Analysis of the short-term game and long-term evolutionary game behaviors of the waste battery remanufacturing market considering government subsidies

Daoming Dai; Lei Liu; Xuanyu Wu

doi:10.3934/jimo.2022119

Article Contents

2023, Volume 19, Issue 6: 3976-4000. Doi: 10.3934/jimo.2022119

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Analysis of the short-term game and long-term evolutionary game behaviors of the waste battery remanufacturing market considering government subsidies

1.
School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China
2.
School of Management, Hefei University of Technology, Hefei 230009, China

^*Corresponding author: Lei Liu
^*Corresponding author: Lei Liu

Received: December 2021

Revised: March 2022

Early access: July 2022

Published: June 2023

The authors acknowledge support from Key Project of Natural Science Research of Universities in Anhui Province (KJ2019A0662) and the Graduate Research and Innovation Fund of Anhui University of Finance and Economics (ACYC2020363)

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Abstract

The popularity of new energy vehicles is undoubtedly the best response to the current global call to protect the environment, and the subsequent waste battery recycling and remanufacturing industry is quietly emerging under government promotion. This paper considers the government provides production subsidy or consumption subsidy for a supply chain consisting of a manufacturer and a remanufacturer. The main theme of this research is to explore the impacts of these two types of subsidy on the short-term game and long-term evolutionary game behaviors of the manufacturer and the remanufacturer. To be specific, a Cournot model is built to exam short-term game behaviors in case of production subsidy and consumption subsidy, respectively. Furthermore, we investigate a nonlinear dynamic system to study the long-term evolutionary trend of the supply chain, including long-term operation strategies, the stability of the equilibrium, and how different subsidies impact the system. Results suggest that: (a) the production subsidy is better for higher output of remanufactured products when the eco-design cost of new products is relatively low. And this subsidy works better when consumers are more environmentally conscious. (b) The government is more likely to choose consumption subsidy when consumers have less acceptance of remanufactured products. (c) In the long-term market, the consumption subsidy is more beneficial for the market to remain stable. Nevertheless, excessive adjustments in output by the manufacturer and the remanufacturer can still lead the market to be uncontrolled.

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Mathematics Subject Classification: Primary: 90B50; Secondary: 91A35, 91A80.

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Figure 1. Remanufacturer profit comparisons between different subsidy policies

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Figure 2. The change of $ q_n^{NS} $, $ {e^{NS}} $ and $ q_r^{NS} $ along with $ s $ and $ \delta $

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Figure 3. The change of $ q_n^{RS} $, $ {e^{RS}} $ and $ q_r^{RS} $ along with $ s $ and $ \delta $

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Figure 4. The profit comparisons between different subsidies

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Figure 5. The feasible domains of government subsidies

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Figure 6. Bifurcation diagram of $ k_1^j $

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Figure 7. Bifurcation diagram of $ k_3^j $

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Figure 8. Lyapunov exponent and Entropy with respect to $ k_1^{NS} $

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Figure 9. Lyapunov exponent and Entropy with respect to $ k_1^{RS} $

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Figure 10. The average profits with respect to $ k_1^j $

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Figure 11. The average profits with respect to $ k_3^j $

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Figure 12. 3D-bifurcation with respect to $ k_1^j $ and $ s $

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Figure 13. 3D-bifurcation with respect to $ k_3^j $ and $ s $

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Table 1. Notation and description

Notation	Description
$ {p_i} $	The price of new or manufactured product
$ {c_i} $	The unit production cost of new or manufactured product
$ {q_i} $	The output of new or manufactured product
$ e $	Eco-design level of new product
$ \theta $	Consumers' acceptance of remanufactured product
$ \delta $	Consumers' environmental awareness
$ s $	Government subsidy
$ v $	Consumers' willingness to pay for new products
$ \eta $	The manufacturer' marginal cost in product eco-design
$ CS $	The total consumer surplus
$ GS $	Subsidy expenditure
$ {\pi _m} $	The profit of the manufacturer
$ {\pi _r} $	The profit of the remanufacturer
$ {\pi _g} $	The profit of the government

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