4.1. Problem Description and Model Hypothesis
In the process of compensation for agricultural land expropriation, it is assumed that both the local government and the expropriated farmers are bounded, rational, and the behavior of the subject has the influence of reciprocal altruistic preference and loss aversion preference. Specifically, reciprocal altruistic preference is under the premise that both parties can obtain reasonable income distribution, and the income improvement of one side can become the source of the increase in psychological utility for the other. As far as farmers are concerned, under the condition of reasonable expropriation and compensation, the government’s expropriation of agricultural land represents the reasonable exercise of public power, and the social benefits will be greatly increased. Farmers recognize the reasonableness and legitimacy of the government’s land expropriation benefits, and farmers’ sense of identity with the government increases, which leads to an increase in psychological effectiveness. As far as the government is concerned, the government collects reasonably and farmers choose to cooperate to accept the performance that can establish a good image of the government. When farmers are satisfied with the benefits of land expropriation compensation, the land expropriation work of the local government will be carried out harmoniously, which not only avoids the outbreak of land expropriation conflicts, but also brings stability to the society, and enhances the reputation and image of the government. This result is a “win-win” performance for both sides, but it can only be achieved on the premise of cooperation between both sides. Loss aversion preference is mainly reflected in the subject’s perception of loss.
Suppose the reciprocal altruism preference coefficient of local government is , and that of farmers is , . Then, under the strategy combination (reasonable collection, cooperation), the utility function of local government is , and that of farmers is .
Suppose the local government’s loss aversion preference coefficient is
, and the farmers’ loss aversion preference coefficient is
,
. Under the combination of the strategy that the local government chooses unreasonable expropriation and the farmers choose cooperation, the local government will have additional income
and the cost will be
,
. The loss suffered by farmers is
, in addition to an additional psychological utility loss, which is related to the additional income seized by the government as a result of unreasonable collection, which is recorded as
. The greater the unreasonable income obtained by the government, the greater the value of farmers’ psychological loss. By the same token, under the strategic combination of reasonable expropriation by local governments and boycott by farmers, farmers will have additional income
and the boycott cost will be
,
. The local government will suffer certain losses as a result of the farmers’ boycott or the punishment of the higher government, which will be recorded as
. In addition, there will be an additional loss of psychological value
, which includes the loss of psychological value caused by extra compensation to farmers, the condemnation of public opinion due to farmers’ boycott, and the loss of government image and reputation. The greater the extra compensation, the greater the psychological utility loss of the government. Therefore, under the strategy combination of unreasonable expropriation and cooperation, the utility of local government is
, and the utility of farmers is
and
. Under the strategy combination of unreasonable expropriation and boycott, the utility of local government is
, and the utility of farmers is
. In this case, both sides have paid a certain cost and suffered certain losses; without any additional benefits, land expropriation compensation conflict is imminent. According to the above analysis, the local government and farmers choose the dynamic game payment matrix as shown in
Figure 2.
4.2. Model Building
Assuming that the land
is the probability that the local government chooses the reasonable expropriation strategy, the probability of choosing the unreasonable expropriation strategy is
. When
, all the local governments chose to levy it reasonably. Suppose
is the probability of choosing cooperation strategy for farmers, then the probability of choosing boycott strategy is
. The strategies of both sides will eventually reach a stable state through continuous evolution and adjustment. The expected income of the local government in choosing a reasonable expropriation strategy is
, the expected return of the unreasonable expropriation strategy is
, and the average expected return is
. The calculated results are as follows:
The expected return of farmers choosing cooperation strategy is
, the expected return of choosing boycott strategy is
and the average expected return is
. The calculated results are as follows:
The replication dynamic equation of reasonable expropriation strategy adopted by local government can be obtained from Formulas (13) and (14) as follows:
The replication dynamic equation of cooperative strategy adopted by farmers can be obtained from Formulas (10) and (11) as follows:
If we let F (x) = 0, we can get x = 0.
When , we can get the results of and . When , we can get the results of and . There are five local equilibrium points in the evolutionary dynamic system of the game between the local government and the land-expropriated farmers, which are , , , (,). When the local equilibrium point satisfies the evolutionary stability condition under different values of variables, it becomes the evolutionary stable point (ESS). Then, the evolutionary stability of the strategy is analyzed.
4.3. Evolutionary Stability Analysis
According to the stability analysis method of the local equilibrium point of the Jacobian matrix, the Jacobian matrix is established and the local stability analysis is carried out. The corresponding Jacobian matrix of the evolution system is:
The calculated results are as follows:
The local equilibrium point becomes the evolutionary stability strategy (ESS) and must satisfy the following two conditions at the same time:
Specific values are taken at the five local equilibrium points, as shown in
Table 3.
The expressions of
and
in
Table 2 are as follows:
,
. At
,
, does not meet the evolutionary stability condition 2, so it is excluded from the combination of evolutionary stability strategies.
According to the results of different evolutionary stability, it is discussed in three cases.
When
,
,
,
, the results of the evolutionary stability analysis of the equilibrium point are shown in
Table 4. It can be seen that
(unreasonable expropriation, boycott) is the combination of evolutionary and stable strategies. At this time, the conflict of agricultural land expropriation broke out.
When and , this means that the government’s loss aversion preference coefficient is greater than the cost paid by unreasonable expropriation to the extra compensation that farmers get to resist unreasonable expropriation. At the same time, when the coefficient of farmers’ preference for loss avoidance is greater than the ratio of the cost of resisting unreasonable expropriation to the additional benefits obtained by the government, both sides have a strong preference for loss avoidance. This shows that both sides are more sensitive to the extra benefits brought by each other’s non-cooperation, so they are more sensitive to the loss of psychological utility when they adopt cooperation strategies, so they tend to adopt non-cooperation strategies. When and , this means that when the government’s reciprocal altruism preference is less than the ratio of the additional net income obtained by unreasonable expropriation to the farmers’ income, and the farmers’ reciprocal altruistic preference is less than the ratio of the additional net income obtained by resisting expropriation to the government income, both sides’ reciprocal altruistic preference is weak, that is, they are not sensitive to the value perception of each other’s income. Therefore, it is not sensitive to the psychological value of reciprocity and altruism obtained by adopting cooperation strategies, so it is not inclined to take cooperation strategies. Therefore, the unreasonable expropriation/ boycott strategy becomes an evolutionarily stable equilibrium. In reality, the local government unreasonable expropriation must reduce the standard of compensation for farmers, in order to obtain more land expropriation benefits. The stronger the farmers’ preference for loss aversion, the greater their perception of the value of the unreasonable benefits obtained by the government, thus the greater their own perception of the value of loss, and the easier it is to adopt resistance strategies. At the same time, the reciprocal altruistic preference of both sides is weak, and the psychological utility of cooperative behavior is not great. As a result, the local government adopts the unreasonable expropriation strategy, the farmers adopt the boycott strategy, the land expropriation compensation conflict breaks out, the income of both sides cannot reach the optimal value, “Both lose and hurt”, and the overall social welfare will decline as a result.
When
,
,
,
, the stability analysis of the four local equilibrium points is shown in
Table 5. Point
is the evolutionary stable strategy point (ESS) at this time. Unreasonable expropriation/cooperation is a combination of evolutionary and stable strategies.
When and , this means that the government’s loss aversion preference coefficient is greater than the ratio of the cost paid by unreasonable expropriation to the extra compensation that farmers get to resist unreasonable expropriation, and the government’s reciprocal altruistic preference is less than the ratio of the extra net income obtained by unreasonable expropriation to the income of farmers, when the government’s stable strategy is unreasonable expropriation. In reality, when the government’s preference for loss aversion is strong and reciprocal altruism is weak, the government is more sensitive to the loss of psychological utility when farmers resist and adopt reasonable expropriation strategies. They are not sensitive to the increase in psychological utility brought about by the increase in farmers’ income, so they tend to adopt unreasonable collection policies. If and , this means that when the coefficient of farmers’ preference for loss avoidance is less than the ratio of the cost of resisting unreasonable expropriation to the additional income obtained by the government, and when the farmers’ reciprocal altruistic preference is greater than the ratio of the extra net income obtained by resisting expropriation to the government’s income, the stable strategy of farmers is cooperative expropriation. In reality, when the farmers’ preference for loss aversion is weak and the preference for reciprocity and altruism is strong, farmers are not sensitive to the loss of their own psychological utility caused by the government’s unreasonable expropriation, but are more sensitive to the increase in psychological utility brought about by the increase in government revenue. Therefore, they tend to adopt cooperative strategies. Under the stable strategy combination that the government chooses unreasonable expropriation and farmers choose cooperation, the conflict of land expropriation does not seem to break out, but there is a potential danger of conflict. In this case, farmers, as a weak party, suffer damage to their interests and a lack of social fairness. There is a hidden danger of instability.
When
,
,
,
, the stability analysis of the four local equilibrium points is shown in
Table 6. The point
is the evolutionary stability strategy point, and reasonable expropriation/ resistance is the evolutionary stability strategy combination.
When and , this means that the government’s loss aversion preference coefficient is less than the ratio of the cost paid by unreasonable expropriation to the additional compensation obtained by farmers resisting unreasonable expropriation; the government’s reciprocal altruistic preference is greater than the ratio of the extra net income obtained by unreasonable expropriation to the income of farmers, when the government’s stable strategy is reasonable expropriation. In reality, when the government’s preference for loss aversion is weak and the preference for reciprocity and altruism is strong, the government is less sensitive to the loss of psychological utility caused by farmers’ boycott, and is more sensitive to the increase in psychological utility brought about by the increase in farmers’ income. Therefore, we tend to adopt reasonable collection measures. When and , this means that when the coefficient of farmers’ preference for loss aversion is greater than the ratio of the cost of resisting unreasonable expropriation to the additional income obtained by the government, and when the farmers’ reciprocal altruism preference is less than the ratio of the extra net income obtained by resisting expropriation to the government’s income, the stable strategy of farmers is to resist expropriation. In reality, when farmers’ preference for loss aversion is strong and reciprocal altruism is weak, farmers are more sensitive to the loss of their own psychological utility caused by the government’s unreasonable expropriation and are less sensitive to the increase in psychological utility brought about by the increase in government revenue. As a result, they tend to adopt resistance strategies. In the case of legal and reasonable expropriation compensation by the local government, when the landless farmers take illegal measures (such as gathering people to cause conflict or obstructing the construction of the expropriation project) to ask for high compensation, it will not only affect the administrative efficiency of the local government, social harmony and fairness, but may also have a negative impact on economic and social development.
When
,
,
, the stability analysis of the four local equilibrium points is shown in
Table 7. Point
D (1,1) is the evolutionary stability strategy point, and the strategy (reasonable expropriation, resistance) is the combination of evolutionary stability strategies, which is also expressed as harmonious expropriation.
When , , this means that the government’s loss aversion preference coefficient is less than the ratio of the cost paid by unreasonable expropriation to the additional compensation obtained by farmers resisting unreasonable expropriation; the government’s reciprocal altruistic preference is greater than the ratio of the extra net income obtained by unreasonable expropriation to the income of farmers when the government’s stable strategy is reasonable expropriation. In reality, when the government’s preference for loss aversion is weak and the preference for reciprocity and altruism is strong, the government is less sensitive to the loss of its own psychological utility when farmers boycott, and is more sensitive to the increase in psychological utility brought about by the increase in farmers’ income. Therefore, we tend to take reasonable collection measures. When , , this means that when the coefficient of farmers’ preference for loss avoidance is less than the ratio of the cost of resisting unreasonable expropriation to the additional income obtained by the government, and when the farmers’ reciprocal altruistic preference is greater than the ratio of the extra net income obtained by resisting expropriation to the government’s income, the stable strategy of farmers is to resist expropriation. In reality, it can be explained that when farmers have a weak preference for loss aversion and a strong preference for reciprocity and altruism, farmers are less sensitive to the loss of their own psychological utility caused by the government’s unreasonable expropriation, and are more sensitive to the increase in psychological utility brought about by the increase in government income, that is, farmers support government policies and cooperative farmland expropriation, so they tend to adopt cooperative strategies. In this case, the government and land-lost farmers have reached a state of mutual understanding and mutual trust, the compensation work of agricultural land expropriation can be carried out smoothly, and the social welfare is optimal.