Managing piracy: Dual-channel strategy for digital contents

Yan-Xin Chai; Steven Ji-Fan Ren; Jian-Qiang Zhang

doi:10.3934/jimo.2021100

Article Contents

2022, Volume 18, Issue 4: 3001-3027. Doi: 10.3934/jimo.2021100

This issue Previous Article A novel quality prediction method based on feature selection considering high dimensional product quality data Next Article

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

Received: August 2020

Revised: March 2021

Early access: May 2021

Published: July 2022

Abstract / Introduction Full Text(HTML) Figure(3) / Table(5) Related Papers Cited by

Abstract

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:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Full Text(HTML)

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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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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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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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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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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