According to the evolutionary game analysis of carbon surplus and carbon deficit local governments provided above, without the intervention of the central government, no compensation is the evolutionarily stable strategy of carbon deficit local governments, and the socially optimal goal (conservation and compensation) cannot be achieved. The central government must establish incentive and restraint mechanisms to guide local government strategies to converge to the socially optimal goal. The central government can construct the following three types of incentives and restraints to guide local government behavior toward the socially optimal goal.
3.4.1. Game Analysis of Carbon Offsetting under Incentive and Restraint Mechanism 1
Constructing the local government carbon offsetting game model according to Incentive and Restraint Mechanism 1, the benefit matrix of the carbon surplus and carbon deficit local governments game can be obtained, as shown in
Table 3, where
The replicator dynamics of a strategy adjustment by carbon surplus local governments are
When , that is, carbon surplus local governments stop strategy adjustment to reach equilibrium, then , . When , is the evolutionarily stable strategy of carbon surplus local governments; otherwise, is the evolutionarily stable strategy of carbon surplus local governments.
Similarly, the replicator dynamics of a strategy adjustment by carbon deficit local governments remains the same: . Subsequently, is the evolutionarily stable equilibrium point of carbon deficit local governments.
Therefore, according to the above analysis, the incentive and restraint mechanism for carbon surplus local governments only affects their equilibrium strategy. Adjusting the reward and penalties can encourage them to promote carbon emission reduction or strengthen carbon storage projects. Furthermore, the rewards and penalties can replace each other to achieve the same results. However, they cannot change the behavior of carbon deficit local governments, and the “no compensation” strategy is still the evolutionarily stable strategy of carbon deficit local governments. Therefore, the incentive and restraint mechanism that only targets carbon surplus local governments does not work effectively.
3.4.2. Game Analysis of Carbon Offsetting under Incentive and Restraint Mechanism 2
Constructing the local government carbon offsetting game model according to Incentive and Restraint Mechanism 2, the benefit matrix of the carbon surplus and carbon deficit local governments game can be obtained, as shown in
Table 4. The replicator dynamics of the carbon surplus local governments strategy adjustment remains the same:
When , that is, the carbon surplus local government stops strategy adjustment to reach equilibrium, then , , When , is the evolutionarily stable equilibrium point of carbon surplus local governments.
The expected benefits of adopting compensation and no compensation for carbon deficit local governments are
The replicator dynamics of strategy adjustment then becomes
Let , that is, the carbon deficit local government stops strategy adjustment to reach equilibrium, then , .
When , is the stable equilibrium strategy—when the sum of rewards and penalties from the central government to carbon deficit local governments is greater than the compensation paid to carbon surplus local governments, carbon deficit local government choose the compensation strategy as the evolutionarily stable strategy. Otherwise, the no compensation strategy is the evolutionarily stable strategy for carbon deficit local governments.
According to the above analysis, the restraint and incentive mechanism for carbon deficit local governments only affects their equilibrium strategy. When the conservation benefit to carbon surplus local governments is greater than the cost, the restraint and incentive mechanism for carbon deficit local governments can have better role results. Adjusting the rewards and penalties can encourage carbon deficit local governments to compensate carbon surplus local governments and help carbon surplus local governments choose the conservation strategy.
3.4.3. Game Analysis of Carbon Offsetting under Incentive and Restraint Mechanism 3
Constructing the local government carbon offsetting game model according to Incentive and Restraint Mechanism 3, the benefit matrix of the game between the carbon surplus and the carbon deficit local governments can be obtained, as shown in
Table 5.
The replicator dynamics equations for strategy adjustments by carbon surplus local governments and carbon deficit local governments, respectively, are
Let , can give . , , , , . If , , then there are five equilibria in the evolutionary game between carbon surplus and carbon deficit local governments: , , , ,.
Let
and
. We use the Jacobian matrix to analyze the stability of each local equilibrium point of this two-dimensional dynamical system:
The stable equilibrium point of the replicator dynamics equation satisfies the following two conditions.
- (1)
.
- (2)
.
Table 6 was obtained from the Jacobian matrix of the replicator dynamics equation.
The stability of the equilibrium points can be judged from the Jacobian matrix as follows.
(1) When
,
,
, and
, (1, 1) is the only stable equilibrium point. The phase diagram of the dynamic evolution of carbon surplus and carbon deficit local governments is shown in
Figure 1a. That is, the central government’s incentives and penalties for carbon surplus and carbon deficit local governments’ behavioral strategies are sufficiently strong to compensate for the net costs of compensation and conservation in any case, and local governments’ behavior will converge to the social optimum, ensuring that the central government’s carbon offset policy can be effectively implemented. However, larger rewards and penalties require not only greater financial support from the central government, but also more administration costs in the process of implementing the rewards and penalties.
(2) When
,
,
, and
, both (0, 0) and (1, 1) are stable equilibrium points, and
are saddle points. The phase diagram of the dynamic evolution of carbon surplus and carbon deficit local governments are shown in
Figure 1b. That is, there is no guarantee that the (1, 1) state will definitely be realized, and according to the phase diagram of the dynamic evolution of carbon surplus local governments and carbon deficit local governments (
Figure 1b), it is known that the probability of convergence to the equilibrium state (1, 1) is
, whereby the larger the area of ABCH, the higher the probability of convergence to the (1, 1) state, and the more effectively the carbon offset policy can be implemented. The area of ABCH is related to the saddle point H. When point H converges to (0, 0), its area is larger, and the coordinates of point H are
; therefore, when
is larger, point H will converge to the origin (0, 0). This indicates that the greater the rewards and penalties from the central government, the higher the probability that the local government game will converge to (1, 1), and the more effectively carbon offset policies can be implemented.
(3) When
,
,
, and
, (0, 0) is the only stable equilibrium point. The phase diagram of the dynamic evolution of carbon surplus and carbon deficit local governments is shown in
Figure 1c.
(4) When
,
,
, and
, (0, 1) and (1, 0) are stable equilibrium points, and
are saddle points. The phase diagram of the dynamic evolution of carbon surplus and carbon deficit local governments is shown in
Figure 1d.
The above discussion states that under Incentive and Restraint Mechanism 3, the central government’s rewards and penalties for both carbon surplus and carbon deficit local governments have a greater impact on both parties’ decisions. Only when certain conditions are met can local governments’ decisions be driven closer to the socially optimal goal.