3.1. Stakeholders
Adopting the Xiaomi SU7 vehicle as an example, the key to manufacturing green new energy vehicles is the integration of various suppliers. Therefore, green innovation in the supply chain cannot be separated from the role of ISs, mainly because they enable the screening and elimination of suppliers that do not meet the requirements of green standards. GAs play a key role in promoting the green and sustainable development of supply chains. Notably, a GA is both an important driver of green development and a beneficiary in the development process. The main reason is that GAs can guide the behavioural strategies of ISs through policy regulation and improve the social welfare of people. In addition, the realisation of green development is inseparable from the support of FIs, so the main players participating in the evolutionary game are ISs, GAs and FIs.
In the process of evolution, ISs are always accustomed to the pursuit of profit maximisation, and the motivation for choosing green development mainly comes from the government’s subsidy mechanism and willingness to assume social responsibility. In the early stage of evolution, the government guides ISs and FIs to participate in green development through a subsidy mechanism, and whether FIs are willing to provide financial support to ISs depends on the profitability of the ISs, and the sustained profitability of ISs will attract more FIs to participate in green development. However, in the development of a green supply chain in which ISs, GAs, and FIs participate, the decision-making behaviours of the three and their influence relationships are extremely complex, and the correlation relationships among them need to be further analysed through the EGM. Therefore, this paper studies the evolution of green supply chain stakeholders’ behaviour strategies under the government compensation mechanism. The evolutionary relationships among the three stakeholders are shown in
Figure 1.
On the basis of the literature, three assumptions are made regarding the evolutionary game encompassing ISs, GAs, and FIs.
Assumption 1. The participating entities are ISs, GAs, and FIs. The strategy selection of ISs includes two options: investing in green technology to achieve green development, which is referred to as green development (GD), and not engaging in green technology innovation to achieve conventional development, which is referred to as conventional development (CD). The strategy selection of GAs includes positive support (PS) and negative support (NS). The strategy selection of FIs includes two options, namely, open green credit (OGC) and closed green credit (CGC). The probabilities of an IS choosing the GD strategy, a GA choosing the PS strategy, and an FI choosing the OGC strategy are , respectively.
Assumption 2. All participants are rational individuals, and all three parties adopt the best strategies to maximise their profits [52,53,54]. When an IS chooses green technology innovation, the FI gains greater benefits from conducting a green credit business. Conversely, when an IS does not choose green technology innovation, the FI gains greater profits from not conducting green credit business. Assumption 3. To encourage ISs to choose green technology innovation and FIs to conduct green credit business, the GA must implement certain regulatory measures [39,55,56]. In this paper, the considered GA measures include subsidies or punishments. When the ISs implement green measures and the FI conducts green credit business, the GA will provide certain rewards and subsidies to the ISs and FIs. Conversely, when the ISs do not implement green measures and the FI does not conduct green credit business, the GA will impose certain penalties on the ISs and FIs. The mathematical symbols are defined in Table 1. The ISs can choose between the GD and CD strategies, the probability of choosing the GD is , and the probability of choosing the CD is . The GA can choose between the PS and NS strategies, the probability of choosing the PS strategy is , and the probability of choosing the NS strategy is . The FI can choose between the OGC and CGC strategies. The probability of choosing OGC is , and the probability of choosing CGC is .
3.2. Payoffs for Various Stakeholders
According to the different selection strategies of the different stakeholders, 8 scenarios can be defined, as detailed in
Table 2.
Under the GPO scenario, the ISs choose the GD strategy, the GA chooses the PS strategy, and the FI chooses the OGC strategy. The income obtained by the ISs comprises the credit income obtained from the green credit provided by the FI; the investment income obtained from the green upgrade provided by the ISs; the added value for the green innovation benefits of the ISs ; the GAs incentive mechanism added value for the green innovation benefits of the ISs ; and the incentive income obtained from the GAs. The investment cost of green transformation and upgrading is .
According to the literature [
22,
57,
58], the benefits of the GA include the following: the investment feedback income
obtained by the ISs from green innovation, the feedback income
of innovation benefit appreciation obtained by the FIs through green credit, the feedback income
of green innovation benefit appreciation obtained by the GAs, the cost of the incentive subsidy
issued by the GA to the ISs, and the incentive subsidy
issued by the GA to the FI. The cost of GA participation in green transformation is
, in which GA subsidies and value-added feedback are variables. The income functions are expressed as Equations (1)–(3).
The benefits of the FI include the following: the basic benefits obtained by the FIs for conducting green credit business with the ISs; the GA subsidies obtained by the FIs for conducting green credit business with the ISs; and the costs incurred by the FIs for conducting green credit business.
Under the CPO scenario, the ISs choose the CD strategy, the GA chooses the PS strategy, and the FI chooses the OGC strategy. The benefits of the ISs include credit income
, the cost of obtaining green credit without green innovation
, and the GA penalty
for not implementing green innovation. The benefits provided by the FIs in supporting the green development of the ISs include the basic benefits
for the ISs not to implement GD when conducting green credit business; the subsidies
obtained from the GAs when conducting green credit business; and the cost
of conducting green credit business. The benefits resulting from active GA participation in the green transformation of the ISs include the following: the GA penalties
applied to the ISs when they do not implement green innovation, GA subsidies
, management costs
, and governance costs
. Under this scenario, the income functions of ISs, FIs, and GAs are expressed as Equations (4)–(6).
Under the GPC scenario, the ISs choose the GD strategy, the GA chooses the PS strategy, and the FIs choose the CGC strategy. The revenue components resulting from the green transformation and upgrading of the ISs include the following: when the FIs do not open a special fund for green credit to the ISs, the latter receives credit income
. Moreover, the ISs receive investment income
when implementing green upgrading, the ISs receive government incentive mechanism added value for green innovation benefits
, the GAs receive incentive income
, and the ISs pay the cost of green transformation and upgrading
. The benefits resulting from FI support for the transformation and upgrading of the ISs are the basic benefits
resulting from the FIs not conducting green credit business with the ISs. The benefits of the GAs’ participation in the green transformation of the ISs include the following: the investment income feedback
received by the ISs when implementing green upgrading; the government incentive mechanism feedback
on the value added of IS green innovation benefits; the incentive and subsidy cost paid by the GAs to the ISs
; and the cost paid by the GAs for participating in green transformation
. The revenue functions obtained by the ISs, FIs, and GAs are expressed in Equations (7)–(9).
Under the CPC scenario, the ISs choose the CD strategy, the GA chooses the PS strategy, and the FI chooses the CGC strategy. The income components resulting from the ISs not implementing green transformation and upgrading include the credit income
obtained by the ISs when the FIs do not open a special fund for green credit and the GA penalty
. The benefits resulting from FIs’ support for green transformation and upgrading of the IS are the basic benefits
obtained by the FIs from not conducting green credit business with the ISs. The benefits of active GA participation in IS green transformation include the penalty
for the IS when it does not implement green innovation, the cost
for GA participation in green transformation, and the cost
for treating environmental pollution by the GAs when the IS does not implement green transformation. Under this scenario, the revenue functions obtained by the ISs, FIs, and GAs are expressed in Equations (10)–(12).
Under the GNO scenario, the ISs choose the GD strategy, the GA chooses the NS strategy, and the FIs choose the OGC strategy. The benefits of the ISs when implementing green transformation and upgrading include the following: the credit return
when the FIs establish a special fund for green credit, the investment return
obtained during green upgrading, the value added
of green innovation benefits when conducting green credit business with the FIs, and the investment cost
of green transformation and upgrading. The benefits of FI support for IS green transformation and upgrading include the basic returns
obtained by the FIs from providing green credit to the ISs, and the cost paid is the cost
of FIs’ green credit. The benefits of active GA participation in IS green transformation include the investment return feedback
obtained during green upgrading and the value-added feedback
of green innovation benefits through FI green credit. The income functions obtained by ISs, FIs, and GAs are expressed as Equations (13)–(15).
Under the CNO scenario, the ISs choose the CD strategy, the GA chooses the NS strategy, and the FI chooses the OGC strategy. The revenue components generated by the ISs when not implementing green transformation and upgrading include the following: the credit income
obtained when the FI establishes a special green credit fund and the cost
incurred when obtaining green credit without conducting green innovation. The revenue generated by FI support for the ISs’ green transformation and upgrading comprises the basic income
earned by the FIs from providing green credit to the ISs, whereas the ISs do not undergo green transformation and the cost
is incurred by the FIs in offering green credit. Moreover, the revenue generated by active GA participation in IS green transformation includes the penalty
imposed on the GAs for adopting a passive policy towards local governments and the governance cost
incurred by the GA. Under this scenario, the revenue functions of ISs, FIs, and GAs are expressed as Equations (16)–(18).
Under the GNC scenario, the ISs choose the GD strategy, the GA chooses the NS strategy, and the FIs choose the CGC strategy. The revenue components generated by IS green transformation and upgrading include the credit revenue
obtained when the FI does not establish a special green credit fund, the investment return
obtained through green upgrading, and the investment cost
of green transformation and upgrading. The revenue generated by FIs to support IS green transformation and upgrading is the basic revenue
obtained by the FIs from not providing green credit to the ISs. The revenue generated by active GA participation in IS green transformation is the investment return feedback
obtained by the ISs through green upgrading. Under this scenario, the revenue functions obtained by ISs, FIs, and GAs are expressed as Equations (19)–(21).
Under the CNC scenario, the ISs choose the CD strategy, the GA chooses the NS strategy, and the FIs choose the CGC strategy. The revenue generated by the ISs when not implementing green transformation and upgrading is the credit revenue
when the FIs do not establish a special green credit fund. The revenue generated by FI support for IS transformation and upgrading is the basic revenue
when green credit is not provided to the ISs, and the revenue generated by active GA participation in IS green transformation includes the punishment
imposed on the ISs by the GAs and the governance cost
paid by the GAs. Under this scenario, the revenue functions obtained by ISs, FAs, and GAs are expressed in Equations (22)–(24).
In the decision-making process, stakeholders make decisions on the basis of maximising their interests, and their decision strategies ultimately affect the evolutionary trend. The payoff matrices of the ISs, GAs, and FIs are summarised in
Table 3.
Next, on the basis of the payoff matrices, the stability strategies of the stakeholders can be analysed via differential equations and dynamic evolution equations.
3.3. Stakeholders’ Analysis of Stability
For ISs, the initial benefits of choosing the GD and CD strategies are
and
, respectively, as expressed in Equations (24) and (26) respectively.
The Malthusian dynamic equation indicates that within a game theory context, when the strategy chosen by the ISs exceeds the average payoff of the FI and GA, it possesses the ability to resist mutant strategies and is better suited to adapt to population evolution [
59]. The dynamic replication equation for ISs can be expressed as Equations (27) and (28).
Assuming that
, the stability theorem of differential equations indicates that for
,
, the probability of the ISs choosing the GD strategy will remain stable since
, where
is a monotonically increasing function. Therefore, when
,
,
, and
, the ISs cannot determine a stable strategy. Moreover, for
,
,
, and
are ESS points. Conversely,
is an ESS point. Notably,
can be expressed as Equation (29):
Assuming that the probabilities of the ISs adopting the GD and CD strategies are
and
, respectively, the intersection points of the projection line of
onto the
plane with the
and
axes are
and
, respectively. In this case,
and
can be calculated via Equations (30) and (31) respectively.
Proposition 1. When , occurs, and when , there is a positive correlation between and the probability of the IS adopting the GD strategy. Moreover, is inversely proportional to the probability of the IS adopting the GD strategy, and is independent of .
Proof of Proposition 1. When , holds true, which suggests that and are also valid. In this case, and . When , holds true. Because , both the numerator and denominator are non-negative numbers. Thus, always holds true. Therefore, there is a positive correlation between and . Because is true, , , , , , and . Notably, , , , , , , and always hold true, indicating a negative correlation between and . Owing to and , is independent of . □
For GAs, the initial benefits of choosing the PS and SN strategies are
and
, respectively, as expressed in Equations (32) and (33) respectively.
The dynamic replication equation for GAs can be expressed as Equations (34) and (35).
When
and
are true, the probability of the GA choosing the PS strategy remains stable. Assuming that
,
is always true since
is a monotonically increasing function. Therefore,
can be chosen such that when
,
and
are always true. At this time, the GA cannot determine a stable strategy. When
,
and
are always true, and
is an ESS point. Otherwise,
is an ESS point. Notably,
can be expressed as Equation (36).
Assuming that the probability of the GA adopting the PS strategy is
, the intersections of
projected onto the
surface are
and
. Notably,
can be calculated with Equation (37).
The probability of the GA adopting the NS strategy is
, which can be calculated via Equation (38).
Proposition 2. When , then and . Moreover, is negatively correlated with the probability of the GA adopting the PS strategy; and are positively correlated with the probability of the GA adopting the PS strategy; and the values of , , , , and are uncertain.
Proof of Proposition 2. When , is always true. Therefore, and are always true. For any value, is always true. Thus, is negatively correlated with . When , is always true. Hence, and are positively correlated with . In addition, there is uncertainty in . For any value, and are uncertain, which is also true for both and . Therefore, there is uncertainty in the relationships among , , , , , and . □
For FIs, the initial benefits of choosing the OGC and CGC strategies are
and
, respectively, as expressed in Equations (39) and (40) respectively.
The dynamic replication equation for GAs can be expressed as Equations (41) and (42).
According to the fundamental theorem of differential equations [
60], when both
and
are true, the probability of the FI choosing the OGC strategy remains stable. Assuming that
,
is always true, which indicates that
is a monotonically decreasing function. Therefore, there exists
such that
, and
is always true for
. In this case, the GA cannot determine a stable strategy. However, when
is true,
and
are always true, which suggests that
is an ESS point. Otherwise,
is an ESS point. Notably,
can be expressed as Equation (43).
Assuming that the probability of the FI adopting the OGC strategy is
, the intersection points of the projection of
onto the plane
are
and
. Then,
can be calculated via Equation (44).
Then, the probability of the FI adopting the CGC strategy is
, which can be calculated with Equation (45).
Proposition 3. When , , and are positively correlated, then and are negatively correlated. However, when , , , and are negatively correlated, and and are positively correlated.
Proof of Proposition 3. When
,
can always be established, and at this time,
and
. For any given value,
is always valid. Therefore,
and
are negatively correlated. When
is met,
and
are always valid. Therefore, when
,
,
, and
are negatively correlated, and
and
are positively correlated. According to EGT, when all the eigenvalues of the Jacobian matrix are negative, the equilibrium point is the ESS point. The eigenvalues of the ESS points are provided in
Table 4. □
Proposition 4. and cannot be ESS points simultaneously, and cannot be ESS points simultaneously, and cannot be ESS points simultaneously, and and cannot be ESS points simultaneously.
Proof of Proposition 4. With the initial values remaining unchanged, as and are opposite numbers, and cannot be ESS points simultaneously. Moreover, and are opposite numbers, so and cannot be ESS points simultaneously. Similarly, and are opposite numbers, so and cannot be ESS points simultaneously. Analogously, and are opposite numbers, so and cannot be ESS points simultaneously. □
Proposition 5. and cannot be simultaneous ESS points, and cannot be simultaneous ESS points, and cannot be simultaneous ESS points, and and cannot be simultaneous ESS points.
Proof of Proposition 5. With the initial values remaining unchanged, as and are opposite numbers, and cannot be simultaneous ESS points. Moreover, and are opposite numbers, so and cannot be simultaneous ESS points. Similarly, and are opposite numbers, so and cannot be simultaneous ESS points. Analogously, and are opposite numbers, so and cannot be simultaneous ESS points. □