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doi: 10.3934/jimo.2021056

## 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

Received  March 2019 Revised  December 2020 Published  March 2021

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

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.

Citation: Jinsen Guo, Yongwu Zhou, Baixun Li. The optimal pricing and service strategies of a dual-channel retailer under free riding. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021056
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##### References:
Channel structures of dual-channel retailers
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
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
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
The impact of $\lambda$ on the optimal decision and profit of the retailer's two channels under the TC-Stackelberg and RS-Stackelberg scenarios">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
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
 $p_{i}$ 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
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
 $a$ $\Omega$ 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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