American Institute of Mathematical Sciences

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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  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 & Management Optimization, 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[9]

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

[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.  Google Scholar

[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.  Google Scholar

[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/. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[20]

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

[21]

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

[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.  Google Scholar

[23]

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

[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.  Google Scholar

[25]

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

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[9]

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

[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.  Google Scholar

[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.  Google Scholar

[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/. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[20]

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

[21]

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

[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.  Google Scholar

[23]

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

[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.  Google Scholar

[25]

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

[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.  Google Scholar

[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.  Google Scholar

Figure 1.  In the pirated market, the influences of dual-channel marketing on the wholesale price, retail price and retail profit margin, respectively
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Figure 2.  The win-win region by the online-direct channel's introduction in the pirated market
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Figure 3.  The win-win regions by the online-direct channel's introduction in the pirated market when and $ n = 1 $, $ n = 2 $, respectively
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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} $
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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}} $
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$ 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} $
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$ 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}} $
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$ 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}}} $
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$ 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}}} $
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