Evolutionary Game Analysis of Emergency Grain Storage Regulatory Mechanisms Under Government Digital Governance

Abstract

Grain storage is one of the important means of national macro-control, significantly impacting people’s livelihood and social stability. In emergencies, grain storage enhances disaster relief efficiency and victim resettlement. Currently, developing countries primarily use government storage and government–enterprise joint storage. In response to the speculative behavior caused by the profit-seeking tendencies of agent storage enterprises in the process of joint government–enterprise grain storage, this study considers the current status of digital governance reform by the government and takes the government–enterprise emergency joint grain storage mechanism as its research object. We construct an evolutionary game model between the government and agent storage enterprises, analyze the evolutionary stability of the strategy choices of the two parties, explore the impact of various factors on the strategy choices of both parties, and discuss different stable strategy combinations. Through simulation analysis of the cost–benefit systems of both sides, initial strategy probabilities, key factor sensitivity, and the impact of digital governance levels, we propose a number of management recommendations that can effectively reduce speculative behavior and provide guidance for the government to improve its emergency grain storage system.

1. Introduction

Grain security has been a fundamental requirement for human development and an important aspect of national security. However, factors such as industrialization, population growth, and extreme weather have led to issues such as unstable grain production and declining grain quality, posing challenges to grain security in developing countries [1]. For example, in India, 6 million tons of grain are at risk of rotting due to a lack of professional management and official corruption [2]; in sub-Saharan Africa, due to poor storage facilities and severe pest and fungal contamination, post-harvest losses (PHLs) account for up to 30% of total grain production [3]. Based on data provided by the Grain and Agriculture Organization, in 2022, due to the economic impact of COVID-19 and other issues, a total of 258 million people in 58 countries faced persistent grain insecurity [4]. Adequate strategic grain storages and a balanced grain supply and demand are critical to preserving people’s safety, stabilizing regional grain prices, ensuring a continuous supply of grain, and maintaining healthy agricultural development [5]. Governments around the world, especially in developing countries in Asia and Africa, are increasingly concerned about the security of strategic grain storages.

In the national material storage system, the main decision-making bodies are the relevant departments of central and local governments, as well as some social organizations. The government focuses on stockpiling grain with broad applicability, as these grains are the most direct and reliable source of supplies during emergencies. However, due to limited facilities and manpower, as well as issues like elevated grain storage expenses and complexities in rotation, the government typically entrusts a large number of companies with grain storage. Reasonable cooperation not only helps the government carry out disaster relief work more efficiently but also provides companies with social reputations and economic benefits [6].

Due to issues such as spoilage, expiration, and pest infestation, as well as the unpredictability of disasters, the processes of grain storage, rotation, expiration handling, facility maintenance, and quality control all incur costs in terms of labor and funds. Maintaining grain storage entails assuming a certain level of risk [7]. For enterprises, excessively high-risk costs not only lead to economic losses but also undermine their competitiveness and operational capabilities. In pursuit of maximizing profits, enterprises may engage in irregular operations, poor management practices, or speculative behaviors, such as neglecting grain rotation or mishandling processing in joint emergency grain storage, which could potentially result in grain safety issues. The government should focus on incentivizing enterprise participation in joint grain storage rather than relying solely on administrative mandates to mitigate excessive storage costs. Considering the limited resources available to the government and the large number of participating enterprises, regulating all entities through labor-intensive methods is both costly and impractical [8]. Therefore, the government must enhance its digital governance capabilities and leverage new technologies to lower regulatory costs while improving the convenience and reliability of its regulatory measures.

Digitalization and digital governance are mainstream developments of our time. Governments, enterprises, and various industries in society are actively promoting digital reforms. For example, in recent years, the Chinese government has adopted technologies such as artificial intelligence, blockchain, the Internet of Things, and big data to improve governance capabilities in many areas [9]. Efficient digital governance can improve the administrative efficiency of the government, reduce the operating costs of government departments, promote cooperation between different government departments, and have a positive impact on the disclosure of government data, improving government accountability and creating a more open environment [10]. In the context of digital governance, government grain regulatory agencies can combine computer technologies such as blockchain, the Internet of Things, and artificial intelligence with grain monitoring technologies such as radio frequency technology to verify online the compliance of enterprises in storing grain, remotely monitor food quality, and control grain storage turnover. Through the efficiency of digital governance, the government can reduce the probability of speculative behavior.

Evolutionary game theory, a subfield of game theory, asserts that participants exhibit bounded rationality. Drawing upon principles of biological evolution, it develops populations with finite strategies that adapt to one another, evolve, explore optimal paths, and collectively arrive at a strategic equilibrium point under prevailing conditions [11]. In the realm of strategic analysis, game theory is particularly adept at addressing such challenges. In comparison to other methods, game theory offers a more intuitive reflection of how changes in participants’ gains can influence their choice of strategies.

Although existing studies have explored storage optimization, government–enterprise cooperation, and digital technology applications, there are two significant shortcomings. First, most focus on cost, contracts, or traceability, with limited attention to profit-driven speculative strategies and their evolution. Second, while some discuss digital governance in grain regulation, few offer theoretical models that systematically capture the dynamic game between government regulatory capacity and enterprise behavior.

This study focuses on the issue of speculative behavior by enterprises under the government–enterprise joint storage mechanism in emergencies, against the backdrop of government support and regulation. Through the construction of an evolutionary game model, this study analyzes the formation mechanism and response strategies of speculative behavior by enterprises in grain storage regulation. Unlike the traditional human-based grain storage model, this paper takes into account the new features introduced by the government’s digital reform in grain storage regulation. Specifically, digital supervision reduces regulatory costs by replacing manual inspections with real-time data monitoring, enhances the detection of violations through technologies such as blockchain and the Internet of Things, increases the reputational and financial risks associated with non-compliance, and strengthens the credibility and enforceability of government incentive mechanisms. The main contributions of this paper are outlined in the following aspects:

(1)

An evolutionary game model based on the government–enterprise grains joint storage quality supervision mechanism has been established. Additionally, addressing the issues of imperfect grain storage systems and lagging technological levels in some regions, this study analyzes how to effectively prevent speculative behavior by enterprises based on the cost and benefit analysis of different participants. This study provides a model for the government to refine its strategies and offers management approaches to address grain safety issues during storage.

(2)

Within the context of the current state and future trends of government-promoted digital governance, this study analyzes the primary features of digital supervision of grain storages. Differing from traditional supervision, it incorporates the influence of digital governance levels into the evolutionary game process, exploring changes in strategy selection.

Section 2 reviews the relevant literature on government–enterprise joint grain storages, evolutionary game theory, and digital governance. Section 3 details the model assumptions and develops the associated payoff matrix. Section 4 calculates the replicator dynamics and determines stability criteria. Section 5 provides simulation outcomes and sensitivity assessments, analyzing the influence of digitalization on strategic development. Section 6 summarizes the findings and concludes this study.

2. Literature Review

The research literature relevant to this study can be grouped into three main categories. The first category emphasizes optimization models for existing government–enterprise joint grain storage systems. The second explores the application of evolutionary game models. The third focuses on theoretical advancements in digital governance and their applications in grain safety regulation.

2.1. Research on Government–Enterprise Joint Grain Storages

2.1.1. Research on National Grain Storage Mechanisms

A sound grain storage mechanism is a necessary means for developing countries to enhance their ability to respond to emergencies. Many scholars have conducted relevant research on the current status and existing problems of grain emergency storages in various countries. Lassa et al. [12] analyzed strategies in Malaysia, the Philippines, and Indonesia, concluding that robust grain storage systems are crucial for addressing disasters and extreme weather events. Wright and Cafiero [13] examined the willingness of governments in the Middle East and North Africa to invest in strategic grain storage cooperation. Their analysis shows that national-level grain supply cooperation can effectively reduce the grain risks faced by the entire alliance of countries. Belesky [14] viewed ASEAN’s grain storage strategy as long-term. He studied the development process of ASEAN’s grain storages and future directions for improvement and analyzed its current shortcomings in grain storage and the practical significance of improvements. It can be seen that the grain storage systems in some developing countries are currently incomplete or even in their infancy.

2.1.2. Research on Improving the Existing Grain Storage Mechanism

Reducing government grain storage costs is a key research focus. Regarding the selection of enterprises for government–enterprise joint grain storages, Meng et al. [15] designed an emergency cooperation strategy based on a bilateral option contract, enabling the government and emergency supply chain participants to collaboratively minimize storage costs. Zhang et al. [16] introduced a spherical fuzzy set approach to address the selection of emergency supply providers. To balance government cost control with minimizing enterprise burden, the government should implement incentives to boost enterprise cooperation and establish an equitable cost-sharing mechanism. Xie et al. [17] used CVaR for risk assessment and optimal strategy decision-making and analyzed the incentive effect of government subsidies on enterprises based on risk aversion coefficients and mutual cost-sharing ratios. The issue of grain storages has always been a difficult one for both the government and enterprises. To improve the current situation, the efforts of grain storage enterprises are also indispensable. Meng et al. [18] optimized the rotation model of the emergency perishable inventory system in the process of government–enterprise cooperation in material warehousing to reduce enterprise costs. To address waste in food distribution and storage, Giedelmann-L et al. [19] studied the capacity of humanitarian food supply chains to handle and distribute perishable food and proposed a dynamic system model to prevent reports of waste or shortages due to uneven distribution. Zhang et al. [20] were the first to compare emergency material and fund storages, proposing that shifting reliance from material to fund storages can reduce costs for both governments and enterprises.

2.2. The Application of Evolutionary Game Models

2.2.1. Research on the Application of Evolutionary Games in Regulatory Mechanisms

Evolutionary games are widely used in the improvement of regulatory mechanisms and in the field of government–enterprise cooperation. Due to their multi-party participation and multiple strategy characteristics, evolutionary games are widely used to analyze regulatory capacity and outcomes. Zhang and Kong [21] developed a tripartite model involving the government, enterprises, and social organizations to analyze cost-sharing in emergency material storages. To study cooperation in rescue efforts between government rescue teams and social organizations, Liu et al. [22] established the model to analyze the impact of resource allocation on rescue effectiveness. You et al. [23] discussed the cooperative effects of the government and emergency enterprises in terms of production capacity storages. Qiu et al. [24] used the model to study the cross-regional coordination and dispatch of emergency supplies, analyzing the coordination between multiple emergency management departments within the government system.

2.2.2. Research on the Application of Evolutionary Games in Material Storage

Evolutionary game models are widely applied in research on topics including material storage, dynamic interactions in supply chains, and economic management [25]. Zheng et al. [26] developed an evolutionary game model to explore blockchain traceability adoption in agricultural supply chains, finding that cost management and government incentives were critical for promoting adoption among producers, processors, and the government. Bai et al. [27] analyzed behavioral strategies among cold chain participants, consumers, and governments, highlighting that blockchain adoption, government incentives, and participant scale significantly influenced system stability and cooperation in cold chain logistics. Gong et al. [28] applied evolutionary game theory to China’s grain industry, showing that targeted policies, technological adoption, and stakeholder incentives can effectively promote cooperative grain preservation and reduce systemic waste.

2.3. Research on Digital Governance

Digital governance is one of the practical applications of digital management and a concrete manifestation of the modernization of government governance capabilities. Through the application of technologies such as blockchain, management information systems, and the Internet of Things, power control in the digital asset management process, including planning, monitoring, and implementation, can be achieved. Hardian and Ilhami [29] described digital governance as a structured framework that delineates accountability, role assignments, and decision-making authority for an organization’s digital operations.

There have been studies on the application of digital governance in the field of grain security and how to improve the current state of grain security management. Dabbene et al. [30] proposed using blockchain to address traceability, trust, and accountability challenges in the grain industry. The aim was to improve the visibility of the grain supply chain and ensure compliance with regulations, quality control, and grain safety requirements. Jianyao et al. [31] analyzed the safety supervision of distributed grain storage facilities in China and verified that the incorporation of big data will enhance supervisory capabilities. The grain storage supervision model based on big data technology proposed in the article can mine abnormal data. Abbate et al. [32] reviewed previous studies on the agri-food sector. To achieve grain safety and digital technology traceability, some scholars applied blockchain platforms to achieve grain data traceability. Wolfert et al. [33] utilized a theoretical framework to investigate the adoption of digital technologies in the agri-grain sector, evaluating their suitability and practicality from the standpoints of technical assistance, industry-specific challenges, adaptability, and future growth potential.

3. Problem Description and Model Assumptions

3.1. Problem Description

In the government–enterprise joint grain storage mechanism, grain storage enterprises mainly exhibit two types of behavior: one is non-speculative behavior, namely, fulfilling the tasks entrusted by the government and assuming the corresponding storage costs, management responsibilities, and quality requirements; the other is speculative behavior, which involves violations during the implementation of storages, specifically manifested as reducing rotation frequency, falsifying inventory quantities, lowering grain storage standards, or failing to allocate storage materials as required at critical moments, among other operations to evade constraints and obtain additional benefits. When regulatory coverage is insufficient or enforcement is weak, speculative behavior is more likely to occur and harder to detect, thereby impacting the stability of the storage system.

To address emergencies, the government, as the principal authority in disaster relief, has established a government–enterprise joint grain storage mechanism through contractual agreements with multiple grain storage enterprises. During the collaboration period, the government compensates enterprises with storage fees to incentivize the fulfillment of their storage obligations and deter speculative behavior. To safeguard the quality and safety of grain storages, the government may implement strict regulatory measures, including revoking profits from non-compliant enterprises, imposing fines, offering subsidies to those adhering to regulations, and conducting additional procurement when storages fall short to ensure food security. However, given the extensive number and widespread distribution of grain storage enterprises, supervision costs remain substantial, posing challenges in effectively curbing speculative behavior across the board.

The introduction of digital governance technology has enabled the government to monitor storage status and verify information in real time through data platforms built using technologies such as blockchain and the Internet of Things, replacing some manual verification, improving the efficiency of identifying violations, and increasing storage transparency [34]. Cross-departmental data sharing publicly discloses enterprises’ violations, increasing their reputational damage and future cooperation risks and raising the cost of fraudulent behavior. The establishment and annual maintenance of a digital governance system require additional investment, but they can significantly reduce regulatory costs and difficulties. The government needs to balance improving regulatory efficiency with controlling governance costs. However, there is still some debate over whether digital governance technology should be widely adopted. On the one hand, the high costs of construction and ongoing maintenance may place considerable pressure on regions with limited fiscal resources; on the other hand, digital governance may contain technical vulnerabilities, making them susceptible to cyberattacks or data tampering [35].

This study focuses on the strategic interaction between the government and grain storage enterprises, constructs an evolutionary game model for both parties, and analyzes the dynamic evolution of their strategic choices. We compare the differences in strategic choices under traditional and digital governance scenarios to explore the impact of the level of digital governance on strategic evolution and stability. The flowchart is shown in Figure 1.

3.2. Model Assumptions

The following hypotheses are posited below:

Assumption 1.

The government and grain storage enterprises are limitedly rational, so it is impossible for both sides to obtain the optimal strategy at the beginning. They need to continuously adjust their own strategies based on the decision-making behavior of the other party to obtain an evolutionary stable strategy. The probabilities of storage enterprises choosing “speculative behavior” or “non-speculative behavior” are $x$ and $1-x$, $x\in [0,1]$; the probabilities of the government choosing “strict regulation” or “loose regulation” are $y$ and $1-y$, $y\in [0,1]$.

Assumption 2.

In the context of grain storage regulation, the interactions between the government and enterprises exhibit regional characteristics, whereby a regional government primarily engages in games with grain reserve enterprises within its jurisdiction.

Assumption 3.

If the government adopts a “strict supervision” strategy and implement policies to encourage the improvement of the grain storage system, the government subsidy distribution method discussed in this article will be a one-period payment.

Assumption 4.

The meanings of variables and parameters are presented in

Table 1. Meanings of variables and parameters.

Notations	Description
$R_1$	Regular income of grain storage enterprises
$Q_1$	Government payments to grain storage enterprises for grain storage costs
$Q_3$	Grain security in emergency situations, social benefits of disaster relief obtained by government
$q$	Percentage of storage enterprises that choose to devote all of capacity to emergency grain storages
$F_1$	Regular operating costs of grain storage enterprises
$F_3$	In emergency situations where grain security issues arise, the comprehensive costs incurred by the government in addressing issues such as grain storages, quality inspection, and maintaining social stability.
$H_1$	Quality inspection costs for grain storage enterprises
$Fe$	Comprehensive costs borne by storage enterprises, including grain storage risk costs, rotation costs, and emergency grain management costs
$t$	Duration of joint government–enterprise grain storages
$r_1$	When the government imposes strict regulations, it provides compliance subsidies to grain storage enterprises.
$F{w}_1$	Penalties imposed by the government when speculative behavior by grain storage enterprises are discovered
$F{x}_1$	In the context of digital governance, the potential future losses incurred by grain storage enterprises when speculative behavior is discovered.
$o_1$	Falsification costs under traditional circumstances of grain storage enterprises
$O_1$	Falsification costs under digital governance of grain storage enterprises
$F{t}_3$	Administrative penalties imposed by higher-level government authorities on disaster relief departments ($F{t}_3>C_3$)
$n$	Government regulation duration, measured in years
$C_3$	When the government imposes strict regulations, traditional manpower supervision costs
$Z$	Cost of establishing a digital governance system
$c_3$	When the government imposes strict regulations, system maintenance costs under digital governance
$F{y}_3$	When grain storage enterprises adopt speculative behavior, the cost of remedial grain purchases by government departments ($F{y}_3>q*Q_1$)

, with each variable maintaining a positive value.

3.3. Cost–Benefit Matrix of the Game Between the Two Sides

Based on the assumptions and descriptions, we present the cost–benefit analysis of different strategy combinations for both parties in the evolutionary game in

Table 2. Cost–benefit matrix for both parties in evolutionary games under traditional situation.

Government	Grain Storage Enterprises
	Speculative Behavior x	Non-Speculative Behavior 1 − x
strict regulation y	$R_1-o_1-q*F{w}_1-F_1$	$(1-q)*(R_1-F_1)+q*Q_1+r_1-q*H_1-q*Fe*t$
	$Q_3-n*C_3-F{y}_3+q*F{w}_1$	$Q_3-n*C_3-q*Q_1-r_1$
loose regulation 1 − y	$q*Q_1+R_1-o_1-F_1$	$(1-q)*(R_1-F_1)+q*Q_1-q*H_1-q*Fe*t$
	$-F_3-F{t}_3-q*Q_1$	$Q_3-q*Q_1$

and

Table 3. Cost–benefit matrix for both sides in evolutionary games under digital governance.

Government	Grain Storage Enterprises
	Speculative Behavior x	Non-Speculative Behavior 1 − x
strict regulation y	$R_1-O_1-q*F{w}_1-F{x}_1-F_1$	$(1-q)*(R_1-F_1)+q*Q_1+r_1-q*H_1-q*Fe*t$
	$Q_3-(Z+n*c_3)-F{y}_3+q*F{w}_1$	$Q_3-(Z+n*c_3)-q*Q_1-r_1$
loose regulation 1 − y	$q*Q_1+R_1-O_1-F_1$	$(1-q)*(R_1-F_1)+q*Q_1-q*H_1-q*Fe*t$
	$-F_3-F{t}_3-q*Q_1$	$Q_3-q*Q_1$

.

4. Evolutionary Game Between Two Parties

4.1. Stability Analysis of Evolutionary Games Between Two Parties Under Traditional Situations

4.1.1. The Replicator Dynamic Equation of Grain Storage Enterprises

The expected payoffs of grain storage enterprises choosing to adopt speculative behavior or not engaging in speculative behavior, as well as the average expected payoff ($E_{11}$, $E_{12}$, ${\overline{E}}_1$), can be expressed as follows:

$$\left\{\begin{array}{l}\begin{array}{cc}{E}_{11}=& y(R_1-o_1-q*F{w}_1-F_1)+(1-y)(q*Q_1+R_1-o_1-F_1)\end{array}\\ \begin{array}{cc}{E}_{12}=& \begin{array}{l}y[(1-q)*(R_1-F_1)+q*Q_1+r_1-q*H_1-q*Fe*t]\\ +(1-y)[(1-q)*(R_1-F_1)+q*Q_1-q*H_1-q*Fe*t]\end{array}\end{array}\\ {\overline{E}}_1=x{E}_{11}+(1-x)E_{12}\end{array}\right..$$

(1)

The replicated dynamic equation for the strategic choice of grain storage enterprises is

$$\begin{array}{cc}F(x,y)& ={\displaystyle \frac{dx}{dt}}=x(E_{11}-{\overline{E}}_1)=x(1-x)(E_{11}-E_{12})\\ & =x(1-x)\left\{\begin{array}{l}-y(r_1+q*F{w}_1+q*Q_1)\\ +q(R_1+H_1+Fe*t-F_1)-o_1\end{array}\right\}\end{array},$$

(2)

where $F(x,y)$ is the speed of strategy evolution of grain storage enterprises; points can be considered evolutionarily stable only when they satisfy $F(x,y)=0$ and $F_x(x,y)<0$, in which $F_x(x,y)$ denotes the partial derivative of $F(x,y)$ with respect to $x$. Assume that $\left\{\begin{array}{l}-y(r_1+q*F{w}_1+q*Q_1)\\ +q(R_1+H_1+Fe*t-F_1)-o_1\end{array}\right\}$ is $H(\mathrm{y})$; there are three cases where $F(x,y)=0$, that is, $x=0$, $x=1$, or $H(y)=0$. In the instance $H(y)=0$, we can convert it to

$$y*={\displaystyle \frac{-q*(R_1+H_1+Fe*t-F_1)+o_1}{[q(F{w}_1+Q_1)+r_1]}}.$$

(3)

So, when $y=y*$, $H(y)=0$ and $F(x,y)=0$.

To determine whether it is an evolutionary stable strategy, another condition is required, which is $F_x(x,y)<0$.

$$F_x(x,y)={\displaystyle \frac{\partial F(x,y)}{\partial x}}=(1-2x)\left\{\begin{array}{l}-y[r_1+q*F{w}_1+q*Q_1]\\ +q(R_1+H_1+Fe*t-F_1)-o_1\end{array}\right\}.$$

(4)

4.1.2. Inference and Theoretical Analysis of Grain Storage Enterprises

When $H(y)=0$, $F(x,y)\equiv 0$ and $F_x(x,y)\equiv 0$, the strategy of grain storage enterprises is uncertain. Find the partial derivative of $H(\mathrm{y})$ with respect to y:

$${\displaystyle \frac{d(H(y))}{dy}}=-r_1-q*F{w}_1-q*Q_1$$

(5)

It can be seen that $H’(y)$ is a monotonically decreasing function of y, so when $0<y<y*<1$, $H(y)>0$, at this time $F_x{(x,y)}_{x=0}>0$ and $F_x{(x,y)}_{x=1}<0$. At this point, $x=1$, grain storage enterprises adopt speculative behavior to achieve a stable state. When $0<y*<y<1$, $H(y)<0$, at this time ${\left.F_x(x,y)\right|}_{x=0}<0$ and ${\left.F_x(x,y)\right|}_{x=1}>0$. At this point, $x=0$, and grain storage enterprises do adopt non-speculative behavior as an evolutionary stable state.

4.2. Cost–Benefit Analysis and Dynamic Stability of Government Under Traditional Situations

4.2.1. The Replicator Dynamic Equation of the Government

The expected payoffs of the government choosing strict or loose regulation, as well as the average expected payoff ($E_{21}$, $E_{22}$, ${\overline{E}}_2$), can be expressed as follows:

$$\left\{\begin{array}{l}\begin{array}{cc}{E}_{21}=& x(Q_3-n*C_3-F{y}_3+q*F{w}_1)+(1-x)(Q_3-n*C_3-q*Q_1-r_1)\end{array}\\ \begin{array}{cc}{E}_{22}=& x[-F_3-F{t}_3-q*Q_1]+(1-x)(Q_3-q*Q_1)\end{array}\\ {\overline{E}}_2=y{E}_{21}+(1-y)E_{22}\end{array}\right..$$

(6)

The replicated dynamic equation for the strategic choice of the government is

$$\begin{array}{l}G(x,y)={\displaystyle \frac{dy}{dt}}=y(E_{21}-{\overline{E}}_2)=y(1-y)(E_{21}-E_{22})\\ =y(1-y)[x(q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1-F{y}_3)-n*C_3-r_1]\end{array},$$

(7)

where $G(x,y)$ is the speed of strategy evolution of the government; points can be considered evolutionarily stable only when they satisfy $G(x,y)=0$ and $G_y(x,y)<0$, in which $G_y(x,y)$ denotes the partial derivative of $G(x,y)$ with respect to $y$. Assume that $[x(q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1-F{y}_3)-n*C_3-r_1]$ is $L(x)$; there are three cases where $G(x,y)=0$, that is, $y=0$, $y=1$, or $L(x)=0$. In the instance $L(x)=0$, we can convert it to

$$x*={\displaystyle \frac{n*C_3+r_1}{q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1-F{y}_3}}.$$

(8)

So, when $x=x*$, $L(x)=0$ and $G(x,y)=0$.

To determine whether it is an evolutionary stable strategy, another condition is required, which is $G_y(x,y)<0$.

$$\begin{array}{c}{G}_y(x,y)={\displaystyle \frac{\partial G(x,y)}{\partial y}}\\ =(1-2y)[x(q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1-F{y}_3)-n*C_3-r_1]\end{array}.$$

(9)

4.2.2. Inference and Theoretical Analysis of the Government

When $L(x)=0$, $G(x,y)\equiv 0$ and $G_y(x,y)\equiv 0$, the strategy of the government is uncertain. Find the partial derivative of $L(x)$ with respect to $x$:

$${\displaystyle \frac{\mathrm{d}(L(x))}{dx}}=q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1-F{y}_3.$$

(10)

When $q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1>F{y}_3$, $L’(x)>0$, $L(x)$ is a monotonically increasing function. When $0<x<x*<1$, $L(x)<0$, at this time ${\left.G_y(x,y)\right|}_{y=0}<0$ and ${\left.G_y(x,y)\right|}_{y=1}>0$. At this point, $y=0$, the government adopts loose regulation as an evolutionary stable state. When $0<x*<x<1$, $L(x)>0$, at this time ${\left.G_y(x,y)\right|}_{y=0}>0$ and ${\left.G_y(x,y)\right|}_{y=1}<0$. At this point, $y=1$, and the government adopts strict regulation as an evolutionary stable state. When $q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1<F{y}_3$, $G_y(x,y)<0$, $L(x)$ is a monotonically decreasing function. When $0<x<x*<1$, $L(x)>0$, at this time ${\left.G_y(x,y)\right|}_{y=0}>0$ and ${\left.G_y(x,y)\right|}_{y=1}<0$. At this point, $y=1$, and the government adopts strict regulation as an evolutionary stable state. When $0<x*<x<1$, $L(x)<0$, at this time ${\left.G_y(x,y)\right|}_{y=0}<0$ and ${\left.G_y(x,y)\right|}_{y=1}>0$. At this point, $y=0$, and the government adopts loose regulation as an evolutionary stable state.

4.3. Analysis of the Practical Significance of the Model

4.3.1. Analysis of Jacobian Matrix and ESS Points

Based on the replicated dynamic equation by grain storage enterprises and the government, we can determine an evolutionary game system. According to the definition of the replicated dynamic equation, when ${\displaystyle \frac{dx}{dt}}={\displaystyle \frac{dy}{dt}}=0$, the five stable points of the system can be obtained: $E_1(0,0)$, $E_2(1,0)$, $E_3(0,1)$, $E_4(1,1)$, $E_5(x*,y*)$. These points are not necessarily evolutionarily stable strategies (ESSs), so further judgment is required. We use Lyapunov’s method to judge the stability of equilibrium points by judging the Jacobian matrix of the system [36]. The Jacobian matrix is as follows:

$$J=\left[\begin{array}{cc}{J}_1& J_2\\ J_3& J_4\end{array}\right]=\left[\begin{array}{cc}{\displaystyle \frac{\partial F(x,y)}{\partial x}}& {\displaystyle \frac{\partial F(x,y)}{\partial y}}\\ {\displaystyle \frac{\partial G(x,y)}{\partial x}}& {\displaystyle \frac{\partial G(x,y)}{\partial y}}\end{array}\right].$$

(11)

Among them

$${\displaystyle \frac{\partial F(x,y)}{\partial x}}=(2x-1)[y(q*F{w}_1+q*Q_1+r_1)+q(F_1-Fe*t-H_1-R_1)+o_1],$$

$${\displaystyle \frac{\partial F(x,y)}{\partial y}}=x(x-1)(r_1+q*F{w}_1+q*Q_1),$$

$${\displaystyle \frac{\partial G(x,y)}{\partial x}}=y(1-y)(F_3+F{t}_3+Q_3+r_1+q*F{w}_1+q*Q_1-F{y}_3),$$

$${\displaystyle \frac{\partial G(x,y)}{\partial y}}=(1-2y)[x(F_3+F{t}_3-F{y}_3+Q_3+r_1+q*F{w}_1+q*Q_1)-r_1-n*C_3].$$

In bilateral evolutionary games, the Friedman method is typically used to determine equilibrium points. A stable equilibrium point must satisfy the conditions $\det (A)>0$ and $tr(A)<0$. When conditions are met, the equilibrium point is stable. Specific equilibrium point combinations are shown in

Table 4. Equilibrium point determinants and traces.

Equilibrium Point	det(A)	tr(A)
$E_1(0,0)$	$\begin{array}{l}-(n*C_3+r_1)*[q*(t*Fe\\ -F_1+H_1+R_1)-o_1]\end{array}$	$\begin{array}{l}q*(t*Fe-F_1+H_1+R_1)\\ -o_1-r_1-n*C_3\end{array}$
$E_2(1,0)$	$\begin{array}{l}-[q*(t*Fe-F_1+H_1+R_1)-\\ o_1]*[F_3-n*C_3+F{t}_3-F{y}_3+\\ Q_3+q*(F{w}_1+Q_1)]\end{array}$	$\begin{array}{l}{F}_3-n*C_3+F{t}_3-F{y}_3+o_1\\ +Q_3+q*(F{w}_1+Q_1)\\ -q*(t*Fe-F_1+H_1+R_1)\end{array}$
$E_3(0,1)$	$\begin{array}{l}-(n*C_3+r_1)*[o_1+r_1\\ +q*(F_1-t*Fe+F{w}_1\\ -H_1+Q_1-R_1)]\end{array}$	$\begin{array}{l}n*C_3-o_1-q*(F{w}_1-Q_1)\\ +q*(t*Fe-F_1+H_1+R_1)\end{array}$
$E_4(1,1)$	$\begin{array}{l}-[F_3-n*C_3+F{t}_3-F{y}_3+Q_3+\\ q*(F{w}_1+Q_1)]*[o_1+r_1+q*(F_1\\ -t*Fe+F{w}_1-H_1+Q_1-R_1)]\end{array}$	$\begin{array}{l}n*C_3-F_3-F{t}_3+F{y}_3\\ +o_1-Q_3+r_1-q*(t*Fe\\ -F_1+H_1+R_1)\end{array}$

.

(1)

Stability analysis of point $E_1(0,0)$

To make point $E_1$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$q*(t*Fe-F_1+H_1+R_1)<o_1.$$

(12)

At this point, $E_1$ is the ESS equilibrium point, and the strategies chosen by both parties are non-speculative behavior and loose regulation.

According to the parameters and assumptions, when the gains from speculative behavior by grain storage enterprises are less than the costs of such behavior, grain storage enterprises will tend to adopt non-speculative behavior, and the government will choose loose regulation.

(2)

Stability analysis of point $E_2(1,0)$

To make point $E_2$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$\left\{\begin{array}{l}[q*(t*Fe-F_1+H_1+R_1)-o_1]*[F_3-n*C_3+F{t}_3-F{y}_3+Q_3+F{y}_3+Q_3+q*(F{w}_1+Q_1)]<0\\ F_3+F{t}_3+O_1+Q_3+q*(F{w}_1+Q_1)<q*(t*Fe-F_1+H_1+R_1)+C_3+F{y}_3\end{array}\right..$$

(13)

At this point, $E_2$ is the ESS equilibrium point, and the strategies chosen by both parties are non-speculative behavior and strict regulation.

(3)

Stability analysis of point $E_3(0,1)$

To make point $E_3$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$\left\{\begin{array}{l}(n*C_3+r_1)*[o_1+r_1+q*(F_1-t*Fe+F{w}_1-H_1+Q_1-R_1)]<0\\ n*C_3+q*(t*Fe-F_1+H_1+R_1)<o_1+q*(F{w}_1-Q_1)\end{array}\right..$$

(14)

At this point, $E_3$ is the ESS equilibrium point, and the strategies chosen by both parties are speculative behavior and loose regulation.

(4)

Stability analysis of point $E_4(1,1)$

To make point $E_4$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$\left\{\begin{array}{l}[F_3-n*C_3+F{t}_3-F{y}_3+Q_3+q*(F{w}_1+Q_1)]*[o_1+r_1+q*(F_1-t*Fe+F{w}_1-H_1+Q_1-R_1)]<0\\ n*C_3+F{y}_3+o_1+r_1<F_3+F{t}_3+Q_3+q*(t*Fe-F_1+H_1+R_1)\end{array}\right..$$

(15)

At this point, $E_4$ is the ESS equilibrium point, and the strategies chosen by both parties are speculative behavior and strict regulation.

4.3.2. Management Implications Analysis

In the case of the government and grain storage enterprises, there are two main ways to prevent grain storage enterprises from engaging in speculative behavior and ensure the safety of grain storages. One is to increase the government’s willingness and intensity of supervision, and the other is to reduce the willingness of enterprises to engage in speculation. The main conclusions are as follows:

(1)

To deter speculative behavior in grain storage enterprises, three strategies are proposed. First, increase enterprise income through government storage fees, which reduces speculation but raises public expenditure. Second, lower enterprise costs, which rise with storage duration; excessive costs may drive speculation, necessitating government subsidies. Third, enhance penalties through improved digital governance, increasing the financial and reputational risks of speculation, thus effectively curbing such behavior.

(2)

To enhance government regulation of grain storages, two strategies are effective. First, increasing storage fees paid to grain storage enterprises raises government costs but strengthens regulatory willingness, supporting grain security. Second, advancing digital governance reduces manpower, time, and financial costs of traditional regulation, significantly boosting the government’s commitment to stringent oversight.

4.4. Stability Analysis of Evolutionary Games Between Two Parties Under Digital Governance

The replicated dynamic equation for grain storage enterprises and the government under digital governance is derived in the same way as under traditional situations. The replicated dynamic equation for the strategic choices of grain storage enterprises is as follows:

$$\begin{array}{cc}F(x,y)& ={\displaystyle \frac{dx}{dt}}=x(E_{11}-{\overline{E}}_1)=x(1-x)(E_{11}-E_{12})\\ & =x(1-x)\left\{\begin{array}{l}-y(r_1+F{x}_1+q*F{w}_1+q*Q_1)\\ +q(R_1+H_1+Fe*t-F_1)-O_1\end{array}\right\}\end{array}.$$

(16)

The replicated dynamic equation for the strategic choice of the government is

$$\begin{array}{l}G(x,y)={\displaystyle \frac{dy}{dt}}=y(E_{21}-{\overline{E}}_2)=y(1-y)(E_{21}-E_{22})\\ =y(1-y)[x(q*F{w}_1+q*Q_1+F_3+F{t}_3+Q_3+r_1-F{y}_3)-(Z+n*c_3)-r_1]\end{array}.$$

(17)

The Jacobian matrix under digital governance is as follows:

$$J=\left[\begin{array}{cc}{J}_1& J_2\\ J_3& J_4\end{array}\right]=\left[\begin{array}{cc}{\displaystyle \frac{\partial F(x,y)}{\partial x}}& {\displaystyle \frac{\partial F(x,y)}{\partial y}}\\ {\displaystyle \frac{\partial G(x,y)}{\partial x}}& {\displaystyle \frac{\partial G(x,y)}{\partial y}}\end{array}\right].$$

(18)

Among them

$${\displaystyle \frac{\partial F(x,y)}{\partial x}}=(2x-1)[y(q*F{w}_1+q*Q_1+r_1+F{x}_1)+q(F_1-Fe*t-H_1-R_1)+O_1],$$

$${\displaystyle \frac{\partial F(x,y)}{\partial y}}=x(x-1)(F{x}_1+r_1+q*F{w}_1+q*Q_1),$$

$${\displaystyle \frac{\partial G(x,y)}{\partial x}}=y(1-y)(F_3+F{t}_3+Q_3+r_1+q*F{w}_1+q*Q_1-F{y}_3),$$

$${\displaystyle \frac{\partial G(x,y)}{\partial y}}=(1-2y)[x(F_3+F{t}_3-F{y}_3+Q_3+r_1+q*F{w}_1+q*Q_1)-r_1-(Z+n*c_3)].$$

The Friedman method is used to determine equilibrium points, that is, stable equilibrium points must satisfy the following conditions: $\det (A)>0$ and $tr(A)<0$. When the determinant of the matrix is greater than 0 and the trace is less than 0, the equilibrium point is stable. Equilibrium point combinations are shown in

Table 5. Equilibrium point determinants and traces.

Equilibrium Point	det(A)	tr(A)
$E_1(0,0)$	$\begin{array}{l}-(Z+n*c_3+r_1)*[q*(t*Fe\\ -F_1+H_1+R_1)-O_1]\end{array}$	$\begin{array}{l}q*(t*Fe-F_1+H_1+R_1)\\ -O_1-r_1-(Z+n*c_3)\end{array}$
$E_2(1,0)$	$\begin{array}{l}-[q*(t*Fe-F_1+H_1+R_1)-\\ O_1]*[F_3-(Z+n*c_3)+F{t}_3-\\ F{y}_3+Q_3+q*(F{w}_1+Q_1)]\end{array}$	$\begin{array}{l}{F}_3-(Z+n*c_3)+F{t}_3-F{y}_3+O_1\\ +Q_3+q*(F{w}_1+Q_1)\\ -q*(t*Fe-F_1+H_1+R_1)\end{array}$
$E_3(0,1)$	$\begin{array}{l}-(Z+n*c_3+r_1)*[F{x}_1+O_1\\ +r_1+q*(F_1-t*Fe+F{w}_1\\ -H_1+Q_1-R_1)]\end{array}$	$\begin{array}{l}Z+n*c_3-F{x}_1-O_1-q*(F{w}_1-Q_1)\\ +q*(t*Fe-F_1+H_1+R_1)\end{array}$
$E_4(1,1)$	$\begin{array}{l}-[F_3-(Z+n*c_3)+F{t}_3-F{y}_3+Q_3\\ +q*(F{w}_1+Q_1)]*[F{x}_1+O_1+r_1+\\ q*(F_1-t*Fe+F{w}_1-H_1+Q_1-R_1)]\end{array}$	$\begin{array}{l}(Z+n*c_3)-F_3-F{t}_3+F{x}_1\\ +F{y}_3+O_1-Q_3+r_1\\ -q*(t*Fe-F_1+H_1+R_1)\end{array}$

.

(1)

Stability analysis of point $E_1(0,0)$

To make point $E_1$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$q*(t*Fe-F_1+H_1+R_1)<O_1.$$

(19)

At this point, $E_1$ is the ESS equilibrium point, and the strategies chosen by both parties are non-speculative behavior and loose regulation.

According to the parameters and assumptions, when the gains from speculative behavior by grain storage enterprises are less than the costs of such behavior, grain storage enterprises will tend to adopt non-speculative behavior, and the government will choose loose regulation.

(2)

Stability analysis of point $E_2(1,0)$

To make point $E_2$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$\left\{\begin{array}{l}[q*(t*Fe-F_1+H_1+R_1)-O_1]*[F_3-(Z+n*c_3)+F{t}_3-F{y}_3+Q_3+F{y}_3+Q_3+q*(F{w}_1+Q_1)]<0\\ F_3+F{t}_3+O_1+Q_3+q*(F{w}_1+Q_1)<q*(t*Fe-F_1+H_1+R_1)+(Z+n*c_3)+F{y}_3\end{array}\right..$$

(20)

At this point, $E_2$ is the ESS equilibrium point, and the strategies chosen by both parties are non-speculative behavior and strict regulation.

(3)

Stability analysis of point $E_3(0,1)$

To make point $E_3$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$\left\{\begin{array}{l}(Z+n*c_3+r_1)*[F{x}_1+O_1+r_1+q*(F_1-t*Fe+F{w}_1-H_1+Q_1-R_1)]<0\\ Z+n*c_3+q*(t*Fe-F_1+H_1+R_1)<F{x}_1+O_1+q*(F{w}_1-Q_1)\end{array}\right..$$

(21)

At this point, $E_3$ is the ESS equilibrium point, and the strategies chosen by both parties are speculative behavior and loose regulation.

(4)

Stability analysis of point $E_4(1,1)$

To make point $E_4$ a stable point, the following conditions must be satisfied simultaneously, that is, $\det (A)>0$ and $tr(A)<0$:

$$\left\{\begin{array}{l}[F_3-(Z+n*c_3)+F{t}_3-F{y}_3+Q_3+q*(F{w}_1+Q_1)]*[F{x}_1+O_1+r_1+q*(F_1-t*Fe+F{w}_1-H_1+Q_1-R_1)]<0\\ Z+n*c_3+F{x}_1+F{y}_3+O_1+r_1<F_3+F{t}_3+Q_3+q*(t*Fe-F_1+H_1+R_1)\end{array}\right.$$

(22)

At this point, $E_4$ is the ESS equilibrium point, and the strategies chosen by both parties are (speculative behavior and strict regulation).

5. Parameter Simulation

5.1. Numerical Simulation of the Government Grain Storage Enterprise Model Under Traditional Situations

5.1.1. Numerical Simulation of the Government Grain Storage Enterprise Model

This study uses Matlab 2019b for numerical simulation. According to the assumptions required by equilibrium point inference (1) in Section 4 of Chapter 3, array 1 is designed as follows: $q=0.45$, $F_1=7$, $F{w}_1=9$, $Q_1=10$, $Fe=6$, $H_1=3.5$, $R_1=10$, $o_1=6$, $Q_3=50$, $r_1=3$, $F{t}_3=5$, $F{y}_3=25$, $F_3=5$, $n=3$, $C_3=5$. Evolve array 1 with multiple different initial values 40 times; the results are shown in Figure 2.

Under the given parameter conditions, the evolutionary trajectories corresponding to different initial strategy probability combinations all exhibit stable convergence characteristics. Regardless of variations in the initial strategic inclinations of grain storage enterprises and the government, the system ultimately converges to a unique stable equilibrium point $E_1(0,0)$, namely, the strategy combination adopted by grain storage enterprises and the government (non-speculative behavior, loose regulation). This result is fully consistent with theoretical inference (1).

To achieve this result, the government must ensure that grain storage enterprises profit more from contract storages than from speculation and increase the proportion of enterprises participating in joint storages by increasing government funding. In addition, given the high regulatory costs in developing countries at this stage, if the government wishes to save on regulatory costs, it needs to increase the cost of speculation for enterprises.

The above results prove that the simulation analysis is consistent with the conclusions of the theoretical stability analysis of various strategies and directly reflects the relationship between the two. This has practical significance for the government in ensuring grain security storages and high-quality storage, as well as reducing speculative behavior.

5.1.2. Sensitivity Analysis of the Government Grain Storage Enterprises Model

To discuss the effects of the initial probabilities of $x$ and $y$ on the evolutionary rate and trend, this section continues to use the parameters from array 1 without altering other variables, namely, the parameter settings for the evolutionary direction toward equilibrium point $E_1(0,0)$ are such that, while keeping other parameters at 0.5, the initial probabilities are set to $(x=0.2,x=0.5,x=0.8)$ and $(y=0.2,y=0.5,y=0.8)$, respectively, to observe the effects of $x$ and $y$ sensitivity to determine the speed of evolution and changes in the direction of evolution, as shown in Figure 3.

As can be seen in Figure 3, as the initial value $x$ increases, the government’s tendency to choose a loose regulation strategy weakens significantly, and the quality inspection agency’s tendency to choose a rent-seeking strategy also decreases significantly. As the initial value $y$ increases, there is no obvious impact on the strategic choices of the government and grain storage enterprises, but a strong initial willingness to engage in rent-seeking will significantly slow down the pace at which quality inspection agencies adopt rent-seeking rejection strategies. By comparing the overall evolution rates of the three sets of data, we can conclude that the strategic choices of the government and grain storage enterprises influence each other.

(1)

The influence of $Q_1$

As can be seen from Figure 4, as $Q_1$ rises, the speed at which grain storage enterprises evolve toward speculative behavior strategies will decline, but the speed at which the government evolves toward loose regulation strategies will also slow down. Therefore, we infer that as the government increases the funds it pays to grain storage enterprises, the government will bear greater losses when grain storage enterprises adopt speculative behavior and therefore will be more likely to invest additional costs in strict supervision. However, due to the high payments made by the government, the profits from speculative behavior will decrease for grain storage enterprises, so they are more inclined to adopt non-speculative behavior. In order to minimize the government’s costs while maintaining a high level of willingness among enterprises not to engage in speculative behavior, it is necessary to reasonably determine the government’s contract purchase price.

(2)

The influence of $F\mathrm{e}$

As can be seen from Figure 5, as $F\mathrm{e}$ rises, the speed at which grain storage enterprises evolve toward a non-speculative behavior strategy will decline, and when $F\mathrm{e}$ is too high, grain storage enterprises will tend to adopt speculative behavior. Therefore, we infer that the cost of storing grain by grain storage enterprises is the main expenditure, and as the storage time $t$ increases, the tendency of enterprises to speculate will become stronger. Consequently, to aim at minimizing government costs while maintaining a high level of willingness among enterprises to refrain from speculative behavior, it is necessary for grain storage enterprises to reduce their cost coefficients or for the government to increase subsidies to reduce the tendency of grain storage enterprises to engage in speculative behavior.

5.2. Numerical Simulation of the Government Grain Storage Enterprise Model Under Digital Governance

According to the assumptions required by equilibrium point inference (1) in Section 4 of Chapter 3, array 1 is designed as follows: $q=0.45$, $F_1=7$, $F{w}_1=9$, $Q_1=10$, $Fe=6$, $H_1=3.5$, $R_1=10$, $O_1=12$, $Q_3=50$, $r_1=3$, $F{t}_3=5$, $F{x}_1=4$, $F{y}_3=25$, $F_3=5$, $Z=7$, $n=3$, $c_3=2$. Evolve array 1 with multiple different initial values 40 times; the results are shown in Figure 6.

The simulation results under the given parameter settings confirm the findings of theoretical inference (1). Across all initial strategy probability combinations, the system consistently converges to a single stable equilibrium point $E_1(0,0)$, namely, the strategy combination adopted by grain storage enterprises and the government (non-speculative behavior, loose regulation). Regardless of the initial strategic tendencies of the two parties, the evolutionary trajectories display stable convergence, indicating that the system’s long-term dynamics are robust to variations in initial conditions.

By comparing the two situations, it can be seen that under the same conditions and ensuring the same final equilibrium point, the simulation results of digital governance show that grain storage enterprises are more inclined to adopt non-speculative behavior strategies. Compared with the vacillation in strategic choices of grain storage enterprises under traditional situations, grain storage enterprises evolve faster and make strategic choices more quickly under digital governance.

The above results prove that the simulation analysis aligns with the theoretical evaluation of strategy stability across all parties and highlights their interconnection. By comparing with the traditional situation, digital governance notably influences strategic choices, encouraging grain storage enterprises to favor non-speculative behavior approaches.

5.3. Case Analysis of Grain Reserve Enterprise

5.3.1. Numerical Simulation of the Enterprise Under Traditional Governance

Before 2021, a county-level policy grain reserve enterprise in central China had a storage capacity of about 20,000 tons, roughly 5% of the county’s reserves. The facilities, mainly flat warehouses, were outdated and prone to pests and mold. Without a digital governance system, grain conditions were monitored manually with temperature and humidity checks and paper records. Government oversight relied on periodic inspections and sampling, which often delayed the detection of violations.

Under such conditions, cost pressures could lead the enterprise to reduce rotation frequency or simplify inspections to save expenses, increasing risks and potential penalties if caught. The operational and regulatory parameters for this period are derived from the enterprise’s actual operating data: $q=0.39$, $F_1=7.7$, $F{w}_1=11.2$, $Q_1=11.7$, $Fe=6.4$, $H_1=4.5$, $R_1=11.3$, $o_1=5.7$, $Q_3=48.3$, $r_1=2.8$, $F{t}_3=5$, $F{y}_3=23.9$, $F_3=4.6$, $n=3$, $C_3=4.8$. The simulation results are shown in Figure 7.

The simulation results in Figure 7 indicate that the system ultimately converges to a unique stable equilibrium point $E_1(0,0)$. After substituting the enterprise’s operational and regulatory parameters into the model, the simulation results show that the evolutionary trajectories are consistent with the theoretical analysis, ultimately converging to the stable equilibrium point under the traditional governance. This indicates that, under traditional governance conditions, the strategy combination between enterprises and the government tends to the evolutionarily stable state predicted by theory.

5.3.2. Numerical Simulation of the Enterprise Under Digital Governance

Since 2021, the enterprise has been connected to the provincial digital grain supervision platform, with IoT sensors, video monitoring, and automated temperature and humidity systems installed in all storage units. Grain condition data are uploaded in real time and stored tamper-proof, enabling authorities to detect and address anomalies immediately, greatly enhancing the timeliness and deterrent effect of enforcement. The key operational and regulatory parameters for this period include: $q=0.25$, $F_1=7$, $F{w}_1=10.1$, $Q_1=12.3$, $Fe=5.8$, $H_1=3.5$, $R_1=11.2$, $O_1=13.7$, $Q_3=49$, $r_1=3.4$, $F{t}_3=5.9$, $F{x}_1=5.2$, $F{y}_3=25.4$, $F_3=5.1$, $Z=8.4$, $n=3$, $c_3=2.8$. The simulation results are shown in Figure 8.

The simulation results in Figure 8 likewise demonstrate convergence to a unique stable equilibrium point $E_1(0,0)$. With the adoption of digital governance mechanisms, falsification costs increase significantly, greatly reducing the potential gains from non-compliance. Although the enterprise bears additional expenses for system construction and maintenance, reliance on manual inspections decreases and management precision improves. This indicates that, under digital governance conditions, the strategy combination between enterprises and the government not only stabilizes more effectively but also enhances transparency and efficiency in storage management.

6. Conclusions

Amid government digital governance reforms, this study examines speculative behavior by enterprises within the joint government–enterprise emergency grain storage mechanism. Using evolutionary game theory, it constructs evolutionary game models to analyze strategic interactions under varying conditions. Through numerical simulation and sensitivity analysis, it identifies strategic evolution patterns and key influencing factors for both stakeholders, offering targeted management recommendations. The main conclusions are as follows:

(1)

The driving mechanism of speculative behavior under the government–enterprise joint grain storage mechanism

Under the traditional regulation model, the speculative behavior of grain storage enterprises is significantly affected by the ratio of regulatory costs to risk returns. When government regulation costs (such as manpower inspection costs) are too high, grain storage enterprises tend to obtain additional profits through speculative behavior such as reducing the quality of storages or falsifying inventory reports. When government regulation is insufficient, the probability of speculative behavior by enterprises increases significantly.

The introduction of digital governance has effectively curbed the tendency of enterprises to speculate by reducing information asymmetry and improving regulatory efficiency. For example, the transparency and immutability of blockchain technology have significantly increased the cost of fraud for enterprises (such as the difficulty of tampering with inventory data), while the government has significantly reduced regulatory costs by automatically enforcing reward and punishment mechanisms through smart contracts.

(2)

The optimizing effect of digital governance on evolutionary equilibrium

Compared with the traditional model, digital governance promotes convergence toward the ideal state of evolutionary equilibrium (non-speculative behavior, strict regulation) by reducing government regulatory costs and increasing enterprise speculation risk. Simulation results show that under digital governance, the speed of strategy evolution of grain storage enterprises increases by about one-fifth, and the probability of speculation at the stable equilibrium point decreases significantly compared with the traditional model.

The level of digital governance is positively correlated with evolutionary stability. When digital governance coverage reaches 80%, the government can reduce its regulatory manpower investment by about half, while the probability of exposing speculative behavior by enterprises is greatly increased.

(3)

Sensitivity analysis of key parameters

The level of government subsidies is a key factor influencing the strategies of grain storage enterprises. When subsidies exceed the net speculative gains of enterprises, they are highly likely to choose a strategy of compliance. Conversely, if subsidies are insufficient, the tendency of enterprises to speculate will increase significantly as the cost of storage risks increases. The costs of falsification and potential reputational damage for grain storage enterprises have a non-linear impact in the context of digital governance.

Under digital governance, falsification costs and potential reputational damage for grain storage enterprises exhibit a significant threshold effect on the strategic evolution of grain storage enterprises. Once these costs exceed approximately 20% of normal operating profits, speculative returns rapidly fall below compliance returns, and strategies converge toward non-speculation at an accelerated pace.

The conclusions show that, in addition to ensuring grain security from a management perspective by controlling costs and benefits, the level of digital governance has a significant impact on both parties involved in ensuring grain storage security. Strengthening digital governance is crucial to curbing speculative behavior in most situations, as it can free regulation from the traditional dilemma of high costs and low quality.