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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 & Management Optimization, doi: 10.3934/jimo.2021100
##### References:

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##### References:
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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