/HICSS.2002.994188.

[11]

L. Guo and X. Meng, Digital content provision and optimal copyright protection, Management Science, 61 (2015), 1183-1196.  doi: 10.1287/mnsc.2014.1972.

[12]

D. Hayes, Six reasons why dvds still make money – and won't die anytime soon, 2014. Available from: https://www.forbes.com/sites/dadehayes/2013/07/08/six-reasons-why-dvds-still-make-money-and-wont-die-anytime-soon/.

[13]

Y.-S. Huang, S.-H. Lin and C.-C. Fang, Pricing and coordination with consideration of piracy for digitalgoods in supply chains, Journal of Business Research, 77 (2017), 30-40.  doi: 10.1016/j.jbusres.2017.03.023.

[14]

J. Jaisingh, Piracy on file-sharing networks: Strategies for recording companies, Journal of Organizational Computing and Electronic Commerce, 17 (2007), 329-348.  doi: 10.1080/10919390701636239.

[15]

J. J. Kacen, J. D. Hess and W.-Y. K. Chiang, Bricks or clicks? Consumer attitudes toward traditional stores andonline stores, Global Economics and Management Review, 18 (2013), 12-21.  doi: 10.1016/s2340-1540(13)70003-3.

[16]

A. Kim, A. Lahiri and D. Dey, The 'invisible hand' of piracy: An economic analysis of the information-goods supply chain, MIS Quarterly, 42 (2018), 1117–1141. doi: 10.2139/ssrn.2426577.

[17]

D. M. Kreps and J. A. Scheinkman, Quantity precommitment and bertrand competition yield cournot outcomes, The Bell Journal of Economics, 14 (1983), 326-337.  doi: 10.2307/3003636.

[18]

A. Lahiri and D. Dey, Effects of piracy on quality of information goods, Management Science, 59 (2013), 245-264.  doi: 10.1287/mnsc.1120.1578.

[19]

T.-P. Liang and J.-S. Huang, An empirical study on consumer acceptance of products in electronic markets: A transaction cost model, Decision Support Systems, 24 (1998), 29-43.  doi: 10.1016/S0167-9236(98)00061-X.

[20]

E. Priest, The future of music and film piracy in china, Berkeley Technology Law Journal, 21 (2006), 795.

[21]

RIAA, 2008 Year-End Shipment Statistics, 2009. Retrieved September 9, 2011.

[22]

M. D. Smith and R. Telang, Piracy or promotion? The impact of broadband internet penetration on DVD sales, Information Economics and Policy, 22 (2010), 289-298.  doi: 10.1016/j.infoecopol.2010.02.001.

[23]

A. Sundararajan, Managing digital piracy: Pricing and protection, Information Systems Research, 15 (2004), 287-308.  doi: 10.1287/isre.1040.0030.

[24]

A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2009), 93-110.  doi: 10.1111/j.1937-5956.2004.tb00147.x.

[25]

H. R. Varian, Versioning Information Goods, Working paper, University of California in Berkeley, 1997.

[26]

D. A. Vernik, D. Purohit and P. S. Desai, Music downloads and the flip side of digital rights management, Marketing Science, 30 (2011), 1011-1027.  doi: 10.1287/mksc.1110.0668.

[27]

S.-Y. Wu and P.-Y. Chen, Versioning and piracy control for digital information goods, Operations Research, 56 (2008), 157-172.  doi: 10.1287/opre.1070.0414.

Figure 1.  In the pirated market, the influences of dual-channel marketing on the wholesale price, retail price and retail profit margin, respectively
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  The win-win region by the online-direct channel's introduction in the pirated market
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  The win-win regions by the online-direct channel's introduction in the pirated market when and $ n = 1 $, $ n = 2 $, respectively
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  Equilibrium outcomes in the benchmark without piracy where the producer sells discs through the traditional channel and dual channels, respectively
Traditional channel Dual channels
Price
Wholesale price, $ {w^b} $ $ \frac{1}{2} $ $ \frac{\theta }{2} $
Online-direct price, $ p_M^b $ _ $ \frac{\theta }{2} $
Retail price, $ p_R^b $
Demand $ \frac{3}{4} $ $ \frac{1}{2} $
Online-direct demand, $ q_M^b $ _ 0
Retail demand, $ q_R^b $ $ \frac{1}{4} $ $ \frac{1}{2} $
Total demand, $ q_M^b + q_R^b $ $ \frac{1}{4} $ $ \frac{1}{2} $
Profit
Producer profit, $ \pi _M^b $ $ \frac{1}{8} $ $ \frac{\theta }{4} $
Retailer profit, $ \pi _R^b $ $ \frac{1}{{16}} $ $ \frac{{1 - \theta }}{4} $
Table Options

Download as excel

Traditional channel Dual channels
Price
Wholesale price, $ {w^b} $ $ \frac{1}{2} $ $ \frac{\theta }{2} $
Online-direct price, $ p_M^b $ _ $ \frac{\theta }{2} $
Retail price, $ p_R^b $
Demand $ \frac{3}{4} $ $ \frac{1}{2} $
Online-direct demand, $ q_M^b $ _ 0
Retail demand, $ q_R^b $ $ \frac{1}{4} $ $ \frac{1}{2} $
Total demand, $ q_M^b + q_R^b $ $ \frac{1}{4} $ $ \frac{1}{2} $
Profit
Producer profit, $ \pi _M^b $ $ \frac{1}{8} $ $ \frac{\theta }{4} $
Retailer profit, $ \pi _R^b $ $ \frac{1}{{16}} $ $ \frac{{1 - \theta }}{4} $
Table 2.  Equilibrium outcomes in the pirated market when the producer sells discs through the traditional channel
$ c \in (0,\frac{1}{8}] $ $ c \in (\frac{1}{8},\infty ) $
Copyright protection level, $ {e^T} $ 1 $ \frac{1}{{8c}} $
Price
Wholesale price, $ {w^T} $ $ \frac{1}{2} $ $ \frac{1}{{16c}} $
Retail price, $ p_R^T $ $ \frac{3}{4} $ $ \frac{3}{{32c}} $
Demand
Retail (Licensed) demand, $ q_{R(L)}^T $ $ \frac{1}{4} $ $ \frac{1}{4} $
Piracy demand, $ q_P^T $ $ \frac{3}{4} $ $ \frac{3}{4} $
Profit
Producer profit, $ \pi _M^T $ $ \frac{{1 - 4c}}{8} $ $ \frac{1}{{128c}} $
Retail profit, $ \pi _R^T $ $ \frac{1}{{16}} $ $ \frac{1}{{64c}} $
Table Options

Download as excel

$ c \in (0,\frac{1}{8}] $ $ c \in (\frac{1}{8},\infty ) $
Copyright protection level, $ {e^T} $ 1 $ \frac{1}{{8c}} $
Price
Wholesale price, $ {w^T} $ $ \frac{1}{2} $ $ \frac{1}{{16c}} $
Retail price, $ p_R^T $ $ \frac{3}{4} $ $ \frac{3}{{32c}} $
Demand
Retail (Licensed) demand, $ q_{R(L)}^T $ $ \frac{1}{4} $ $ \frac{1}{4} $
Piracy demand, $ q_P^T $ $ \frac{3}{4} $ $ \frac{3}{4} $
Profit
Producer profit, $ \pi _M^T $ $ \frac{{1 - 4c}}{8} $ $ \frac{1}{{128c}} $
Retail profit, $ \pi _R^T $ $ \frac{1}{{16}} $ $ \frac{1}{{64c}} $
Table 3.  Equilibrium outcomes in the pirated market when the producer sells discs through dual channels
$ c \in (0,\frac{1}{4}] $ $ c \in (\frac{1}{4},\infty ) $
Copyright protection level, $ {e^D} $ 1 $ \frac{1}{{4c}} $
Price
Wholesale price, $ {w^D} $ $ \frac{\theta }{2} $ $ \frac{{1 - 4c(1 - \theta )}}{{8c}} $
Online-direct price, $ p_M^D $ $ \frac{\theta }{2} $ $ \frac{{1 - 4c(1 - \theta )}}{{8c}} $
Retail price, $ p_R^D $ $ \frac{1}{2} $ $ \frac{1}{{8c}} $
Demand
Online-direct demand, $ q_M^D $ 0 0
Retail demand, $ q_R^D $ $ \frac{1}{2} $ $ \frac{1}{2} $
Licensed demand, $ q_L^D $ $ \frac{1}{2} $ $ \frac{1}{2} $
Piracy demand, $ q_P^D $ $ \frac{1}{2} $ $ \frac{1}{2} $
Profit
Producer profit, $ \pi _M^D $ $ \frac{{\theta - 2c}}{4} $ $ \frac{{1 - 8c(1 - \theta )}}{{32c}} $
Retail profit, $ \pi _R^D $ $ \frac{{1 - \theta }}{4} $ $ \frac{{1 - \theta }}{4} $
Table Options

Download as excel

$ c \in (0,\frac{1}{4}] $ $ c \in (\frac{1}{4},\infty ) $
Copyright protection level, $ {e^D} $ 1 $ \frac{1}{{4c}} $
Price
Wholesale price, $ {w^D} $ $ \frac{\theta }{2} $ $ \frac{{1 - 4c(1 - \theta )}}{{8c}} $
Online-direct price, $ p_M^D $ $ \frac{\theta }{2} $ $ \frac{{1 - 4c(1 - \theta )}}{{8c}} $
Retail price, $ p_R^D $ $ \frac{1}{2} $ $ \frac{1}{{8c}} $
Demand
Online-direct demand, $ q_M^D $ 0 0
Retail demand, $ q_R^D $ $ \frac{1}{2} $ $ \frac{1}{2} $
Licensed demand, $ q_L^D $ $ \frac{1}{2} $ $ \frac{1}{2} $
Piracy demand, $ q_P^D $ $ \frac{1}{2} $ $ \frac{1}{2} $
Profit
Producer profit, $ \pi _M^D $ $ \frac{{\theta - 2c}}{4} $ $ \frac{{1 - 8c(1 - \theta )}}{{32c}} $
Retail profit, $ \pi _R^D $ $ \frac{{1 - \theta }}{4} $ $ \frac{{1 - \theta }}{4} $
Table 4.  Equilibrium outcomes in the pirated market when the producer sells discs through traditional retailers
$ c \in (0,\frac{n}{{4(1 + n)}}] $ $ c \in (\frac{n}{{4(1 + n)}},\infty ) $
Copyright protection level, $ {e^{nT}} $ 1 $ \frac{n}{{4(1 + n)c}} $
Price
Wholesale price, $ {w^{nT}} $ $ \frac{1}{2} $ $ \frac{n}{{8(1 + n)c}} $
Retail price, $ p_R^{nT} $ $ \frac{{2 + n}}{{2(1 + n)}} $ $ \frac{{{n^2} + 2n}}{{8{{(1 + n)}^2}c}} $
Demand
Retail $ i $'s demand, $ Q_i^{nT} $ $ \frac{1}{{2(1 + n)}} $ $ \frac{1}{{2(1 + n)}} $
Licensed demand, $ Q_R^{nT} $ $ \frac{n}{{2(1 + n)}} $ $ \frac{n}{{2(1 + n)}} $
Piracy demand, $ Q_P^{nT} $ $ \frac{{n + 2}}{{2(1 + n)}} $ $ \frac{{n + 2}}{{2(1 + n)}} $
Profit
Producer profit, $ \pi _M^{nT} $ $ \frac{{n - 2(1 + n)c}}{{4(1 + n)}} $ $ \frac{{{n^2}}}{{32{{(1 + n)}^2}c}} $
Retail profit, $ \pi _R^{nT} $ $ \frac{1}{{4{{(1 + n)}^2}}} $ $ \frac{1}{{16{{(1 + n)}^3}c}} $
Table Options

Download as excel

$ c \in (0,\frac{n}{{4(1 + n)}}] $ $ c \in (\frac{n}{{4(1 + n)}},\infty ) $
Copyright protection level, $ {e^{nT}} $ 1 $ \frac{n}{{4(1 + n)c}} $
Price
Wholesale price, $ {w^{nT}} $ $ \frac{1}{2} $ $ \frac{n}{{8(1 + n)c}} $
Retail price, $ p_R^{nT} $ $ \frac{{2 + n}}{{2(1 + n)}} $ $ \frac{{{n^2} + 2n}}{{8{{(1 + n)}^2}c}} $
Demand
Retail $ i $'s demand, $ Q_i^{nT} $ $ \frac{1}{{2(1 + n)}} $ $ \frac{1}{{2(1 + n)}} $
Licensed demand, $ Q_R^{nT} $ $ \frac{n}{{2(1 + n)}} $ $ \frac{n}{{2(1 + n)}} $
Piracy demand, $ Q_P^{nT} $ $ \frac{{n + 2}}{{2(1 + n)}} $ $ \frac{{n + 2}}{{2(1 + n)}} $
Profit
Producer profit, $ \pi _M^{nT} $ $ \frac{{n - 2(1 + n)c}}{{4(1 + n)}} $ $ \frac{{{n^2}}}{{32{{(1 + n)}^2}c}} $
Retail profit, $ \pi _R^{nT} $ $ \frac{1}{{4{{(1 + n)}^2}}} $ $ \frac{1}{{16{{(1 + n)}^3}c}} $
Table 5.  Equilibrium outcomes in the pirated market when the producer sells discs through traditional retailers and an online-direct channel
$ c \in (0,\frac{n}{{{{(1 + n)}^2}}}] $ $ c \in (\frac{n}{{{{(1 + n)}^2}}},\infty ) $
Copyright protection level, $ {e^{nD}} $ 1 $ \frac{n}{{{{(1 + n)}^2}c}} $
Price
Wholesale price, $ {w^{nD}} $ $ \frac{\theta }{{1 + n}} $ $ \frac{{n - (1 - \theta ){{(1 + n)}^2}c}}{{{{(1 + n)}^3}c}} $
Online-direct price, $ p_M^{nD} $ $ \frac{\theta }{{1 + n}} $ $ \frac{{n - (1 - \theta ){{(1 + n)}^2}c}}{{{{(1 + n)}^3}c}} $
Retail price, $ p_R^{nD} $ $ \frac{1}{{1 + n}} $ $ \frac{n}{{{{(1 + n)}^3}c}} $
Demand
Online-direct demand, $ Q_M^{nD} $ 0 0
Retail $ i $'s demand, $ Q_i^{nD} $ $ \frac{1}{{1 + n}} $ $ \frac{1}{{1 + n}} $
Licensed demand, $ Q_L^{nD} $ $ \frac{n}{{1 + n}} $ $ \frac{n}{{1 + n}} $
Piracy demand, $ Q_P^{nD} $ $ \frac{1}{{1 + n}} $ $ \frac{1}{{1 + n}} $
Profit
Producer profit, $ \pi _M^{nD} $ $ \frac{{2n\theta - {{(1 + n)}^2}c}}{{2{{(1 + n)}^2}}} $ $ \frac{{{n^2} - 2(1 - \theta ){{(1 + n)}^2}cn}}{{2{{(1 + n)}^4}c}} $
Retail profit, $ \pi _R^{nD} $ $ \frac{{1 - \theta }}{{{{(1 + n)}^2}}} $ $ \frac{{1 - \theta }}{{{{(1 + n)}^2}}} $
Table Options

Download as excel

$ c \in (0,\frac{n}{{{{(1 + n)}^2}}}] $ $ c \in (\frac{n}{{{{(1 + n)}^2}}},\infty ) $
Copyright protection level, $ {e^{nD}} $ 1 $ \frac{n}{{{{(1 + n)}^2}c}} $
Price
Wholesale price, $ {w^{nD}} $ $ \frac{\theta }{{1 + n}} $ $ \frac{{n - (1 - \theta ){{(1 + n)}^2}c}}{{{{(1 + n)}^3}c}} $
Online-direct price, $ p_M^{nD} $ $ \frac{\theta }{{1 + n}} $ $ \frac{{n - (1 - \theta ){{(1 + n)}^2}c}}{{{{(1 + n)}^3}c}} $
Retail price, $ p_R^{nD} $ $ \frac{1}{{1 + n}} $ $ \frac{n}{{{{(1 + n)}^3}c}} $
Demand
Online-direct demand, $ Q_M^{nD} $ 0 0
Retail $ i $'s demand, $ Q_i^{nD} $ $ \frac{1}{{1 + n}} $ $ \frac{1}{{1 + n}} $
Licensed demand, $ Q_L^{nD} $ $ \frac{n}{{1 + n}} $ $ \frac{n}{{1 + n}} $
Piracy demand, $ Q_P^{nD} $ $ \frac{1}{{1 + n}} $ $ \frac{1}{{1 + n}} $
Profit
Producer profit, $ \pi _M^{nD} $ $ \frac{{2n\theta - {{(1 + n)}^2}c}}{{2{{(1 + n)}^2}}} $ $ \frac{{{n^2} - 2(1 - \theta ){{(1 + n)}^2}cn}}{{2{{(1 + n)}^4}c}} $
Retail profit, $ \pi _R^{nD} $ $ \frac{{1 - \theta }}{{{{(1 + n)}^2}}} $ $ \frac{{1 - \theta }}{{{{(1 + n)}^2}}} $
[1]

Yan-Xin Chai, Steven Ji-Fan Ren, Jian-Qiang Zhang. The impacts of digital content piracy and copyright protection policies when consumers are loss averse. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021127
[2]

Lisha Wang, Huaming Song, Ding Zhang, Hui Yang. Pricing decisions for complementary products in a fuzzy dual-channel supply chain. Journal of Industrial and Management Optimization, 2019, 15 (1) : 343-364. doi: 10.3934/jimo.2018046
[3]

Chong Zhang, Yaxian Wang, Ying Liu, Haiyan Wang. Coordination contracts for a dual-channel supply chain under capital constraints. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1485-1504. doi: 10.3934/jimo.2020031
[4]

Mingyong Lai, Hongzhao Yang, Erbao Cao, Duo Qiu, Jing Qiu. Optimal decisions for a dual-channel supply chain under information asymmetry. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1023-1040. doi: 10.3934/jimo.2017088
[5]

Wei Chen, Fuying Jing, Li Zhong. Coordination strategy for a dual-channel electricity supply chain with sustainability. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021139
[6]

Xi Zhao, Teng Niu. Impacts of horizontal mergers on dual-channel supply chain. Journal of Industrial and Management Optimization, 2022, 18 (1) : 655-680. doi: 10.3934/jimo.2020173
[7]

Wanting Hu, Jingjing Ding, Pengzhen Yin, Liang Liang. Dynamic pricing and sales effort in dual-channel retailing for seasonal products. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022005
[8]

Hongxia Sun, Yao Wan, Yu Li, Linlin Zhang, Zhen Zhou. Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours. Journal of Industrial and Management Optimization, 2021, 17 (2) : 601-631. doi: 10.3934/jimo.2019125
[9]

Lei Yang, Jingna Ji, Kebing Chen. Advertising games on national brand and store brand in a dual-channel supply chain. Journal of Industrial and Management Optimization, 2018, 14 (1) : 105-134. doi: 10.3934/jimo.2017039
[10]

Lianxia Zhao, Jianxin You, Shu-Cherng Fang. A dual-channel supply chain problem with resource-utilization penalty: Who can benefit from sales effort?. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2837-2853. doi: 10.3934/jimo.2020097
[11]

Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial and Management Optimization, 2022, 18 (1) : 541-560. doi: 10.3934/jimo.2020167
[12]

Solaleh Sadat Kalantari, Maryam Esmaeili, Ata Allah Taleizadeh. Selling by clicks or leasing by bricks? A dynamic game for pricing durable products in a dual-channel supply chain. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021221
[13]

Ning Li, Zheng Wang. Optimal pricing and ordering strategies for dual-channel retailing with different shipping policies. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2021227
[14]

Jinsen Guo, Yongwu Zhou, Baixun Li. The optimal pricing and service strategies of a dual-channel retailer under free riding. Journal of Industrial and Management Optimization, 2022, 18 (3) : 2049-2076. doi: 10.3934/jimo.2021056
[15]

Chao Zhao, Jixiang Song. Coordination of dual-channel supply chain considering differential pricing and loss-aversion based on quality control. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022053
[16]

Haijiao Li, Kuan Yang, Guoqing Zhang. Optimal pricing strategy in a dual-channel supply chain: A two-period game analysis. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022072
[17]

Lizhong Peng, Shujun Dang, Bojin Zhuang. Localization operator and digital communication capacity of channel. Communications on Pure and Applied Analysis, 2007, 6 (3) : 819-827. doi: 10.3934/cpaa.2007.6.819
[18]

Claude Carlet, Sylvain Guilley. Complementary dual codes for counter-measures to side-channel attacks. Advances in Mathematics of Communications, 2016, 10 (1) : 131-150. doi: 10.3934/amc.2016.10.131
[19]

Minjia Shi, Daitao Huang, Lin Sok, Patrick Solé. Double circulant self-dual and LCD codes over Galois rings. Advances in Mathematics of Communications, 2019, 13 (1) : 171-183. doi: 10.3934/amc.2019011
[20]

Suat Karadeniz, Bahattin Yildiz. Double-circulant and bordered-double-circulant constructions for self-dual codes over $R_2$. Advances in Mathematics of Communications, 2012, 6 (2) : 193-202. doi: 10.3934/amc.2012.6.193

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (471)
  • HTML views (408)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy