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

  • * Corresponding author: Bing-Bing Cao

    * Corresponding author: Bing-Bing Cao

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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  • 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.

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


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

    Figure 2.  The green sensitivity demand function

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

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

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

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

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

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

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

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