As more and more regulations on environmental protection are issued in practice, extensive literature on the effects of different types of regulation on manufacturers, such as carbon taxes, subsidies, and cap and trade, has emerged (Zhou and Huang, 2016; Liao and Shi, 2018).

Many scholars have discussed that government intervention and policies are critical to the environmental performance of manufacturers. Hafezi and Zolfagharinia (2018) proposed that governments should impose regulations with caution as firms may opt for a strategy that provides a larger profit at the expense of total environmental performance. Hafezalkotob (2015) developed a competition model of two green and regular supply chains under environmental protection and revenue seeking policies of government. Peng et al. (2019) investigated the main causes of environmental regulation failure and found that governments should strengthen regulations from the aspects of improving laws, establishing a monitoring system, and innovating incentive and constraint mechanisms. Murali et al. (2019) developed a framework for studying the impact of voluntary eco-labels and mandatory environmental regulation on green product development among competing firms.

Most studies from the perspective of governments have been performed on the policy of regulation and analyzing whether the tools and mechanisms effectively influence the decisions of manufacturers. Even though Gouda et al. (2016) addressed a manufacturer’s product quality choice problem and proposed a composite regulatory solution, the study only discussed traditional and environmental qualities. However, the especially for manufacturers to fraud have rarely been analyzed. Ensuring that the quality of NEVs meets the requirements is the premise of developing them. Hence, when considering the incidence of fake and inferior behaviors, it is necessary to examine how to achieve effective regulation policy in its game with both manufacturers and governments.

The behavior strategy selection of stakeholders is becoming increasingly prominent in research (Geng et al., 2021). Thus far, the literature is rich on green supply chains and renewable energy development in terms of different stakeholders (Xu X. F. et al., 2019). Considering the manufacturers and retailers, Zhang et al. (2020) analyzed the optimal decisions of a green supply chain and revealed the impacted difference between manufacturer and retailer behavior on equilibrium solutions in the context of a government subsidy. Deng et al. (2013) proposed a principal-agent model to study a supply chain consisting of a manufacturer and a retailer with asymmetric information. Zhou et al. (2018) discussed a cooperative advertising and ordering issue in a two-echelon supply chain in which a risk-averse manufacturer sells a product through a risk-averse retailer. Choi et al. (2018) and Wang et al. (2019) explored how the stochastic risk preference of retailers affects the values of quick response to the supply chain and its members. Feng et al. (2019) formalized the game’s theoretic model of manufacturers associated with governments in a low-carbon technology market and derived the mixed strategy Nash equilibrium. Ye et al. (2019) introduced the environmental governance cost prediction and showed that different risk coefficients have a greater impact on the investment in environmental governance. Liao et al. (2020) analyzed the effects of behavioral intention on the choice to purchase energy-saving appliances in China and revealed that behavioral intention has a significantly positive effect on the choice of consumers.

The literature mentioned above mainly indicates that behaviors between governments and manufacturers have been widely discussed. The role of consumers and their environmental awareness are also investigated as critical factors for manufacturers to promote ESPs (Li and Li, 2016; Liao and Shi, 2018). Very little research has looked at the impact of consumers’ behavior on NEVs when governments provide regulations for manufacturers. In particular, the incorporating role of synergistic regulatory effects should be discussed in depth. This study takes the perspective of associated production, consumption, and regulation in considering the whole process of NEVs. This could have a great impact on the efficiency of environmental regulation.

Game theory provides a powerful tool with which to unpack the interactive strategies of governments and manufacturers, focusing particularly on the conflict of interests between them under environmental regulation. Assuming the participant is completely rational, Zu et al. (2018) used a Stackelberg differential game with three progressive environmental regulation situations to consider a two-echelon supply chain consisting of one manufacturer and one supplier that tries to increase sustainable profits by making efforts to reduce CO₂ emission. Zhao et al. (2020) constructed a perfect game model including the subsidy policies of governments, manufacturers, and customers. During their study, the crucial influencing factors of the governments’ and manufacturers’ strategies were discussed. Zhou and Huang (2016) modeled a three-stage game and presented an optimal design of the contracts under government regulation for ESPs.

Recently, on the basis of the bounded rationality hypothesis, evolutionary game theory has been widely used on new energy products (Yu et al., 2020). Jiang et al. (2019) implemented a multi-agent environmental regulation strategy under Chinese fiscal decentralization by using an evolutionary game theoretical approach. Xing et al. (2017) constructed an evolutionary game of environmental regulation among local governments in China and analyzed the dynamic evolution rules of the environmental regulation strategy. Sun and Zhang (2019) divided enterprises into two types, dominant and inferior, and analyzed the evolutionarily stable strategy of heterogeneous enterprises in preventing greenwashing. Rocha and Salomao (2019) presented an evolutionary game to study the interaction between polluting firms and auditors. For a tripartite game model, Duan et al. (2016) developed two systems of dynamics-based tripartite evolutionary game models: a government environmental regulation-static punishment model and a dynamic punishment model. Liu and Xia (2020) analyzed the strategies of governments, manufacturers, and consumers according to the evolutionary game model in new energy products.

Most game models assume that information is symmetric and are mainly for two-player games, such as non-cooperative, cooperative and evolutionary game. As far as we know, few works have studied the strategy choices of tripartite coordinated regulation for NEVs with incomplete information. The manufacturer has private information about product quality, and the governments and consumers can only observe the quality level of the products posteriori. Therefore, tripartite dynamic game relationships should be discussed to explore the predicament and countermeasures of governance (Wang D. L. et al., 2020). A Bayesian game is an efficient way to solve the incomplete information game problem and is a more reasonable means to describe the strategies chosen by participants in NEVs (Yang et al., 2018). Therefore, this study attempts to explore the impacts of the interactions of governments, manufacturers, and consumers via the Bayesian game.

To highlight the innovation of this study and clearly show its difference from previous literature, we summarize the literature most related to our paper in Table 1.

Considering the reality of NEVs, such as the tripartite dynamic game model presented by Yang et al. (2019) and Xu et al. (2020), incorporating the characteristics of NEVs and regulation policies, research assumptions are proposed to conduct a better analysis of the game problem in decision-making behaviors. Additionally, the parameters involved in the models are accurately defined.

Assumption 1. We introduce “Nature,” which is considered under different product qualities, and with the products divided into two types i(i = H,L). The strategy set of nature is high-quality products and low-quality products. This is consistent with the literature, such as Cai et al. (2019). So, we only consider two types of products in the market. High-quality products refer to products that adopt energy-saving technology and meet the emission standards set by governments. For NEVs, governments propose standards that mainly include energy consumption over 100 km and emissions. Of course, manufacturers can also implement higher standards to improve product quality. The probability that manufacturers design high-quality products is P(i = H) = θ,θ∈[0,1]. From the perspective of quality standards formulated by the government, only unqualified product standards are considered low-quality products. Thus, the probability is denoted by P(i = L) = 1−θ. The quality of NEVs is private information.

Assumption 2. The strategy set of manufacturers is m_j=(m₁,m₂) = (sales, non-sales), where m₁ is the sales, and m₂ is the non-sales, and the corresponding probabilities are p_m and 1−p_m. We set the benefit of the sales of different products as R_i, and the production cost as C_i. If the governments choose an inspection strategy, the low-quality products produced by manufacturers will be punished, and the penalty is designated as F_L. For example, on 7 February 2017, the Ministry of Industry and Information Technology issued a new ticket for NEV fraudulent compensation manufacturers and announced administrative penalty decisions for seven fraudulent repair manufacturers, including Jinhua Youth Automobile and Chongqing Lifan.

Assumption 3. The behavior set of the governments for environmental regulation is b_j=(b₁,b₂) = (inspection, non-inspection). The probabilities of governments inspection and non-inspection are P_g and 1−P_g, respectively. We define the inspection cost as C_g, as a constant. Here, we assume that F_L > C_g. If manufacturers fail to take green actions, then the governments should bear the loss of non-inspection. There are two scenarios. The first is that manufacturers produce low-quality products and sell them, but governments do not inspect low-quality products. At this time, even though consumers are not buying, there are inferior products on the market. Therefore, governments will be punished by the higher authorities for the lack of inspection. The losses that the government should bear is denoted by L_g2. In the second scenario, consumers buy inferior products. In addition to being punished by superiors, governments can also suffer loss of reputations as consumers distrust them because of poor regulation. L_g1 is the losses of governments when consumers purchase NEVs. Here, we know that L_g1 > L_g2.

Assumption 4. The strategy set of consumers is x_j=(x₁,x₂) = (consumption, non-consumption). The benefit of buying high-quality NEVs is represented by R_c. The cost of consumers’ investment in the selection and confirmation of product quality is given by C_ci e.g., time and effort. To purchase high-quality NEVs, consumers compare the performance of different brands and products.

Assumption 5. The conditional probabilities of the products are P(m_j|H) and P(m_j|L). The consumers will update their beliefs by following the Bayesian rule, where the posteriori probabilities are denoted by P(H|m_j) and P(L|m_j). The above parameters and implications are summarized in Table 2.

In this section, the game process among governments, manufacturers and consumers is analyzed. Figure 2 illustrates the game tree of the three players on the basis of their strategic combinations. The Bayesian game process includes four stages, which can be clearly expressed.

Referring to the game built by Xu L. et al. (2019), we analyze the regulation of the circulation market of product quality, which is a prior-regulation. We set the game order beginning in stage 1. In this stage, the game participant “Nature” randomly picks a possible type of product (for example, high-product NEVs have the probability θ). In stage 2, manufacturers completely know their types of products, while the other two game players do not. Manufacturers then proceed to choose the action from the strategy set. In stage 3, governments receive the signal of the manufacturers’ action, speculate on the types of products, and then determine further action that would gain them the most profit. In stage 4, consumers finally choose one strategy.

Overall, the payoffs of governments, manufacturers, and consumers can be obtained according to the aforementioned assumptions. Table 3 gives the payoffs in different nodes.

The equilibrium solution of the dynamic game can be solved by using reverse induction (Chen et al., 2011). We analyze this game by considering the condition of separating equilibrium. If “Nature” chooses the high-quality NEVs, then the manufacturers will implement the pure strategy, which means P(m₁|H) =  1. If low-quality NEVs are chosen, then the manufacturers will choose to sell with the probability of δ, that is, P(m₁|L) = δ. According to the Bayesian rule, we can obtain the posteriori probabilities P(H|m₁) and P(L|m₁) as follows:

If manufacturers choose to sell low-quality products, then the governments will choose to conduct or not conduct an inspection, and the expected utility functions of the manufacturers will be denoted by E_m(b₁,m₁|L) and E_m(b₂,m₁|L), respectively. These expected utility functions are:

Then, the whole expected utility function of manufacturers that sell low-quality NEVs can be obtained:

When manufacturers select the non-sales strategy, we derive the expected utility functions of manufacturers as E_m(m₂|L) = −C_L.

The expected utility E_m(m₁|L) equals the expected profit E_m(m₂|L), and E_m(m₁|L) = E_m(m₂|L) yields the Bayesian equilibrium probability of consumption pc*, that is, pc*=pg⁢FL(1-pg)⁢RL. Therefore, the equilibrium probability of the non-consumption of consumers is 1-pc*= 1-pg⁢FL(1-pg)⁢RL.

When pc∈(pc*,1], and E_m(m₁|L) > E_m(m₂|L), p_m = 1 can become the optimal strategy, and the optimal response strategy for manufacturers is to sell low-quality NEVs. When pc∈[0,pc*), the optimal strategy of manufacturers is m₁, that is, p_m = 0. If pc=pc*, then it makes no difference which strategy the manufacturers select. Hence, the different scenarios can be expressed as follows:

The equilibrium probability of consumers is affected not only by fines for low-quality NEVs, but also by the benefit of low-quality NEVs. Additionally, it is still influenced by the probability of government regulation.

Similarly, for governments, the expected utility when they choose inspection and non-inspection are denoted by E_g(b₁|m₁) and E_g(b₂|m₁), respectively. By using Table 3, we have the following equations:

Eg⁢(b2|m1)=p⁢(H|m1)⁢Rg+p⁢(L|m1)⁢pc⁢(-Lg⁢1-Lg⁢2)=θθ+(1-θ)⁢δ⁢Rg+(1-θ)⁢δθ+(1-θ)⁢δ⁢(-Lg⁢1-Lg⁢2) With E_g(b₁|m₁) = E_g(b₂|m₁), we obtain the equilibrium probability of the manufacturers selling the low-quality NEVs, δ^∗:

According to the optimal equilibrium probability of manufacturers δ*=θ⁢Cg(1-θ)⁢[FL-Cg+pc⁢(Lg⁢1+Lg⁢2)]. When δ > δ^∗ and E_g(b₁|m₁) > E_g(b₂|m₁), the optimal strategy is p_g = 1; at this point, the optimal strategy for the governments is to perform an inspection. When δ > δ^∗, p_g = 0 is the optimal strategy, that is, the governments will choose non-inspection; if the optimal strategy is δ = δ^∗, then it does not matter which strategy the governments choose. The above analysis can be expressed by:

The equilibrium probability shows that the optimal equilibrium probability of manufacturers is due to several factors, mainly influenced by the governments^,behavioral strategies. That includes the regulation cost, fines for low-quality NEVs, and governmental losses of non-inspection when manufacturers sell low-quality NEVs.

(3) For consumers, the expected utility of consumers who choose or do not choose the consumption of NEVs will be denoted by E_c(x₁|m₁) and E_c(x₂|m₁) respectively. These expected utility functions are:

When E_c(x₁|m₁) = E_c(x₂|m₁), we can obtain the equilibrium probability of the governments’ inspection as Pg*=1-θ⁢(R⁢c-Cc⁢H)(1-θ)⁢δ⁢Cc⁢L. Therefore, the equilibrium probability of governments’ non-inspection is 1-Pg*=θ⁢(R⁢c-Cc⁢H)(1-θ)⁢δ⁢Cc⁢L.

When Pg>Pg* and E_c(x₁|m₁) > E_c(x₂|m₁), p_c = 1 is the optimal consumer strategy. When this condition is met, the consumers’ optimal strategy is the consumption of NEVs. Alternatively, when Pg<Pg*, p_c = 0 becomes the optimal strategy, and the consumers will choose non-consumption. When Pg<Pg*, it does not matter which strategy the consumers choose. The above analysis can be expressed as follows:

The equilibrium probability of the government’s inspection is affected by consumer behavior strategy. The benefit of buying high-quality NEVs and the selection cost of high-or low-quality NEVs are important influencing factors.

The equilibrium probability of manufacturers selling the low-quality NEVs is associated with C_g, F_L, L_g1 and L_g2.

Proposition 1: The probability of manufacturers selling the low-quality NEVs, δ^∗, increases as, C_g, increases.

By calculating the partial derivative of δ^∗, we calculate that

Given that θ ∈ [0,1], it is concluded that ∂⁡δ*∂⁡Cg>0.

From Proposition 1, an increased cost of government inspection lead to an increase im manufacturers with inferior eco-friendly operations. Because the increased cost of government inspection will reduce the probability of inspection, so it will increase the rate of low-quality products. The manufacturers do not care about the risk of deception in NEVs and degrade the quality of their products. In other words, the higher the regulation cost of NEVs, the more likely it is that manufacturers will commit fraud. Accordingly, there will be no reduction in carbon emissions.

Proposition 2: The probability of manufacturers, δ^∗, decreases as the losses L_g1, L_g2 and governmental fines, F_L increase.

Given the solutions for L_g1, L_g2 and F_L for the first derivatives of δ^∗, we have

Proposition 2 illustrates that whether consumers purchase NEVs, the losses of governments that affect the behavior of manufacturers are the same; when these losses increase, the problem of illegal emissions gets better. Proposition 2 also reveals that enhancing fines will decrease illegal emission behaviors. That is, governments contribute to ensuring product quality when they strengthen the punishment mechanism.

The equilibrium probabilities of governments’ inspection, Pg*, are determined by R_c, C_cH and C_cL.

Proposition 3: The probability of governments’ inspection, Pg*, decreases as the consumers’ benefit of high-quality NEVs, R_c, and the selection cost of low-quality NEVs, C_cL, increases.

The first derivatives of the Pg* on R_c and C_cL are as follows:

Proposition 3 shows that as the benefit of high-quality NEVs and the cost of low-quality NEVs increases, consumers will benefit from purchasing the conforming products and will buy the NEVs. Thus, the probability of governments’ inspection will be reduced, and the governments will be unlikely to regulate the manufacturers. Meanwhile, when the cost of identifying low-quality products is low, it is easy for consumers to find substandard products and buy high-quality products. The probability of governments’ inspection can also be decreased.

Proposition 4: The probability of governments’ inspection, Pg*, increases as the selection cost of high-quality NEVs, C_cH, increases.

The solution for C_cH for the first derivatives of Pg* is as follows:

Proposition 4 gives the relationships between the cost of consumption and the probability of governmental inspection. As the values of C_cH grow, Pg* will increase. More specifically, when the selection cost of buying high-quality NEVs is high, and the information asymmetry of product quality is more serious, consumers will be more likely to buy low-quality NEVs. At this point, the government will increase the probability of regulation.

The equilibrium probability of consumers is related to F_L and R_L.

Proposition 5: The probability of consumers’ consumption Pc* is an increasing function of F_L.

The first derivative of the equilibrium probability of consumers in terms of F_L is obtained by:

From Proposition 5, it is clear that the more the governments penalize manufacturers of substandard products, the less they will violate the rules, and thus the more likely that consumers will choose to buy NEVs. This case is good for governments because the lower the carbon emission reduction, the higher the environmental quality.

Proposition 6: The probability of consumers’ consumption, Pc*, is a negative function of R_L.

The first derivative of Pc* in terms of R_L is as follows:

Proposition 6 reveals that the higher the low-quality products that manufacturers produce, the more likely they are to forego compliance emissions. To consumers, the probability of consumers’ consumption of high-quality products will be reduced. In other words, when manufacturers make high profits by producing low-quality products, they will produce more of these products. Manufacturers have no incentive to produce high-quality products, and consumers are inclined to buy low-quality products.

In summary, the changes in equilibrium probability as the model parameters increase are presented in Table 4.