Modeling Formation and Operation of Collaborative Green Innovation between Manufacturer and Supplier: A Game Theory Approach
Abstract
:1. Introduction
2. Theoretical Foundation and Factor Selection
2.1. Green Innovation and CGI
2.2. Motivation Factors for Suppliers to Participate in Green Innovation Cooperation
2.3. Determinants for Suppliers Involvement into CGI
- (1)
- Partnership of mutual trust.
- (2)
- Knowledge complementarity and mutual learning.
- (3)
- Level of collaboration.
- (4)
- Green added value and innovation efficacy.
- (5)
- Green revenue distribution strategy.
3. Modelling Green Innovation Collaboration Formation
3.1. Background of the Model and Assumptions
- (1)
- The green innovation revenue generated from the collaboration is calculated by the added income from the collaborative innovation minus the innovation cost, and the added value is incurred from coordinated efforts and knowledge spill-overs.
- (2)
- The two partners obtain the green knowledge stock based on the initial cost input of green knowledge, and they determine the level of knowledge sharing according to the level of trust granted to each other.
- (3)
- CGI could reduce the overall cost of green innovation, but collaboration still incurs a cost for the involved partners. CGI incurs costs, which include the knowledge input cost, green innovation development cost, and collaboration cost. As two partners need to invest in green development, we assume that collaboration can improve innovation efficiency and reduce overall green development costs compared with independent green innovation. Here, the collaborative cost refers to the capital investment cost for information technology capability enhancement and the additional integration cost for the division of the development [53], which needs to be shared by the two partners.
3.2. Description of the Model
- (1)
- Definition of absorptive capacity function , mutual learning level function and knowledge stock function .
- (2)
- Definition of green innovation development cost function .
- (3)
- Definition of cooperative cost function and cost-sharing ratio .
- (4)
- Definition of green innovation value , innovation conversion efficiency , and profit distribution coefficient .
3.3. Mathematical Model
3.4. Model Solution by Using Nash Bargaining Equilibrium
- (1)
- Based on the revenue function, the manufacturer calculates the optimal CGI level , which maximize the value in the formula (8).
- (2)
- Based on the CGI level proposed by the manufacturer, the supplier calculates the optimal cost-sharing rate through formula (9).
- (3)
- Based on the Nash bargaining game, the two partners determine the profit distribution ratio . As the collaboration aim is to maximize the anticipative total green revenue we obtain the objective function in function (11). That is, for any ω, ,
4. Simulation in Different Scenarios
4.1. The effect of trust on total CGI revenue
4.2. The Effect of Knowledge Complementarity on Total CGI Revenue
4.3. The Effect of Product Type and Innovation Efficiency on Total CGI Revenue
4.4. The Effect of Green Knowledge Input on Total CGI Revenue
5. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Notations/Variables | Description | |
---|---|---|
status symbols | F refers to the leading manufacturer, and S refers to the supplier. | |
a | Initial value of the product (a > 0). | |
b | The added green value generated by CGI, defined as the marginal benefit of each unit of sales of green innovative products. | |
status variables | β | The complementarity of green knowledge between the two firms. |
tFS | The manufacturer’s trust level towards the supplier. | |
tSF | The supplier’s trust level towards the manufacturer. | |
zF | The stock of the manufacturer’s green innovation knowledge. | |
zs | The stock of the supplier’s green innovation knowledge. | |
qF | The manufacturer’s knowledge input of green innovation (efforts). | |
qS | The supplier’s knowledge input of green innovation (efforts). | |
control variable | θ | Green collaboration level. |
Distribution ratio of collaboration costs. | ||
independent varible | Green profit distribution ratio for manufacturer F. | |
function notations | Knowledge absorptive capacity of manufacturer F and supplier S. | |
Learning level of Manufacturer F and supplier S. | ||
Total knowledge storage owned the two firms for green innovation. | ||
Green development costs of manufacturer F and supplier S. | ||
Cooperative cost function for CGI. | ||
The efficiency of successful green innovation development | ||
Green innovation revenue for manufacturer F and supplier S. |
Scenarios | ||||||
---|---|---|---|---|---|---|
Figure 1 | 0.2, 0.2 0.4, 0.4 0.6, 0.6 0.8, 0.8 0.8, 0.2 | 1100, 1000 | 3000, 3000 | 0.05, 0.05 | 0.8 | 0, 0.6 |
Figure 2 | 1100, 1000 | 3000, 3000 | 0.05, 0.05 | 0.2 | 0, 0.6 | |
Figure 3 | 1000, 100 | 3000, 3000 | 0.05, 0.05 | 0.8 | 0, 0.6 | |
Figure 4 | 1000, 100 | 3000, 3000 | 0.05, 0.05 | 0.2 | 0, 0.6 | |
Figure 5 | 0.8, 0.8 | 1100,1000 | 3000, 3000 | 2, 2 | 0.2 0.4 0.6 0.8 0.9 | 0, 0.6 |
Figure 6 | 0.8, 0.8 | 1000, 200 | 3000, 3000 | 2, 2 | 0, 0.6 | |
Figure 7 | 0.8, 0.8 | 200, 200 | 300, 3000 | 2, 2 | 0, 0.6 | |
Figure 8 | 0.8, 0.8 | 1000, 1000 | 3000, 3000 | 0.05, 0.05 | 0.6 | 0, 0.2 0, 0.8 |
Figure 9 | 0.8, 0.8 | (50, 100, 200, 400, 600, 800, 900, 1000), 1000 | 3000, 3000 | 0.05, 0.05 | 0.6 | 0, 0.6 |
Figure 10 | 0.8, 0.8 | (50, 100, 200, 400, 600, 800, 900, 1000), 1000 | 3000, 3000 | 2, 0.05 | 0.6 | 0, 0.6 |
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Li, Q.; Kang, Y.; Tan, L.; Chen, B. Modeling Formation and Operation of Collaborative Green Innovation between Manufacturer and Supplier: A Game Theory Approach. Sustainability 2020, 12, 2209. https://doi.org/10.3390/su12062209
Li Q, Kang Y, Tan L, Chen B. Modeling Formation and Operation of Collaborative Green Innovation between Manufacturer and Supplier: A Game Theory Approach. Sustainability. 2020; 12(6):2209. https://doi.org/10.3390/su12062209
Chicago/Turabian StyleLi, Qian, Yuanfei Kang, Lingling Tan, and Bo Chen. 2020. "Modeling Formation and Operation of Collaborative Green Innovation between Manufacturer and Supplier: A Game Theory Approach" Sustainability 12, no. 6: 2209. https://doi.org/10.3390/su12062209