The optimal pricing and service strategies of a dual-channel retailer under free riding

Jinsen Guo; Yongwu Zhou; Baixun Li

doi:10.3934/jimo.2021056

Article Contents

2022, Volume 18, Issue 3: 2049-2076. Doi: 10.3934/jimo.2021056

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The optimal pricing and service strategies of a dual-channel retailer under free riding

1.
Business School, Henan Normal University, Xinxiang 453007, China
2.
School of Business Administration, South China University of Technology, , Guangzhou 510640, China
3.
Business School, Shantou University, Shantou 515063, China
4.
Research Institute of Innovation Competitiveness of Guangdong, HongKong and Macao Bay Area, Guangdong University of Finance and Economics, Guangzhou 510320, China

^* Corresponding author: Baixun Li
^* Corresponding author: Baixun Li

Received: February 28, 2019

Revised: November 30, 2020

Published: May 2022

This research is supported by the National Natural Science Foundation of China with Grant Numbers 71902055, 71401042, 71701051

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Abstract

Free riding refers to that in a multi-channel market, consumers enjoy the presale service of a product at one channel but purchase the product at another channel. In this paper, we study the optimal pricing and service strategies for a dual-channel retailer, who sells a product through both a traditional retail channel and an online channel. We assume that the offline channel provides the presale service but the online channel does not. We investigate how the changes of the degree of free riding affect the pricing/service strategies and profits of the two channels under three different scenarios: Stackelberg competition, Bertrand competition and channel integration. Our analysis shows that when the dual-channel retailer operates the two channels separately, no matter under which competitive scenario, free riding has a negative effect on both channels. And it is much more beneficial for the dual-channel retailer to let one channel work as a leader and another channel as a follower than to let the two channels make their decision simultaneous. In contrast, when the dual-channel retailer runs the two channels jointly, i.e., employs the channel-integration scenario, free riding may be beneficial to the retailer. Finally, this paper proposes and analyzes a revenue-sharing contract to coordinate a decentralized dual-channel retailer to achieve beneficial outcomes for both channels.

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

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Figure 1. Channel structures of dual-channel retailers

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Figure 2a-2b. The impact of $ \beta $ on the dual-channel retailer's profit under the four scenarios and his/her optimal decision under the channel-integration scenario.Channel structures of dual-channel retailers

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Figure 3a-3b. The impact of $ \eta $ on the dual-channel retailer's profit under the four scenarios and his/her optimal decision under the channel-integration scenario

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Figure 4a-4b. The impact of $ r $ on the dual-channel retailer's profit under the four scenarios and his/her optimal decision under the channel-integration scenario

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Figure 1. Figure 5 The impact of $ \lambda $ on the optimal decision and profit of the retailer's two channels under the TC-Stackelberg and RS-Stackelberg scenarios

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Table 1. Notations used in the paper

$ p_{i} $	Retail price of channel $ i $
$ d_{i} $	Demand of the channel $ i $
$ a_{i} $	Market base or potential demand of channel $ i $
$ \theta_{i} $	Cross-price sensitivity for the two channels, where 0 < $ \theta_{i} $ < 1
$ S $	The pre-sales service level of the traditional channel
$ c_{s} $	The traditional channel's service cost incurred by providing service level $ S $
$ \beta $	The degree of free riding, where 0$ \le \beta \le r $
$ r $	Service sensitivity parameter
$ \lambda $	Revenue sharing rate of the online channel, where 0$ \le \lambda \le $1
$ \pi_{i} $	Profit of the channel $ i $
$ \pi $	The total profit of the dual-channel retailer Subscripts:
$ i= $1	represents the retailer's traditional channel and $ i= $2 the retailer's online channel

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Table 2. The retailer's optimal pricing/service policies and profits of the two channels under different scenarios

$ a$	$\Omega $	Channel integration					TC-Stackelberg						OC-Stackelberg						Bertrand
		$p_{1}^{I^{\ast} }$	$S^{I^{\ast} }$	$p_{2}^{I^{\ast} }$	$\pi^{I\ast }$ (× 10$^{4})$	Sales mode	$p_{1}^{TC}$	$S^{TC}$	$p_{2}^{TC}$	$\pi_{1}^{TC}$ (× 10$^{4})$	$\pi_{2}^{TC}$ (× 10$^{4})$	$\pi^{\, TC}$ (× 10$^{4})$	$p_{1}^{OC}$	$S^{OC}$	$p_{2}^{OC}$	$\pi_{1}^{OC}$ (× 10$^{4})$	$\pi_{2}^{OC}$ (× 10$^{4})$	$\pi^{\, OC}$ (× 10$^{4})$	$p_{1}^{B}$	$S^{B}$	$p_{2}^{B}$	$\pi_{1}^{\, B}$ (× 10$^{4})$	$\pi_{2}^{\, B}$ (× 10$^{4})$	$\pi^{\, B}$ (× 10$^{4})$
40	65.5	—-	107.4	289	7.0234	Single-channel	284	58.7	136	1.1585	1.8385	2.9970	232	50	121	1.1393	1.3513	2.4907	231	50	116	1.1179	1.3490	2.4669
70	65.5 and $\Psi $ < 0	—-	112.5	326	8.9311	Single-channel	304	58.7	155	1.5977	2.3871	3.9849	251	50	141	1.5788	1.8229	3.4017	249	50	135	1.5495	1.8197	3.3692
500	65.5 and $\Psi $ > 0	—-	161.8	802	54.017	Single-channel	584	58.7	426	15.633	18.113	33.746	522	50	421	15.740	16.321	32.062	518	50	404	15.463	16.293	31.756
3500	65.5 and $\Psi $ > 0	3879	139.0	3248	1146.6	Dual-channel	2541	58.7	2317	516.20	536.80	1053.0	2413	50	2378	523.51	520.13	1043.6	2393	50	2279	514.49	519.22	1033.7
5000	65.5 and $\Psi $ > 0	5140	140.1	4500	2258.0	Dual-channel	3519	58.7	3263	1030.6	1064.4	2095.0	3359	50	3356	1045.7	1036.2	2081.8	3331	50	3216	1027.7	1034.4	2062.0

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