Cost-sharing strategy for carbon emission reduction and sales effort: A nash game with government subsidy

Xue-Yan Wu; Zhi-Ping Fan; Bing-Bing Cao

doi:10.3934/jimo.2019040

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2020, Volume 16, Issue 4: 1999-2027. Doi: 10.3934/jimo.2019040

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Cost-sharing strategy for carbon emission reduction and sales effort: A nash game with government subsidy

1.
Department of Information Management and Decision Sciences, School of Business Administration, Northeastern University, Shenyang 110169, China
2.
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
3.
School of Management, Guangzhou University, Guangzhou 510006, China

^* Corresponding author: Bing-Bing Cao
^* Corresponding author: Bing-Bing Cao

Received: July 31, 2018

Revised: October 31, 2018

Early access: May 2019

Published: May 2020

The first author is supported by the National Natural Science Foundation of China (Project No. 71871049) and the 111 Project (B16009)

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Abstract

We investigate the cost-sharing strategies of a retailer and a manufacturer in a Nash game considering government subsidy, consumers' green preference and retailer's sales effort. We provide a function to describe the demand for green products considering the effect of green preference of consumers and the sales effort of the retailer. Next, we construct profit functions of the manufacturer and the retailer considering government subsidy for four scenarios: no sharing of cost (NSC), sharing of carbon emission reduction cost (SCERC), sharing of sales effort cost (SSEC), and sharing both carbon emission reduction cost and sales effort cost (SBC). Furthermore, we determine the optimal policies of price, sales effort level, wholesale price and carbon emission reduction effort level for the four scenarios by maximizing the profits of the manufacturer and the retailer in the Nash game. We find that the sales effort cost-sharing ratio and the carbon emission reduction cost-sharing ratio can affect the optimal policies of the manufacturer and the retailer, and the trends and extent of effects may be different. Our results show that it is advantageous for the manufacturer and the retailer to consider the cost-sharing effects of sales effort and carbon emission reduction effort, and the optimal policies of the retailer and the manufacturer are different for different scenarios.

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Mathematics Subject Classification: Primary: 90B05, 68W27; Secondary: 68W40.

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Figure 1. The structure and communication process of a green supply chain

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Figure 2. The green sensitivity demand function

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Figure 3. The impacts of sharing ratios $ {\gamma _A} $ and $ {\gamma _e} $ on price $ p $

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Figure 4. The impacts of sharing ratios $ {\gamma _A} $ and $ {\gamma _e} $ on sales effort level $ A $

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Figure 5. The impacts of sharing ratios $ {\gamma _A} $ and $ {\gamma _e} $ on wholesale price $ w $

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Figure 6. The impacts of sharing ratios $ {\gamma _A} $ and $ {\gamma _e} $ on carbon emission reduction effort level $ e $

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Figure 7. The impacts of sharing ratios $ {\gamma _A} $ and $ {\gamma _e} $ on the retailer's profit $ \pi {_R^{4*} } $

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Figure 8. The impacts of sharing ratios $ {\gamma _A} $ and $ {\gamma _e} $ on the manufacturer's profit $ {\pi _M} $

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Figure 9. The impacts of sharing ratios $ {\gamma _A} $ and $ {\gamma _e} $ on profit $ {\pi _{SC}} $ of the supply chain

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