Digital transformation in rural governance: unraveling the micro-mechanisms and the role of government subsidies
Based on the theoretical analysis in Section 2.2.2, digital technology enhances rural governance by reducing the costs of information searching, transmission, and tracking, thereby improving rule supply, enforcement, and maintenance. In this section, we adopt a tripartite evolutionary game model involving three stakeholders—local government, villagers, and village collectives—each with distinct strategy choices and payoff structures. By constructing the payoff matrices for all stakeholders and incorporating replicator dynamics, we analyze the evolutionary process and stability of their strategic interactions, aiming to explore the behavioral evolution mechanism of rural governance under the empowerment of digital technology. In this model, the level of digital infrastructure development (β) is used to capture the impact of digital technology on governance participation costs, reflecting the cost-reduction mechanism proposed in the theoretical analysis. Meanwhile, digital literacy (λ) represents the stakeholders’ capacity and willingness to engage in digital governance, which in turn affects their expected payoffs—corresponding to the theoretical discussion on how digital technology enhances governance efficiency and mobilization. In addition, the model introduces other benefit and cost parameters to reflect how digital technology reshapes the incentive mechanisms and responsibility structures in the tripartite game.
The model construction process is as follows:
Scenario description
Evolutionary game theory combines principles from biological evolution and game theory, starting from the assumption of bounded rationality. It focuses on individuals adjusting their strategies during the dynamic evolutionary process through learning and imitation to reach a stable state, effectively addressing the limitations of the complete rationality assumption and multiple equilibrium issues in classical game theory. Evolutionary game theory can provide an analytical framework to explain how to promote digital rural governance, serving as an effective tool for understanding the behavioral strategies and interactions among local governments, village collectives, and villagers.
Specifically, digital rural governance is a process of “reconstructing the countryside with digital technology.” Its characteristics of informatization, networking, and intelligence are gradually being embedded into grassroots governance, unleashing the “digital dividend” that supports comprehensive agricultural upgrades, rural progress, and overall farmer development (Liao, 2023; Bing, 2023). However, the non-uniform development of digital infrastructure and the diversity in digital technology user groups have inevitably led to the emergence of “digital divide” phenomena such as digital barriers, digital inequality, and digital space segregation (Salemink et al., 2017). Rural population aging further exacerbates the marginalization of vulnerable groups. Older laborers, limited by learning capabilities and risk-averse attitudes, tend to prefer traditional rural governance models, making it difficult for digital technology to achieve the desired outcomes in rural areas (Lu, 2023). Digital technology can enhance the scientific basis of government decision-making and improve management efficiency. However, the dispersal and mobility of villagers lead to increasingly diverse interests and needs, resulting in significant organizational costs for local governments (Li, 2023). Government participation in rural governance urgently requires the intervention of intermediary organizations to offset organizational costs. The cooperative tradition, resource advantages, and organizational strengths of village collectives can significantly reduce organizational costs (Zhou, 2020). Local governments, relying on village collectives to build digital service platforms, can effectively lower platform construction investment as well as communication and coordination costs. The standardization of village collectives can also significantly reduce platform operation and government supervision costs. Successful organizations may be rewarded to boost their governance motivation. Villagers, as direct beneficiaries of the digital rural governance, gain from the collaboration between local governments and village collectives, thereby enhancing their willingness to participate in governance and establishing a multi-stakeholder governance structure. Based on this, this paper constructs a “local governments—village collectives—villagers” three-party evolutionary game model. The game tree among the three parties is shown in Fig. 3.
Model assumption
Assumption 1: One of the central principles of evolutionary game theory is that agents participate in repeated games under the assumption of bounded rationality until the game system evolves toward a stable state over time. This model involves three primary stakeholders: local governments, village collectives and farmers. Every stakeholder operates under bounded rationality, continuously learning from one another throughout the game process to make decisions that best align with the evolving environment and their own interests.
Assumption 2: Local governments, as administrators, have two strategies. The first strategy is to subsidize, which is denoted as \({F}_{1}\), with a probability of \(x\). And the second strategy is not to subsidize, which is denoted as \({F}_{2}\), with a probability of \(1-x\). The set of strategies for governments is \(\left({F}_{1},{F}_{2}\right)=(x,1-x)\).
Assumption 3: Village collectives, as coordinators, and there are also two strategies. The first strategy is digital governance, which is denoted as \({E}_{1}\), with a probability of \(y\). And the second strategy is traditional governance, which is denoted as \({E}_{2}\), with a probability of \(1-y\). The set of strategies for village collectives is \(\left({E}_{1},{E}_{2}\right)=(y,1-y)\).
Assumption 4: Farmers, as direct participants in rural governance, and there are two strategies. The first strategy is to participate, which is denoted as \({J}_{1}\), with a probability of \(z\). And the second strategy is not to participate, which is denoted as \({J}_{2}\), with a probability of \(1-z\). The set of strategies for farmers is \(\left({J}_{1},{J}_{2}\right)=(z,1-z)\).
The game tree is shown in Fig. 3.
The variables and their denotations used in this paper are listed in Table1.
Expected payoff and replicator dynamics equation
Payoff matrix
Based on the above assumptions, the payoff matrix for the “local governments—village collectives—villagers” three-party game can be obtained, as shown in Table 2.
Expected Payoff
Let the expected payoffs for local governments when choosing to subsidize and not subsidize be \({E}_{11}\) and E12, respectively, with an average payoff of \(\bar{{E}_{1}}\). Then:
$${E}_{11}={yz}{R}_{g1}+\left(y+z-2{yz}\right){R}_{g2}-\left(1-\beta \right){C}_{g}-y\lambda {A}_{O}-z\lambda {A}_{V}$$
(1)
$${E}_{12}={yz}{R}_{g1}+\left(y+z-2{yz}\right){R}_{g2}-{C}_{g}$$
(2)
$$\bar{{E}_{1}}=x{E}_{11}+(1-x){E}_{12}$$
(3)
Let the expected payoffs for village collectives when choosing between digital governance and traditional governance be \({E}_{21}\) and \({E}_{22}\), respectively, with an average payoff of \(\bar{{E}_{2}}\). Then:
$${E}_{21}=x\lambda {A}_{O}+z\alpha R-\left(1-\beta \right){C}_{O1}-{C}_{O2}$$
(4)
$${E}_{22}=z{R}_{O}-{C}_{O1}$$
(5)
$$\bar{{E}_{2}}=y{E}_{21}+(1-y){E}_{22}$$
(6)
Let the expected payoffs for villagers when choosing to participate and not participate be \({E}_{31}\) and \({E}_{32}\), respectively, with an average payoff of \(\bar{{E}_{3}}\). Then:
$${E}_{31}=x\lambda {A}_{V}+y\left(1-\alpha \right)R-\left(1-\beta \right){C}_{V1}-{C}_{V2}$$
(7)
$${E}_{32}=y{R}_{V}-{C}_{V1}$$
(8)
$$\bar{{E}_{3}}=z{E}_{31}+(1-z){E}_{32}$$
(9)
Replicator dynamics equation
$$\left\{\begin{array}{l}F\left(x\right)=x({E}_{11}-\bar{{E}_{1}})=x\left(1-x\right)\left(\beta {C}_{g}-y\lambda {A}_{O}-z\lambda {A}_{V}\right)\\ F\left(y\right)=y({E}_{21}-\bar{{E}_{2}})=y\left(1-y\right)\left(x\lambda {A}_{O}+z\alpha R+\beta {C}_{O1}-{C}_{O2}-z{R}_{O}\right)\\ F\left(z\right)=z({E}_{31}-\bar{{E}_{3}})=z(1-z)[x\lambda {A}_{V}+y\left(1-\alpha \right)R+\beta {C}_{V1}-{C}_{V2}-y{R}_{V}]\end{array}\right.$$
(10)
Local stability strategy analysis
Local governments
According to the stability conditions of the replicator dynamics equation, when \(F\left(x\right)=0\) and \({F}^{{\prime} }(x) < 0\), the point is an evolutionary stable point. (1) When \(\beta {C}_{g}-y\lambda {A}_{O}-z\lambda {A}_{V}=0\), \(F\left(x\right)\equiv 0\). In this case, the local governments’ strategy is not influenced by the evolutionary system, and any strategy is a stable strategy. (2) When \(\beta {C}_{g}-y\lambda {A}_{O}-z\lambda {A}_{V} > 0\), \(F^{\prime} (x)|(x=1) < 0\), \(F^{\prime} (x)|(x=0) > 0\). In this case, \(x=1\) is local governments’ evolutionary stable strategy. (3) When \(\beta {C}_{g}-y\lambda {A}_{O}-z\lambda {A}_{V} < 0\), \(F{\prime} (x)|(x=1) > 0\), \(F^{\prime} (x)|(x=0) < 0\). In this case, \(x=0\) is local governments’ evolutionary stable strategy.
Village collectives
According to the stability conditions of the replicator dynamics equation, when \(F\left(y\right)=0\) and \({F}^{{\prime} }(y) < 0\), the point is an evolutionary stable point. (1) When \(x\lambda {A}_{O}+z\alpha R+\beta {C}_{O1}-{C}_{O2}-z{R}_{O}=0\), \(F\left(y\right)\equiv 0\). In this case, the village collectives’ strategy is not influenced by the evolutionary system, and any strategy is a stable strategy. (2) When \(\lambda {A}_{O}+z\alpha R+\beta {C}_{O1}-{C}_{O2}-z{R}_{O} > 0\), \(F{\prime} (y)|(y=1) < 0\), \(F{\prime} (y)|(y=0) > 0\). In this case, \(y=1\) is village collectives’ evolutionary stable strategy. (3) When \(x\lambda {A}_{O}+z\alpha R+\beta {C}_{O1}-{C}_{O2}-z{R}_{O} < 0\), \(F{\prime} (y)|(y=1) > 0\), \(F{\prime} (y)|(y=0) < 0\). In this case, \(x=0\) is village collectives’ evolutionary stable strategy.
Villagers
According to the stability conditions of the replicator dynamics equation, when \(F\left(z\right)=0\) and \({F}^{{\prime} }(z) < 0\), the point is an evolutionary stable point. (1) When \(x\lambda {A}_{V}+y\left(1-\alpha \right)R+\beta {C}_{V1}-{C}_{V2}-y{R}_{V}=0\), \(F\left(z\right)\equiv 0\). In this case, the villagers’ strategy is not influenced by the evolutionary system, and any strategy is a stable strategy. (2) When \(x\lambda {A}_{V}+y\left(1-\alpha \right)R+\beta {C}_{V1}-{C}_{V2}-y{R}_{V} > 0\), \(F{\prime} (z)|(z=1) < 0\), \(F{\prime} (z)|(z=0) > 0\). In this case, \(z=1\) is villagers’ evolutionary stable strategy. (3) When \(x\lambda {A}_{V}+y\left(1-\alpha \right)R+\beta {C}_{V1}-{C}_{V2}-y{R}_{V} < 0\), \(F{\prime} (z)|(z=1) > 0\), \(F{\prime} (z)|(yz=0) < 0\). In this case, \(z=0\) is villagers’ evolutionary stable strategy.
Stability analysis
Under conditions of information asymmetry, the evolutionary stable strategy is necessarily a pure strategy. Letting \(F\left(x\right)=F\left(y\right)=F\left(z\right)=0\), eight pure strategy equilibrium points are obtained: E1 = (0,0,0), E2 = (1,0,0), E3 = (0,1,0), E4 = (0,0,1), E5 = (1,1,0), E6 = (0,1,1), E7 = (1,0,1), E8 = (1,1,1). According to Lyapunov’s stability theory, a local equilibrium point satisfies the condition of asymptotic stability if and only if all eigenvalues of the Jacobian matrix are negative. Therefore, based on the replicator dynamics equation, the Jacobian matrix is constructed, its eigenvalues are determined, and the evolutionary stability trend among local governments, village collectives, and villagers is analyzed.
$$J=\left[\begin{array}{ccc}{J}_{11} & {J}_{12} & {J}_{13}\\ {J}_{21} & {J}_{22} & {J}_{23}\\ {J}_{31} & {J}_{32} & {J}_{33}\end{array}\right]=\left[\begin{array}{ccc}\frac{\partial F\left(x\right)}{\partial x} & \frac{\partial F\left(x\right)}{\partial y} & \frac{\partial F\left(x\right)}{\partial z}\\ \frac{\partial F\left(y\right)}{\partial x} & \frac{\partial F\left(y\right)}{\partial y} & \frac{\partial F\left(y\right)}{\partial z}\\ \frac{\partial F\left(z\right)}{\partial x} & \frac{\partial F\left(z\right)}{\partial y} & \frac{\partial F\left(z\right)}{\partial z}\end{array}\right]$$
(11)
$${J}_{11}=(1-2x)\left(\beta {C}_{g}-y\lambda {A}_{O}-z\lambda {A}_{V}\right)$$
$${J}_{12}=x\left(1-x\right)(-\lambda {A}_{O})$$
$${J}_{13}=x\left(1-x\right)\left(-\lambda {A}_{V}\right)$$
$${J}_{21}=y\left(1-y\right)\lambda {A}_{O}$$
$${J}_{22}=\left(1-2y\right)\left(x\lambda {A}_{O}+z\alpha R+\beta {C}_{O1}-{C}_{O2}-z{R}_{O}\right)$$
$${J}_{23}=y\left(1-y\right)\left(\alpha R-{R}_{O}\right)$$
$${J}_{31}=z\left(1-z\right)\lambda {A}_{V}$$
$${J}_{32}=z\left(1-z\right)[\left(1-\alpha \right)R-{R}_{V}]$$
$${J}_{33}=(1-2z)[x\lambda {A}_{V}+y\left(1-\alpha \right)R+\beta {C}_{V1}-{C}_{V2}-y{R}_{V}]$$
Substituting each equilibrium solution into the Jacobian matrix yields the corresponding eigenvalues, as shown in Table3.
Currently, digital rural governance in China is in an early stage, with government-led governance still being the main model(Ren, 2023). The government-led model primarily involves top-down resource integration, specifically through the establishment of government information service platforms to achieve “precise governance and refined management,” thereby improving government administrative efficiency. Digital technologies such as big data enable the integration of regional administrative resources, significantly enhancing public service capabilities (Feng, 2020; Kosec and Wantchekon, 2020). To implement the digital rural strategy, local governments actively promote related policies and provide incentives. However, the current progress of digital governance in China is slow, mainly due to the following reasons:
On the one hand, according to the theory of organizational inertia, organizations tend to maintain the status quo and adopt a conservative attitude toward change (Kelly and Amburgey, 1991). Village collectives have long relied on traditional rural governance models. Familiarity with traditional governance, the lag in adapting to the digital environment, and the investment costs are all factors that may lead village collectives to reject digital governance. On the other hand, according to the technology acceptance model, villagers’ acceptance of digital technology is mainly determined by two factors: perceived ease of use and perceived usefulness (Marangunić and Granić, 2015). Due to the continuous outflow of young talent, rural hollowing and aging are becoming more severe. Insufficient digital literacy among villagers makes it difficult for them to master digital technologies, preventing them from benefiting from the “digital dividend” and thus making them reluctant to participate in digital governance.
Based on the above description, this paper assumes the following scenario:
Scenario 1: When \(\lambda {A}_{O}+\beta {C}_{O1}-{C}_{O2} < 0\) and \(\lambda {A}_{V}+\beta {C}_{V1}-{C}_{V2} < 0\), meaning that government subsidies and the “cost-reduction effect” brought by digital technology cannot compensate for the costs of transforming the traditional governance model, neither village collectives nor villagers will participate in digital governance. In this case, (1,0,0) is the evolutionary stable strategy of the game system.
Constrained by the digital literacy of stakeholders, village collectives and villagers find it difficult to experience the “digital dividend” objectively and are unwilling to participate in digital governance subjectively. As a result, the government-led governance model fails to achieve the expected outcomes. To improve the current situation, the central government has been strengthening the promotion of digital policies and introducing related policies to guide talent resources into rural areas. Under the background of rural revitalization, rural elites, leveraging their resource and technological advantages, improve villagers’ digital literacy through policy education, digital training, and other means, thereby encouraging villagers to participate in digital rural governance. With government support, when both village collectives and villagers actively participate in digital governance, on the one hand, higher governance efficiency can be achieved at lower costs, bringing considerable synergy benefits to both parties as well as government subsidies. On the other hand, collaborative governance by village collectives and villagers generates economic benefits for local governments, which in turn supports digital rural governance, enhancing the visibility and social status of local governments and achieving a “win-win-win” situation. Based on the above description, this paper assumes the following scenario:
Scenario 2: When \(\beta {C}_{g}-\lambda {A}_{O}-\lambda {A}_{V} > 0\), \(\lambda {A}_{O}+\alpha R+\beta {C}_{O1}-{C}_{O2}-{R}_{O} > 0\), and \(\lambda {A}_{V}+\left(1-\alpha \right)R+\beta {C}_{V1}-{C}_{V2}-{R}_{V} > 0\) i.e., for village collectives and villagers, when the policy rewards, synergy benefits, and the “cost-reduction effect” of digital governance exceed their respective traditional governance costs and speculative gains, all three stakeholders will participate in digital governance. In this case, (1,1,1) is the evolutionary stable strategy of the game system.
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