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doi: 10.3934/jimo.2021100
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Managing piracy: Dual-channel strategy for digital contents

 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 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.

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, 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.

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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.
In the pirated market, the influences of dual-channel marketing on the wholesale price, retail price and retail profit margin, respectively
The win-win region by the online-direct channel's introduction in the pirated market
The win-win regions by the online-direct channel's introduction in the pirated market when and $n = 1$, $n = 2$, respectively
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, $\pi _R^b$ $\frac{1}{{16}}$ $\frac{{1 - \theta }}{4}$
 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, $\pi _R^b$ $\frac{1}{{16}}$ $\frac{{1 - \theta }}{4}$
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, $\pi _R^T$ $\frac{1}{{16}}$ $\frac{1}{{64c}}$
 $c \in (0,\frac{1}{8}]$ $c \in (\frac{1}{8},\infty )$ 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, $\pi _R^T$ $\frac{1}{{16}}$ $\frac{1}{{64c}}$
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, $\pi _R^D$ $\frac{{1 - \theta }}{4}$ $\frac{{1 - \theta }}{4}$
 $c \in (0,\frac{1}{4}]$ $c \in (\frac{1}{4},\infty )$ 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, $\pi _R^D$ $\frac{{1 - \theta }}{4}$ $\frac{{1 - \theta }}{4}$
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, $\pi _R^{nT}$ $\frac{1}{{4{{(1 + n)}^2}}}$ $\frac{1}{{16{{(1 + n)}^3}c}}$
 $c \in (0,\frac{n}{{4(1 + n)}}]$ $c \in (\frac{n}{{4(1 + n)}},\infty )$ 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, $\pi _R^{nT}$ $\frac{1}{{4{{(1 + n)}^2}}}$ $\frac{1}{{16{{(1 + n)}^3}c}}$
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, $\pi _R^{nD}$ $\frac{{1 - \theta }}{{{{(1 + n)}^2}}}$ $\frac{{1 - \theta }}{{{{(1 + n)}^2}}}$
 $c \in (0,\frac{n}{{{{(1 + n)}^2}}}]$ $c \in (\frac{n}{{{{(1 + n)}^2}}},\infty )$ 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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