# Evolutionary Game and Simulation Research of Blockchain-Based Co-Governance of Emergency Supply Allocation

Authors: Huawei Zhao; Lili Ma
Journal: Discrete Dynamics in Nature and Society
 (2022)

---

## Abstract

Recently, with the spread of COVID-19 pandemic, emergency supply allocation system is drawing more and more social attention. Emergency supply allocation system is an important part of emergency governance system. It reflects social organizations’ credibility, public safety, and the modernization level of social governance. However, emergency supply allocation system still has some problems, such as information asymmetry, different desires of participants, unreasonable allocation, and so on. At present, it is widely accepted that the advantage of blockchain in co-governance could be of great help in solving above problems. And in order to distinguish the effect of blockchain to the emergency supply allocation, the paper builds a tripartite evolutionary game model among the government, social organizations, and the public to analyse the impact of blockchain platform on emergency supply allocation. The simulation analysis shows the following: (1) The strategy choices of the government have a crucial impact on the evolution and stability of social organizations’ strategies. It needs a long-term process to guide social organizations practicing active allocation, and the government should accelerate to build the blockchain platform to promote this process. (2) With the help of blockchain platform, the increment of penalty intensity of the government is conductive to increasing the probabilities that social organizations practice active allocation and the government practices strict supervision. (3) Blockchain platform has a significant impact on social organizations’ choice for active allocation in many aspects, such as the positive and negative effects of social organizations, effect’s increasing multiple, and the cost of the public informing. In the end, some suggestions are presented to improve the co-governance of emergency supply allocation.


---

## Body

## 1. Introduction

Emergency supply allocation is a significant part of emergency management system [1]. However, the emergency supply allocation still has problems at present; for example, in the early control of COVID-19, the improper allocation of supplies due to poor data collection and sharing led to serious crisis of confidence; patients were unable to obtain essential emergency supplies due to poor coordination among different departments [2]. The assessment of the status of emergency management collaboration by the United Nations and Economic and Social Commission for Asia and the Pacific indicated that it is necessary to improve the level of collaboration at all levels [3]. It can be seen that, in the emergency supply allocation, scientific allocation is the key, and the collaborative participation among the government, social organizations, and the public is the trend. Therefore, to improve emergency supply allocation, it is necessary to research the promotion effect of information technology and decision strategies of participants co-governance on emergency allocation.With the rapid evolution of the new round technology revolution, technological innovation plays an important role in promoting the optimization of social governance mechanisms and upgrading of social governance model, and at the same time, technological innovation is becoming an important driving force for the innovation of emergency management. In this background, with the development of blockchain, many studies showed that blockchain had the features of collaborative consensus, traceability, and immutability of information [4–8], and it played an important role in the innovation of emergency management. Recently, researchers begun to study the improvement of emergency management with the help of blockchain. Yao and Xue [9] summarized the applications of blockchain in emergency management and found that the blockchain had great application values in the realms of emergency information transmission, emergency prevention and control early warning, and emergency charitable donation. Hu et al. [10] used blockchain to construct emergency information system and realized the storage integrity, distributed sharing, and information’s traceability. Wang [1] designed a blockchain platform architecture, organizational structure, and operation mode for social donations of emergency supplies, aiming to solve the problem of information asymmetry. Deng et al. [11] made use of blockchain to build an emergency logistics system and realized traceability and anticounterfeiting of emergency supplies, automatic matching of supply and demand, and whole-process monitoring of distribution. Wu et al. [12] also demonstrated the application prospect of blockchain in promoting emergency logistics to achieve efficient guarantee, trust governance, and intelligent operation from the perspective of epidemic material security’s prevention and control by combining theory analysis with application cases. In addition, some institutes and companies constructed information exchange platforms for emergency supplies and emergency donation based on blockchain. For example, BitGive, BitNation, Start Network, and other international organizations established relevant blockchain platforms to manage funds and supplies from social donations after emergencies [13]. These platforms have played a key role in the information collection on supply and demand of emergency supplies and reliable traceability of supplies [9]. From above, it can be seen that people have gradually noticed the importance of blockchain to emergency management.In emergency management, different requirements of participants will influence the choice of their strategies, and the dynamic adjustment of strategies is suitable to be studied by evolutionary game theory [14]. Therefore, many researchers used evolutionary game method to study emergency management recently. As a whole, the game study of emergency management mainly includes cross-regional governance, emergency reserve mechanism, information exchange, and dissemination mechanism. Xiao et al. [15] used the analysis framework of regional evolutionary game to study the cross-regional governance of emergencies and found that when the regional spill-over effect and governance cost are small or the economic and social losses caused by emergencies are large, all regions will choose co-governance. Pi [16] discussed the mechanism construction of the national medical emergency supply reserve system with the combination of government and enterprise based on evolutionary game and proposed to give full play to the role of financial incentives in guiding enterprises to participate. Xu et al. [17] took SARS as a background and analysed the mechanisms of information communication by using evolutionary game theory. They found that the measures taken by the government to disclose information are conducive to restraining the spreading trend of emergencies. Deng et al. [18] further constructed a tripartite evolutionary game model among producers, transmitters, and decomposers of information and analysed the stability strategy. They found that information quality and punishment intensity of information producers are key factors affecting the dissemination of online public opinion information under emergencies. Xu et al. [19] constructed and analysed the tripartite evolutionary game model among the government, enterprises, and the public to deal with emergencies. Through model construction and simulation analysis, they found that the government can promote tripartite cooperation to fight the emergency by strengthening supervision, formulating reasonable reward and punishment mechanisms, and encouraging public participation.From the above literature review, it can be seen that blockchain can promote the innovation of emergency management, and evolutionary game theory is an important grasp to analyse the strategies of participants in co-governance of emergence, and more and more researchers proposed solutions from the above aspects, respectively. However, there is little research developed by using evolutionary game theory to analyse emergency management based on blockchain, especially in the scenario of emergency supply allocation.Therefore, based on the assumption of bounded rationality, this paper develops evolutionary game research on the co-governance of emergency supply allocation based on blockchain. The main contributions of this paper are as follows: (1) This paper introduces tripartite participants, namely, the government, social organizations, and the public into evolutionary game, which is different from the relevant literates [14, 20]. (2) Analysing the advantage and mechanism of blockchain promoting emergency supply allocation. (3) Analysing the stability of tripartite evolutionary game and researching the impact of blockchain on emergency supply allocation. (4) Using simulation to verify the validity of evolutionary game analysis and giving the suggestions to promote the co-governance of emergency supply allocation.


## 2. Mechanism of Blockchain to Emergency Supply Allocation

Emergency supply allocation has the following requirements: First, the complexity of the emergency events brings about the requirement of decentralize governance. Second, multipart participation of emergency supply allocation brings about the requirement of information sharing and multiparticipant collaboration. And finally, the motivating multiparticipant taking part in emergency supply allocation brings about the requirement of traceability.Fortunately, with the development of blockchain technology, many studies showed that the openness, distributed storage, traceability, and other features of blockchain could meet the above requirements, promoting the modernization of emergency supply allocation system and capability. First, the blockchain platform is open to all authorized participants and they can store and read all kinds of information about emergency supply allocation, which can meet the requirement of decentralize governance and improve the public’s trust in social organizations. Second, blockchain adopts distributed accounting method to realize real-time sharing data between multiple subjects, which meets the need of emergency supply allocation information sharing and multiparticipant collaboration. Third, the timestamp technology of blockchain achieves data tamper-proofing and traceability. It provides support for the government and the public to monitor the source and destination of emergency supplies and to hold those who are involved responsible, which meets the requirement of information traceability [21]. The mechanism of blockchain to emergency supply allocation is shown in Figure 1.Figure 1
Mechanism of blockchain to emergency supply allocation.


## 3. Game Analysis of Emergency Supply Allocation Based on Blockchain

### 3.1. Basic Assumptions of Game Model

This paper focuses on the strategic interaction among the government, social organizations, and the public during the emergency supply allocation, by modelling a tripartite evolutionary game. The three subjects follow the basic assumptions of bounded rationality and information asymmetry. Their choices will be influenced by other participants, and they will purse maximum profits by adjusting their strategies. Therefore, the following hypothesis are proposed.Hypothesis 1.
Strategic Space of Participants. As the supervisor, the government tends to invest a lot of human and material resources to construct information platform based on blockchain and implement strict supervision on social organizations. However, the construction of information platform and strict supervision will greatly increase the government’s expenditure, and based on the consideration of short-term interests and responsibility avoidance, the government maybe practice relaxing supervision on social organizations. Therefore, the strategy space of the government is (strict supervision, relaxing supervision).
As the bridge connecting the supply and requisitioning parts of emergency supply allocation, social organizations tend to actively allocate emergency supplies to establish a good social image. However, for the reasons of poor professional ability, the higher cost of allocation or the lighter penalties, social organizations maybe passively allocate emergency supplies or practice jobbery to pursue the higher profits. Therefore, the strategy space of the social organizations is (active allocation, passive allocation).
Facing the passive allocation of social organizations, on one hand, the public may choose to inform against social organizations to protect their own benefits; on the other hand, the public may choose tolerance for the reasons of high cost of informing. Therefore, the strategy space of the public is (informing, tolerance).Hypothesis 2.
The Probability Parameters of the Participants’ Strategies. The probability of social organizations’ active allocation is x0≤x≤1, and the passive allocation is 1−x; the probability of the public’s informing is y0≤y≤1, and the tolerance is 1−y; the probability of the government’s strict supervision is z0≤z≤1, and the relaxing supervision is 1−z. In addition, x, y, z are all functions of time t.Hypothesis 3.
The Parameters of the Government. For the government, the cost of strict supervision is defined by Cy, which includes the expenses of constructing and maintaining blockchain platform and the expenses of daily supervision. Once the government receives information against passive allocation of social organizations and verifies it, the government will fine social organizations with Fa and award the informant with Fe. And in the situation of strict supervision, the government will achieve positive effect Rg.
To the government, the cost of relaxing supervision is defined by 0. And the negative effect caused by relaxing supervision is defined byNg, which includes poor emergency management, damage of the public safety, and loss of credibility. In addition, the government will cost Cn to coordinate the emergency supplies and maintain social stability, in the condition that the social organizations practice passive allocation.Hypothesis 4.
The Parameters of Social Organizations. The profit of social organizations’ normal operation is Ya. The cost of social organizations’ active allocation is Ca; the positive effect caused by active allocation is Rn. The cost of social organizations’ passive allocation is Cp, and Ca>Cp>0. If social organizations passively allocate emergency supplies or practice jobbery, they will achieve extra profits Yp, which will cause negative effect Nn. In addition, when the government uses blockchain platform to strengthen supervision, Nn and Rn will both increase for the reason of the great enhancement of information transparency, and the coefficient of increment is defined by λ (λ≥1).Hypothesis 5.
The Parameters of the Public. If social organizations actively allocate emergency supplies, the public will receive emergency supplies timely, and the positive effect is defined by Rp. If the public informs against social organizations maliciously, the government will fine the public with Rn under the strict supervision.
On the contrary, if the social organizations passively allocate emergency supplies, the public will not receive emergency supplies in time, and the negative effect is defined byNp. The cost of the public informing against social organizations is defined by Cr. And if social organizations correct the behaviour of passive allocation, the public will achieve additional effect Up. In addition, in the situation of strict supervision, the government will award the informants with Fe.


### 3.2. The Payoff Matrix

Based on above assumptions, the payoff matrix including various strategies of the government, social organizations, and the public is constructed, as shown in Table1.Table 1
The payoff matrix.
Social organizationsThe publicGovernmentStrict supervisionzRelaxing supervision1−zActive allocationxInformingyYa−Ca+λRn−Fe−CrRg+Fe−CyYa−Ca+Rn−CrRgTolerance1−yYa−Ca+λRnRpRg−CyYa−Ca+RnRpRgPassive allocation1−xInformingyYa+Yp−Cp−Fa−λNnUp+Fe−Cr−NpRg+Fa−Fe−Cy−CnYa+Yp−Cp−Nn−Cr−Np−Cn−NgTolerance1−yYa+Yp−Cp−Fa−λNnUp−NpRg+Fa−Cy−CnYa+Yp−Cp−Nn−Np−Cn−Ng


## 3.1. Basic Assumptions of Game Model

This paper focuses on the strategic interaction among the government, social organizations, and the public during the emergency supply allocation, by modelling a tripartite evolutionary game. The three subjects follow the basic assumptions of bounded rationality and information asymmetry. Their choices will be influenced by other participants, and they will purse maximum profits by adjusting their strategies. Therefore, the following hypothesis are proposed.Hypothesis 1.
Strategic Space of Participants. As the supervisor, the government tends to invest a lot of human and material resources to construct information platform based on blockchain and implement strict supervision on social organizations. However, the construction of information platform and strict supervision will greatly increase the government’s expenditure, and based on the consideration of short-term interests and responsibility avoidance, the government maybe practice relaxing supervision on social organizations. Therefore, the strategy space of the government is (strict supervision, relaxing supervision).
As the bridge connecting the supply and requisitioning parts of emergency supply allocation, social organizations tend to actively allocate emergency supplies to establish a good social image. However, for the reasons of poor professional ability, the higher cost of allocation or the lighter penalties, social organizations maybe passively allocate emergency supplies or practice jobbery to pursue the higher profits. Therefore, the strategy space of the social organizations is (active allocation, passive allocation).
Facing the passive allocation of social organizations, on one hand, the public may choose to inform against social organizations to protect their own benefits; on the other hand, the public may choose tolerance for the reasons of high cost of informing. Therefore, the strategy space of the public is (informing, tolerance).Hypothesis 2.
The Probability Parameters of the Participants’ Strategies. The probability of social organizations’ active allocation is x0≤x≤1, and the passive allocation is 1−x; the probability of the public’s informing is y0≤y≤1, and the tolerance is 1−y; the probability of the government’s strict supervision is z0≤z≤1, and the relaxing supervision is 1−z. In addition, x, y, z are all functions of time t.Hypothesis 3.
The Parameters of the Government. For the government, the cost of strict supervision is defined by Cy, which includes the expenses of constructing and maintaining blockchain platform and the expenses of daily supervision. Once the government receives information against passive allocation of social organizations and verifies it, the government will fine social organizations with Fa and award the informant with Fe. And in the situation of strict supervision, the government will achieve positive effect Rg.
To the government, the cost of relaxing supervision is defined by 0. And the negative effect caused by relaxing supervision is defined byNg, which includes poor emergency management, damage of the public safety, and loss of credibility. In addition, the government will cost Cn to coordinate the emergency supplies and maintain social stability, in the condition that the social organizations practice passive allocation.Hypothesis 4.
The Parameters of Social Organizations. The profit of social organizations’ normal operation is Ya. The cost of social organizations’ active allocation is Ca; the positive effect caused by active allocation is Rn. The cost of social organizations’ passive allocation is Cp, and Ca>Cp>0. If social organizations passively allocate emergency supplies or practice jobbery, they will achieve extra profits Yp, which will cause negative effect Nn. In addition, when the government uses blockchain platform to strengthen supervision, Nn and Rn will both increase for the reason of the great enhancement of information transparency, and the coefficient of increment is defined by λ (λ≥1).Hypothesis 5.
The Parameters of the Public. If social organizations actively allocate emergency supplies, the public will receive emergency supplies timely, and the positive effect is defined by Rp. If the public informs against social organizations maliciously, the government will fine the public with Rn under the strict supervision.
On the contrary, if the social organizations passively allocate emergency supplies, the public will not receive emergency supplies in time, and the negative effect is defined byNp. The cost of the public informing against social organizations is defined by Cr. And if social organizations correct the behaviour of passive allocation, the public will achieve additional effect Up. In addition, in the situation of strict supervision, the government will award the informants with Fe.


## 3.2. The Payoff Matrix

Based on above assumptions, the payoff matrix including various strategies of the government, social organizations, and the public is constructed, as shown in Table1.Table 1
The payoff matrix.
Social organizationsThe publicGovernmentStrict supervisionzRelaxing supervision1−zActive allocationxInformingyYa−Ca+λRn−Fe−CrRg+Fe−CyYa−Ca+Rn−CrRgTolerance1−yYa−Ca+λRnRpRg−CyYa−Ca+RnRpRgPassive allocation1−xInformingyYa+Yp−Cp−Fa−λNnUp+Fe−Cr−NpRg+Fa−Fe−Cy−CnYa+Yp−Cp−Nn−Cr−Np−Cn−NgTolerance1−yYa+Yp−Cp−Fa−λNnUp−NpRg+Fa−Cy−CnYa+Yp−Cp−Nn−Np−Cn−Ng


## 4. Game Model Solving and Evolutionary Stability Analysis

### 4.1. Stability Analysis of Tripartite Subjects

#### 4.1.1. Stability Analysis of Social Organizations

Define the expected profits of social organizations in “active allocation” and “passive allocation” byU11 and U12, respectively, and the average profit is U1; then,(1)U11=yzYa−Ca+λRn+y1−zYa−Ca+Rn+z1−yYa−Ca+λRn+1−y1−zYa−Ca+RnU12=yzYa+Yp−Cp−Fa−λNn+y1−zYa+Yp−Cp−Nn+z1−yYa+Yp−Cp−Fa−λNn+1−y1−zYa+Yp−Cp−NnU1=xU11+1−xU12..Therefore, the replication dynamic equation and its first derivative of social organizations strategy selection are(2)Fx=dxdt=xU11−U1=x1−xU11−U12=x1−xzλRn−Rn+λNn−Nn+Fa+Rn+Cp−Ca−Yp+Nn,F′x=dFxdx=1−2xzλRn−Rn+λNn−Nn+Fa+Cp−Ca+Rn+Nn−Yp.According to the stability theorem of differential equations, if the probability that social organizations choose active allocation is in a stable state, it must meet the conditions thatFx=0 and F′x<0. And letting Fx=0, we can get x=0, x=1, z=Ca−Cp−Rn−Nn+Yp/λ−1Rn+Nn+Fa=z∗. When z=z∗, we can get Fx≡0, any value of x is the evolutionary stable strategy of social organizations, and the strategy of social organizations does not change over time. When z≠z∗, there will be two situations:(1)
Whenz>z∗, we can get F'0>0, F'1<0. Thus, x=1 is the steady state.(2)
Whenz<z∗, we can get F'0<0, F'1>0. Thus, x=0 is the steady state. Figure 2 shows the phase diagram of social organizations’ strategy evolution.Figure 2
Phase diagram of social organizations’ strategy evolution.Proposition 1.
The probability that social organizations choose the strategy of “active allocation” is positively related to positive and negative effects, the effect’s increasing multiple and the government penalty intensity, and is negatively related to the cost saved by negative allocation and extra profits.Proof.
It can be seen from Figure2 that the probabilities of social organizations adopting the strategies of “active allocation” and “negative allocation” are the volumes of A1 and A2, respectively, calculated as(3)VA1=1−Ca−Cp−Rn+Nn+Ypλ−1Rn+Nn+FaVA2=1−VA1.
According to the expression ofVA1 when social organizations choose “active allocation,” the first-order partial derivative of each element can be obtained: ∂VA1/∂Rn+Nn>0, ∂VA1/∂λ>0, ∂VA1/∂Fa>0, ∂VA1/Ca−Cp<0, ∂VA1/Yp<0. Therefore, increasing positive and negative effects, the effect’s increasing multiple and the government penalty intensity, or decreasing the cost saved by negative allocation and extra profits can all increase the probability of social organizations choosing “active allocation.”Proposition 2.
In the process of evolution, the probability that social organizations choose the strategy of “active allocation” is positively related to the probability that the government chooses “strict supervision.”Proof.
According to the stability analysis of social organizations, whenz<z∗, we can get F′0<0; thus, x=0 is the steady state; otherwise, x=1 is the steady state.
Therefore, with the increase ofz, the probability that social organizations choose the strategy of “active allocation” will be increased from x=0 to x=1. It can be seen that through constructing the blockchain platform by the government to strengthen supervision, social organizations can effectively allocate emergency supplies.


#### 4.1.2. Stability Analysis of the Public

Suppose the expected profits of the public in “informing” and “tolerance” areU21 and U22, respectively, and the average profit is U2; then,(4)U21=xz−Fe−Cr+x1−z−Cr+1−xzUp+Fe−Cr−Np+1−x1−z−Cr−NpU22=xzRp+x1−zRp+1−xzUp−Np+1−x1−z−NpU2=yU21+1−yU22..Therefore, the replication dynamic equation and its first derivative of the public strategy selection are(5)Fy=dydt=yU21−U2=y1−yU21−U22=y1−y−2xzFe−xRp+zFe−Cr,F′y=dFydy=1−2y−2xzFe−xRp+zFe−Cr.According to the stability theorem of differential equations, if the probability that the public chooses to inform is stable, it must meet the conditions thatFy=0 and F′y<0. Let Fy=0, we can get y=0, y=1, x=zFe−Cr/2zFe+Rp=x∗. When x=x∗, we can get Fy≡0; any value of y is the evolutionary stable strategy of the public, and the strategy of the public does not change over time. When x≠x∗, there will be two situations:(1)
Whenx>x∗, we can get F'0<0, F'1>0. Thus, y=0 is the steady state.(2)
Whenx<x∗, we can get F'0>0, F'1<0. Thus, y=1 is the steady state. Figure 3 shows the phase diagram of the public’s strategy evolution.Figure 3
Phase diagram of the public’s strategy evolution.Proposition 3.
The probability that the public chooses the “informing” strategy is positively related to the informants’ award, and it is negatively related to the cost of the public informing and the positive effect brought to the public by social organizations’ active allocation supplies.Proof.
Figure3 shows that the probabilities that the public adopts the strategies of “informing” and “tolerance” are the volumes of B1 and B2, respectively, calculated as(6)VB1=∫01∫Cr/Fe1zFe−Cr2zFe+Rpdzdy=Fe−Cr2Fe−2Cr+Rp4Feln2Fe+Rp2Cr+RpVB2=1−VB1=Fe+Cr2Fe+2Cr+Rp4Feln2Fe+Rp2Cr+Rp.
According to the expression ofVB1, when the public adopts the strategy of “informing,” the first-order partial derivative of each element can be obtained: ∂VB1/∂Fe>0, ∂VB1/∂Cr<0, ∂VB1/∂Rp<0. Therefore, increasing the informants’ award or decreasing the cost of the public informing can all increase the probability of the public choosing “informing.” In addition, when the positive effect brought to the public by social organizations’ active allocation supplies exceeds a certain limit, the public’s psychological endurance will be greatly improved. Thus, when the negative effect brought by social organizations’ passive allocation supplies is far below the acceptance boundary [22], the probability of public informing will be reduced accordingly.Proposition 4.
In the process of evolution, the probability that the public chooses the strategy of “informing” is positively related to the probability that the government chooses “strict supervision.” However, it is negatively related to the probability that social organizations choose “active allocation.”Proof.
According to the stability analysis of the public, whenx>x∗ and z<xRp+Cr/1−2xFe, we can get F′0<0; thus, y=0 is the steady state; otherwise, y=1 is the steady state. Thus, as x decreases or z increases, the probability of public informing will be increased from y=0 to y=1.
Therefore, in order to improve the enthusiasm of the public to participate in emergency supply allocation management, the government should strengthen supervision and create an open and transparent environment for the public to safeguard their rights with the help of emergency supply allocation information exchanging platform based on blockchain. In addition, as social organizations become more conscious of active allocation under strict supervision, the public can gain the highest benefits by choosing tolerance.


#### 4.1.3. Stability Analysis of the Government

Similarly, suppose the expected profits of the government choosing “strict supervision” and “relaxing supervision” areU31 and U32, respectively, and the average profit is U3; then,(7)U31=xyRg+Fe−Cy+x1−yRg−Cy+1−xyRg+Fa−Fe−Cy−Cn+1−x1−yRg+Fa−Cy−CnU32=xyRg+x1−yRg+1−xy−Cn−Ng+1−x1−y−Cn−NgU3=zU31+1−zU32..Therefore, the replication dynamic equation and its first derivative of the government strategy selection are(8)Fz=dzdt=zU31−U3=z1−zU31−U32=z1−z2xyFe+1−xRg+Ng+Fa−yFe−Cy,F′z=dFzdz=1−2z2xyFe+1−xRg+Ng+Fa−yFe−Cy.According to the stability theorem of differential equations, if the probability that the government chooses strict supervision is in a stable state, it must meet the conditions thatFz=0 and F′z<0. Letting Fz=0, we can get z=0, z=1, y=1−xRg+Ng+Fa−Cy/1−2xFe=y∗. When y=y∗, Fz≡0, any value of z is the evolutionary stable strategy of the government, and the strategy of the government does not change over time. When y≠y∗, there will be two situations:(1)
Wheny>y∗, we can get F'0<0, F'1>0. Thus, z=0 is the steady state.(2)
Wheny<y∗, we can get F'0>0, F'1<0. Thus, z=1 is the steady state. Figure 4 shows the phase diagram of the government’s strategy evolution.Figure 4
Phase diagram of the government’s strategy evolution.Proposition 5.
The probability that the government chooses the “strict supervision” strategy is positively related to the fines imposed on social organizations and the positive and negative effects of the government and it is negatively related to the award for informants.Proof.
Figure4 shows that the probabilities that the government adopts the strategies of “strict supervision” and “relaxing supervision” are the volumes of C1 and C2, respectively, calculated as(9)VC1=∫01∫011−xRg+Ng+Fa−Cy1−2xFedxdz=Rg+Ng+Fa2FeVC2=1−VC1=2Fe−Rg−Ng−Fa2Fe.
According to the expression ofVC1, when the government adopts the strategy of “strict supervision,” the first-order partial derivative of each element can be obtained: ∂VC1/∂Fa>0, ∂VC1/∂Rg+Ng>0, ∂VC1/∂Fe<0. Therefore, increasing the fines imposed on social organizations and the positive and negative effects of the government or decreasing the rewards for informants can all prompt the government to practice strict supervision.Proposition 6.
In the evolution process, the probability that the government chooses the strategy of “strict supervision” is negatively related to the probability that the social organizations choose “active allocation” and the probability that the public chooses “informing.”Proof.
The proving process is the same as Proposition4.
Therefore, when the probability that the social organizations choose “active allocation” and the probability that the public chooses “informing” is high, the government will reduce the probability of strict supervision, which is easy to lead to the lack of supervision.


### 4.2. Stability Analysis of Tripartite Evolutionary Game System

In order to carry out the analysis of the evolutionary stable strategies under the mutual interaction among social organizations, the public, and the government, we first build a tripartite dynamic replication system for emergency supply allocation according to equations (2), (6), and (10).(10)Fx=x1−xzλRn−Rn+λNn−Nn+Fa+Cp−Ca+Rn+Nn−YpFy=y1−y−2xzFe−xRp+zFe−CrFz=z1−z2xyFe+1−xRg+Ng+Fa−yFe−Cy..LettingFx=Fy=Fz=0, we can get 8 equilibrium points of the dynamic system: E10,0,0, E21,0,0, E30,0,1, E40,1,1, E50,1,0, E61,1,0, E71,0,1, and E81,1,1. According to the replication dynamic equation in the tripartite game, a Jacobian matrix can be obtained:(11)J=∂Fx∂x∂Fx∂y∂Fx∂z∂Fy∂x∂Fy∂y∂Fy∂z∂Fz∂x∂Fz∂y∂Fz∂z.To be specific, each element in the Jacobian matrixJ is expressed as follows:(12)∂Fx∂x=1−2xzλRn−Rn+λNn−Nn+Fa+Rn+Nn−Ca−Yp+Cp∂Fx∂y=0∂Fx∂z=x1−xλ−1Rn+Nn+Fa∂Fy∂x=y1−y−2zFe−Rp∂Fy∂y=1−2y−2xzFe−xRp+zFe−Cr∂Fy∂z=y1−y−2xFe+Fe∂Fz∂x=z1−z2yFe−Fa−Rg−Ng∂Fz∂y=z1−z2xFe−Fe∂Fz∂z=1−2z2xyFe+1−xFa+Rg+Ng−yFe−Cy.InputtingE1∼E8 into Jacobian matrix J, we can get the eigenvalues corresponding to each equilibrium point, as shown in Table 2.Table 2
The eigenvalues corresponding to each equilibrium point.
Equilibrium pointEigenvaluesλ1λ2λ3E10,0,0−Ca−Cp+Yp+Rn+Nn−Cr−Cy−Fa+Rg+NgE21,0,0Ca−Cp+Yp−Rn+Nn−Cr−Rp−CyE30,0,1−Ca−Cp+Yp+λRn+Nn+FaFe−CrCy−Fa−Rg+NgE40,1,1−Ca−Cp+Yp+λRn+Nn+FaCr−FeCy−Fa−Rg+Ng−FeE50,1,0−Ca−Cp+Yp+Rn+NnCr (+)−Cy−Fa+Rg+Ng−FeE61,1,0Ca−Cp+Yp−Rn+NnRp+Cr (+)Fe−CyE71,0,1Ca−Cp+Yp−λRn+Nn+Fa−Cr−Rp−FeCy (+)E81,1,1Ca−Cp+Yp−λRn+Nn+FaCr+Rp+Fe (+)Cy−FeAccording to the point of Friedman [23], when the eigenvalues of Jacobian matrix J are all negative, the equilibrium point is the asymptotic stable point of the system. It can be seen from Table 2 that the equilibrium points E5, E6, E7, and E8 all have positive eigenvalues, so they cannot be evolutionary stability strategies. Equilibrium points E1∼E4 are evolutionary stability strategies if the stability conditions in Table 3 are satisfied.Table 3
The condition of equilibrium point’ stability.
Equilibrium pointConditionE10,0,0Ca−Cp+Yp > Rn+Nn, Cy−Fa > Rg+NgE21,0,0Ca−Cp+Yp < Rn+NnE30,0,1Ca−Cp+Yp > λRn+Nn+Fa, Cr > Fe, Cy−Fa < Rg+NgE40,1,1Ca−Cp+Yp > λRn+Nn+Fa, Cr < Fe, Cy−Fa < Rg+Ng−FeScenario 1.
WhenCa−Cp+Yp > Rn+Nn and Cy−Fa>Rg+Ng, that is, when the extra profits obtained from social organizations’ passive allocation are higher than the sum of positive and negative effects under relaxing supervision, as well as when the extra cost of the government’ supervision (i.e., the cost of the government’s strict supervision minus the fines the government carries on to social organizations) is higher than the sum of positive and negative effects, as shown in Table 3, there is only one stable point E10,0,0 in the dynamic replication system.
This means that it is expensive for the government to construct the blockchain platform for strict supervision, and for the sake of maximizing the benefits, the government will choose relaxing supervision. In this case, the lack of the government supervision will make it difficult for the blockchain to play a role, which will cause the problems of information asymmetry and information isolated island [22] and further cause social organizations to allocate passively in order to achieve extra profits. In addition, without the blockchain platform, the cost for the public to collect information and inform against the passive allocation of social organizations will greatly increase, and it will be more difficult to protect their rights. Therefore, the public tends to be tolerant.Scenario 2.
WhenCa−Cp+Yp<Rn+Nn, that is, when the extra profits of social organizations’ passive allocation of supplies are less than the sum of positive and negative effects under relaxing supervision, as shown in Table 3, there is only one stable point E21,0,0 in the dynamic replication system. This equilibrium means that when social organizations obtain little benefit in passive allocation, they do not want to take risks to practice passive allocation. And at the same time, the government do not want to construct blockchain platform to optimize emergency supply allocation for the sake of the cost. In this case, the government’s strategy is relaxing supervision, and the public’s strategy is tolerance.Scenario 3.
WhenCa−Cp+Yp>λRn+Nn+Fa, that is, when the extra profits obtained from social organizations’ passive allocation are higher than the sum of positive and negative effects under strict supervision, as shown in Table 3, the stable point may be E30,0,1 or E40,1,1, which means that no matter how the government and the public make strategy choices, social organizations will still choose passive allocation in order to seek high profits. On this basis, only when Cr<Fe and Cy−Fa<Rg+Ng−Fe, that is, only when the cost of the public’s informing is lower than the reward for informing, and the extra cost of strict supervision by the government is low, there will be only one stable point E40,1,1 in the dynamic replication system, which means the government and the public will stabilize their strategy choices on strict supervision and informing against social organizations respectively. In this case, even if government practices strict supervision with the help of blockchain platform and punishes social organizations for their passive allocation, social organizations still choose passive allocation in order to seek high profits.
In summary, the co-governance of emergency supply allocation can be divided into three stages: the ineffective stage, the intermediate stage, and the useless stage. The ineffective stage corresponds to Scenario 3, and in this case, no matter whether the government practices strict supervision with the help of blockchain platform, social organizations will choose passive allocation as the optimum strategy, and the emergency supply allocation management system is extremely deteriorating. The useless stage corresponds to Scenario 2, and in this case, social organizations will practice active allocation, and the government’s blockchain platform will be useless. The emergency supply allocation management system is in a complete stage. The intermediate stage is the transition from the ineffective stage to the useless stage. At this stage, there are few evolutionary stable points in the system, and the strategies of social organizations are constantly adjusted according to the strategies of the public and the government. Therefore, it is necessary to build the blockchain platform to promote the optimization and adjustment of relevant parameters and realize the co-governance of emergency supply allocation from ineffective stage to useless stage [24].


## 4.1. Stability Analysis of Tripartite Subjects

### 4.1.1. Stability Analysis of Social Organizations

Define the expected profits of social organizations in “active allocation” and “passive allocation” byU11 and U12, respectively, and the average profit is U1; then,(1)U11=yzYa−Ca+λRn+y1−zYa−Ca+Rn+z1−yYa−Ca+λRn+1−y1−zYa−Ca+RnU12=yzYa+Yp−Cp−Fa−λNn+y1−zYa+Yp−Cp−Nn+z1−yYa+Yp−Cp−Fa−λNn+1−y1−zYa+Yp−Cp−NnU1=xU11+1−xU12..Therefore, the replication dynamic equation and its first derivative of social organizations strategy selection are(2)Fx=dxdt=xU11−U1=x1−xU11−U12=x1−xzλRn−Rn+λNn−Nn+Fa+Rn+Cp−Ca−Yp+Nn,F′x=dFxdx=1−2xzλRn−Rn+λNn−Nn+Fa+Cp−Ca+Rn+Nn−Yp.According to the stability theorem of differential equations, if the probability that social organizations choose active allocation is in a stable state, it must meet the conditions thatFx=0 and F′x<0. And letting Fx=0, we can get x=0, x=1, z=Ca−Cp−Rn−Nn+Yp/λ−1Rn+Nn+Fa=z∗. When z=z∗, we can get Fx≡0, any value of x is the evolutionary stable strategy of social organizations, and the strategy of social organizations does not change over time. When z≠z∗, there will be two situations:(1)
Whenz>z∗, we can get F'0>0, F'1<0. Thus, x=1 is the steady state.(2)
Whenz<z∗, we can get F'0<0, F'1>0. Thus, x=0 is the steady state. Figure 2 shows the phase diagram of social organizations’ strategy evolution.Figure 2
Phase diagram of social organizations’ strategy evolution.Proposition 1.
The probability that social organizations choose the strategy of “active allocation” is positively related to positive and negative effects, the effect’s increasing multiple and the government penalty intensity, and is negatively related to the cost saved by negative allocation and extra profits.Proof.
It can be seen from Figure2 that the probabilities of social organizations adopting the strategies of “active allocation” and “negative allocation” are the volumes of A1 and A2, respectively, calculated as(3)VA1=1−Ca−Cp−Rn+Nn+Ypλ−1Rn+Nn+FaVA2=1−VA1.
According to the expression ofVA1 when social organizations choose “active allocation,” the first-order partial derivative of each element can be obtained: ∂VA1/∂Rn+Nn>0, ∂VA1/∂λ>0, ∂VA1/∂Fa>0, ∂VA1/Ca−Cp<0, ∂VA1/Yp<0. Therefore, increasing positive and negative effects, the effect’s increasing multiple and the government penalty intensity, or decreasing the cost saved by negative allocation and extra profits can all increase the probability of social organizations choosing “active allocation.”Proposition 2.
In the process of evolution, the probability that social organizations choose the strategy of “active allocation” is positively related to the probability that the government chooses “strict supervision.”Proof.
According to the stability analysis of social organizations, whenz<z∗, we can get F′0<0; thus, x=0 is the steady state; otherwise, x=1 is the steady state.
Therefore, with the increase ofz, the probability that social organizations choose the strategy of “active allocation” will be increased from x=0 to x=1. It can be seen that through constructing the blockchain platform by the government to strengthen supervision, social organizations can effectively allocate emergency supplies.


### 4.1.2. Stability Analysis of the Public

Suppose the expected profits of the public in “informing” and “tolerance” areU21 and U22, respectively, and the average profit is U2; then,(4)U21=xz−Fe−Cr+x1−z−Cr+1−xzUp+Fe−Cr−Np+1−x1−z−Cr−NpU22=xzRp+x1−zRp+1−xzUp−Np+1−x1−z−NpU2=yU21+1−yU22..Therefore, the replication dynamic equation and its first derivative of the public strategy selection are(5)Fy=dydt=yU21−U2=y1−yU21−U22=y1−y−2xzFe−xRp+zFe−Cr,F′y=dFydy=1−2y−2xzFe−xRp+zFe−Cr.According to the stability theorem of differential equations, if the probability that the public chooses to inform is stable, it must meet the conditions thatFy=0 and F′y<0. Let Fy=0, we can get y=0, y=1, x=zFe−Cr/2zFe+Rp=x∗. When x=x∗, we can get Fy≡0; any value of y is the evolutionary stable strategy of the public, and the strategy of the public does not change over time. When x≠x∗, there will be two situations:(1)
Whenx>x∗, we can get F'0<0, F'1>0. Thus, y=0 is the steady state.(2)
Whenx<x∗, we can get F'0>0, F'1<0. Thus, y=1 is the steady state. Figure 3 shows the phase diagram of the public’s strategy evolution.Figure 3
Phase diagram of the public’s strategy evolution.Proposition 3.
The probability that the public chooses the “informing” strategy is positively related to the informants’ award, and it is negatively related to the cost of the public informing and the positive effect brought to the public by social organizations’ active allocation supplies.Proof.
Figure3 shows that the probabilities that the public adopts the strategies of “informing” and “tolerance” are the volumes of B1 and B2, respectively, calculated as(6)VB1=∫01∫Cr/Fe1zFe−Cr2zFe+Rpdzdy=Fe−Cr2Fe−2Cr+Rp4Feln2Fe+Rp2Cr+RpVB2=1−VB1=Fe+Cr2Fe+2Cr+Rp4Feln2Fe+Rp2Cr+Rp.
According to the expression ofVB1, when the public adopts the strategy of “informing,” the first-order partial derivative of each element can be obtained: ∂VB1/∂Fe>0, ∂VB1/∂Cr<0, ∂VB1/∂Rp<0. Therefore, increasing the informants’ award or decreasing the cost of the public informing can all increase the probability of the public choosing “informing.” In addition, when the positive effect brought to the public by social organizations’ active allocation supplies exceeds a certain limit, the public’s psychological endurance will be greatly improved. Thus, when the negative effect brought by social organizations’ passive allocation supplies is far below the acceptance boundary [22], the probability of public informing will be reduced accordingly.Proposition 4.
In the process of evolution, the probability that the public chooses the strategy of “informing” is positively related to the probability that the government chooses “strict supervision.” However, it is negatively related to the probability that social organizations choose “active allocation.”Proof.
According to the stability analysis of the public, whenx>x∗ and z<xRp+Cr/1−2xFe, we can get F′0<0; thus, y=0 is the steady state; otherwise, y=1 is the steady state. Thus, as x decreases or z increases, the probability of public informing will be increased from y=0 to y=1.
Therefore, in order to improve the enthusiasm of the public to participate in emergency supply allocation management, the government should strengthen supervision and create an open and transparent environment for the public to safeguard their rights with the help of emergency supply allocation information exchanging platform based on blockchain. In addition, as social organizations become more conscious of active allocation under strict supervision, the public can gain the highest benefits by choosing tolerance.


### 4.1.3. Stability Analysis of the Government

Similarly, suppose the expected profits of the government choosing “strict supervision” and “relaxing supervision” areU31 and U32, respectively, and the average profit is U3; then,(7)U31=xyRg+Fe−Cy+x1−yRg−Cy+1−xyRg+Fa−Fe−Cy−Cn+1−x1−yRg+Fa−Cy−CnU32=xyRg+x1−yRg+1−xy−Cn−Ng+1−x1−y−Cn−NgU3=zU31+1−zU32..Therefore, the replication dynamic equation and its first derivative of the government strategy selection are(8)Fz=dzdt=zU31−U3=z1−zU31−U32=z1−z2xyFe+1−xRg+Ng+Fa−yFe−Cy,F′z=dFzdz=1−2z2xyFe+1−xRg+Ng+Fa−yFe−Cy.According to the stability theorem of differential equations, if the probability that the government chooses strict supervision is in a stable state, it must meet the conditions thatFz=0 and F′z<0. Letting Fz=0, we can get z=0, z=1, y=1−xRg+Ng+Fa−Cy/1−2xFe=y∗. When y=y∗, Fz≡0, any value of z is the evolutionary stable strategy of the government, and the strategy of the government does not change over time. When y≠y∗, there will be two situations:(1)
Wheny>y∗, we can get F'0<0, F'1>0. Thus, z=0 is the steady state.(2)
Wheny<y∗, we can get F'0>0, F'1<0. Thus, z=1 is the steady state. Figure 4 shows the phase diagram of the government’s strategy evolution.Figure 4
Phase diagram of the government’s strategy evolution.Proposition 5.
The probability that the government chooses the “strict supervision” strategy is positively related to the fines imposed on social organizations and the positive and negative effects of the government and it is negatively related to the award for informants.Proof.
Figure4 shows that the probabilities that the government adopts the strategies of “strict supervision” and “relaxing supervision” are the volumes of C1 and C2, respectively, calculated as(9)VC1=∫01∫011−xRg+Ng+Fa−Cy1−2xFedxdz=Rg+Ng+Fa2FeVC2=1−VC1=2Fe−Rg−Ng−Fa2Fe.
According to the expression ofVC1, when the government adopts the strategy of “strict supervision,” the first-order partial derivative of each element can be obtained: ∂VC1/∂Fa>0, ∂VC1/∂Rg+Ng>0, ∂VC1/∂Fe<0. Therefore, increasing the fines imposed on social organizations and the positive and negative effects of the government or decreasing the rewards for informants can all prompt the government to practice strict supervision.Proposition 6.
In the evolution process, the probability that the government chooses the strategy of “strict supervision” is negatively related to the probability that the social organizations choose “active allocation” and the probability that the public chooses “informing.”Proof.
The proving process is the same as Proposition4.
Therefore, when the probability that the social organizations choose “active allocation” and the probability that the public chooses “informing” is high, the government will reduce the probability of strict supervision, which is easy to lead to the lack of supervision.


## 4.1.1. Stability Analysis of Social Organizations

Define the expected profits of social organizations in “active allocation” and “passive allocation” byU11 and U12, respectively, and the average profit is U1; then,(1)U11=yzYa−Ca+λRn+y1−zYa−Ca+Rn+z1−yYa−Ca+λRn+1−y1−zYa−Ca+RnU12=yzYa+Yp−Cp−Fa−λNn+y1−zYa+Yp−Cp−Nn+z1−yYa+Yp−Cp−Fa−λNn+1−y1−zYa+Yp−Cp−NnU1=xU11+1−xU12..Therefore, the replication dynamic equation and its first derivative of social organizations strategy selection are(2)Fx=dxdt=xU11−U1=x1−xU11−U12=x1−xzλRn−Rn+λNn−Nn+Fa+Rn+Cp−Ca−Yp+Nn,F′x=dFxdx=1−2xzλRn−Rn+λNn−Nn+Fa+Cp−Ca+Rn+Nn−Yp.According to the stability theorem of differential equations, if the probability that social organizations choose active allocation is in a stable state, it must meet the conditions thatFx=0 and F′x<0. And letting Fx=0, we can get x=0, x=1, z=Ca−Cp−Rn−Nn+Yp/λ−1Rn+Nn+Fa=z∗. When z=z∗, we can get Fx≡0, any value of x is the evolutionary stable strategy of social organizations, and the strategy of social organizations does not change over time. When z≠z∗, there will be two situations:(1)
Whenz>z∗, we can get F'0>0, F'1<0. Thus, x=1 is the steady state.(2)
Whenz<z∗, we can get F'0<0, F'1>0. Thus, x=0 is the steady state. Figure 2 shows the phase diagram of social organizations’ strategy evolution.Figure 2
Phase diagram of social organizations’ strategy evolution.Proposition 1.
The probability that social organizations choose the strategy of “active allocation” is positively related to positive and negative effects, the effect’s increasing multiple and the government penalty intensity, and is negatively related to the cost saved by negative allocation and extra profits.Proof.
It can be seen from Figure2 that the probabilities of social organizations adopting the strategies of “active allocation” and “negative allocation” are the volumes of A1 and A2, respectively, calculated as(3)VA1=1−Ca−Cp−Rn+Nn+Ypλ−1Rn+Nn+FaVA2=1−VA1.
According to the expression ofVA1 when social organizations choose “active allocation,” the first-order partial derivative of each element can be obtained: ∂VA1/∂Rn+Nn>0, ∂VA1/∂λ>0, ∂VA1/∂Fa>0, ∂VA1/Ca−Cp<0, ∂VA1/Yp<0. Therefore, increasing positive and negative effects, the effect’s increasing multiple and the government penalty intensity, or decreasing the cost saved by negative allocation and extra profits can all increase the probability of social organizations choosing “active allocation.”Proposition 2.
In the process of evolution, the probability that social organizations choose the strategy of “active allocation” is positively related to the probability that the government chooses “strict supervision.”Proof.
According to the stability analysis of social organizations, whenz<z∗, we can get F′0<0; thus, x=0 is the steady state; otherwise, x=1 is the steady state.
Therefore, with the increase ofz, the probability that social organizations choose the strategy of “active allocation” will be increased from x=0 to x=1. It can be seen that through constructing the blockchain platform by the government to strengthen supervision, social organizations can effectively allocate emergency supplies.


## 4.1.2. Stability Analysis of the Public

Suppose the expected profits of the public in “informing” and “tolerance” areU21 and U22, respectively, and the average profit is U2; then,(4)U21=xz−Fe−Cr+x1−z−Cr+1−xzUp+Fe−Cr−Np+1−x1−z−Cr−NpU22=xzRp+x1−zRp+1−xzUp−Np+1−x1−z−NpU2=yU21+1−yU22..Therefore, the replication dynamic equation and its first derivative of the public strategy selection are(5)Fy=dydt=yU21−U2=y1−yU21−U22=y1−y−2xzFe−xRp+zFe−Cr,F′y=dFydy=1−2y−2xzFe−xRp+zFe−Cr.According to the stability theorem of differential equations, if the probability that the public chooses to inform is stable, it must meet the conditions thatFy=0 and F′y<0. Let Fy=0, we can get y=0, y=1, x=zFe−Cr/2zFe+Rp=x∗. When x=x∗, we can get Fy≡0; any value of y is the evolutionary stable strategy of the public, and the strategy of the public does not change over time. When x≠x∗, there will be two situations:(1)
Whenx>x∗, we can get F'0<0, F'1>0. Thus, y=0 is the steady state.(2)
Whenx<x∗, we can get F'0>0, F'1<0. Thus, y=1 is the steady state. Figure 3 shows the phase diagram of the public’s strategy evolution.Figure 3
Phase diagram of the public’s strategy evolution.Proposition 3.
The probability that the public chooses the “informing” strategy is positively related to the informants’ award, and it is negatively related to the cost of the public informing and the positive effect brought to the public by social organizations’ active allocation supplies.Proof.
Figure3 shows that the probabilities that the public adopts the strategies of “informing” and “tolerance” are the volumes of B1 and B2, respectively, calculated as(6)VB1=∫01∫Cr/Fe1zFe−Cr2zFe+Rpdzdy=Fe−Cr2Fe−2Cr+Rp4Feln2Fe+Rp2Cr+RpVB2=1−VB1=Fe+Cr2Fe+2Cr+Rp4Feln2Fe+Rp2Cr+Rp.
According to the expression ofVB1, when the public adopts the strategy of “informing,” the first-order partial derivative of each element can be obtained: ∂VB1/∂Fe>0, ∂VB1/∂Cr<0, ∂VB1/∂Rp<0. Therefore, increasing the informants’ award or decreasing the cost of the public informing can all increase the probability of the public choosing “informing.” In addition, when the positive effect brought to the public by social organizations’ active allocation supplies exceeds a certain limit, the public’s psychological endurance will be greatly improved. Thus, when the negative effect brought by social organizations’ passive allocation supplies is far below the acceptance boundary [22], the probability of public informing will be reduced accordingly.Proposition 4.
In the process of evolution, the probability that the public chooses the strategy of “informing” is positively related to the probability that the government chooses “strict supervision.” However, it is negatively related to the probability that social organizations choose “active allocation.”Proof.
According to the stability analysis of the public, whenx>x∗ and z<xRp+Cr/1−2xFe, we can get F′0<0; thus, y=0 is the steady state; otherwise, y=1 is the steady state. Thus, as x decreases or z increases, the probability of public informing will be increased from y=0 to y=1.
Therefore, in order to improve the enthusiasm of the public to participate in emergency supply allocation management, the government should strengthen supervision and create an open and transparent environment for the public to safeguard their rights with the help of emergency supply allocation information exchanging platform based on blockchain. In addition, as social organizations become more conscious of active allocation under strict supervision, the public can gain the highest benefits by choosing tolerance.


## 4.1.3. Stability Analysis of the Government

Similarly, suppose the expected profits of the government choosing “strict supervision” and “relaxing supervision” areU31 and U32, respectively, and the average profit is U3; then,(7)U31=xyRg+Fe−Cy+x1−yRg−Cy+1−xyRg+Fa−Fe−Cy−Cn+1−x1−yRg+Fa−Cy−CnU32=xyRg+x1−yRg+1−xy−Cn−Ng+1−x1−y−Cn−NgU3=zU31+1−zU32..Therefore, the replication dynamic equation and its first derivative of the government strategy selection are(8)Fz=dzdt=zU31−U3=z1−zU31−U32=z1−z2xyFe+1−xRg+Ng+Fa−yFe−Cy,F′z=dFzdz=1−2z2xyFe+1−xRg+Ng+Fa−yFe−Cy.According to the stability theorem of differential equations, if the probability that the government chooses strict supervision is in a stable state, it must meet the conditions thatFz=0 and F′z<0. Letting Fz=0, we can get z=0, z=1, y=1−xRg+Ng+Fa−Cy/1−2xFe=y∗. When y=y∗, Fz≡0, any value of z is the evolutionary stable strategy of the government, and the strategy of the government does not change over time. When y≠y∗, there will be two situations:(1)
Wheny>y∗, we can get F'0<0, F'1>0. Thus, z=0 is the steady state.(2)
Wheny<y∗, we can get F'0>0, F'1<0. Thus, z=1 is the steady state. Figure 4 shows the phase diagram of the government’s strategy evolution.Figure 4
Phase diagram of the government’s strategy evolution.Proposition 5.
The probability that the government chooses the “strict supervision” strategy is positively related to the fines imposed on social organizations and the positive and negative effects of the government and it is negatively related to the award for informants.Proof.
Figure4 shows that the probabilities that the government adopts the strategies of “strict supervision” and “relaxing supervision” are the volumes of C1 and C2, respectively, calculated as(9)VC1=∫01∫011−xRg+Ng+Fa−Cy1−2xFedxdz=Rg+Ng+Fa2FeVC2=1−VC1=2Fe−Rg−Ng−Fa2Fe.
According to the expression ofVC1, when the government adopts the strategy of “strict supervision,” the first-order partial derivative of each element can be obtained: ∂VC1/∂Fa>0, ∂VC1/∂Rg+Ng>0, ∂VC1/∂Fe<0. Therefore, increasing the fines imposed on social organizations and the positive and negative effects of the government or decreasing the rewards for informants can all prompt the government to practice strict supervision.Proposition 6.
In the evolution process, the probability that the government chooses the strategy of “strict supervision” is negatively related to the probability that the social organizations choose “active allocation” and the probability that the public chooses “informing.”Proof.
The proving process is the same as Proposition4.
Therefore, when the probability that the social organizations choose “active allocation” and the probability that the public chooses “informing” is high, the government will reduce the probability of strict supervision, which is easy to lead to the lack of supervision.


## 4.2. Stability Analysis of Tripartite Evolutionary Game System

In order to carry out the analysis of the evolutionary stable strategies under the mutual interaction among social organizations, the public, and the government, we first build a tripartite dynamic replication system for emergency supply allocation according to equations (2), (6), and (10).(10)Fx=x1−xzλRn−Rn+λNn−Nn+Fa+Cp−Ca+Rn+Nn−YpFy=y1−y−2xzFe−xRp+zFe−CrFz=z1−z2xyFe+1−xRg+Ng+Fa−yFe−Cy..LettingFx=Fy=Fz=0, we can get 8 equilibrium points of the dynamic system: E10,0,0, E21,0,0, E30,0,1, E40,1,1, E50,1,0, E61,1,0, E71,0,1, and E81,1,1. According to the replication dynamic equation in the tripartite game, a Jacobian matrix can be obtained:(11)J=∂Fx∂x∂Fx∂y∂Fx∂z∂Fy∂x∂Fy∂y∂Fy∂z∂Fz∂x∂Fz∂y∂Fz∂z.To be specific, each element in the Jacobian matrixJ is expressed as follows:(12)∂Fx∂x=1−2xzλRn−Rn+λNn−Nn+Fa+Rn+Nn−Ca−Yp+Cp∂Fx∂y=0∂Fx∂z=x1−xλ−1Rn+Nn+Fa∂Fy∂x=y1−y−2zFe−Rp∂Fy∂y=1−2y−2xzFe−xRp+zFe−Cr∂Fy∂z=y1−y−2xFe+Fe∂Fz∂x=z1−z2yFe−Fa−Rg−Ng∂Fz∂y=z1−z2xFe−Fe∂Fz∂z=1−2z2xyFe+1−xFa+Rg+Ng−yFe−Cy.InputtingE1∼E8 into Jacobian matrix J, we can get the eigenvalues corresponding to each equilibrium point, as shown in Table 2.Table 2
The eigenvalues corresponding to each equilibrium point.
Equilibrium pointEigenvaluesλ1λ2λ3E10,0,0−Ca−Cp+Yp+Rn+Nn−Cr−Cy−Fa+Rg+NgE21,0,0Ca−Cp+Yp−Rn+Nn−Cr−Rp−CyE30,0,1−Ca−Cp+Yp+λRn+Nn+FaFe−CrCy−Fa−Rg+NgE40,1,1−Ca−Cp+Yp+λRn+Nn+FaCr−FeCy−Fa−Rg+Ng−FeE50,1,0−Ca−Cp+Yp+Rn+NnCr (+)−Cy−Fa+Rg+Ng−FeE61,1,0Ca−Cp+Yp−Rn+NnRp+Cr (+)Fe−CyE71,0,1Ca−Cp+Yp−λRn+Nn+Fa−Cr−Rp−FeCy (+)E81,1,1Ca−Cp+Yp−λRn+Nn+FaCr+Rp+Fe (+)Cy−FeAccording to the point of Friedman [23], when the eigenvalues of Jacobian matrix J are all negative, the equilibrium point is the asymptotic stable point of the system. It can be seen from Table 2 that the equilibrium points E5, E6, E7, and E8 all have positive eigenvalues, so they cannot be evolutionary stability strategies. Equilibrium points E1∼E4 are evolutionary stability strategies if the stability conditions in Table 3 are satisfied.Table 3
The condition of equilibrium point’ stability.
Equilibrium pointConditionE10,0,0Ca−Cp+Yp > Rn+Nn, Cy−Fa > Rg+NgE21,0,0Ca−Cp+Yp < Rn+NnE30,0,1Ca−Cp+Yp > λRn+Nn+Fa, Cr > Fe, Cy−Fa < Rg+NgE40,1,1Ca−Cp+Yp > λRn+Nn+Fa, Cr < Fe, Cy−Fa < Rg+Ng−FeScenario 1.
WhenCa−Cp+Yp > Rn+Nn and Cy−Fa>Rg+Ng, that is, when the extra profits obtained from social organizations’ passive allocation are higher than the sum of positive and negative effects under relaxing supervision, as well as when the extra cost of the government’ supervision (i.e., the cost of the government’s strict supervision minus the fines the government carries on to social organizations) is higher than the sum of positive and negative effects, as shown in Table 3, there is only one stable point E10,0,0 in the dynamic replication system.
This means that it is expensive for the government to construct the blockchain platform for strict supervision, and for the sake of maximizing the benefits, the government will choose relaxing supervision. In this case, the lack of the government supervision will make it difficult for the blockchain to play a role, which will cause the problems of information asymmetry and information isolated island [22] and further cause social organizations to allocate passively in order to achieve extra profits. In addition, without the blockchain platform, the cost for the public to collect information and inform against the passive allocation of social organizations will greatly increase, and it will be more difficult to protect their rights. Therefore, the public tends to be tolerant.Scenario 2.
WhenCa−Cp+Yp<Rn+Nn, that is, when the extra profits of social organizations’ passive allocation of supplies are less than the sum of positive and negative effects under relaxing supervision, as shown in Table 3, there is only one stable point E21,0,0 in the dynamic replication system. This equilibrium means that when social organizations obtain little benefit in passive allocation, they do not want to take risks to practice passive allocation. And at the same time, the government do not want to construct blockchain platform to optimize emergency supply allocation for the sake of the cost. In this case, the government’s strategy is relaxing supervision, and the public’s strategy is tolerance.Scenario 3.
WhenCa−Cp+Yp>λRn+Nn+Fa, that is, when the extra profits obtained from social organizations’ passive allocation are higher than the sum of positive and negative effects under strict supervision, as shown in Table 3, the stable point may be E30,0,1 or E40,1,1, which means that no matter how the government and the public make strategy choices, social organizations will still choose passive allocation in order to seek high profits. On this basis, only when Cr<Fe and Cy−Fa<Rg+Ng−Fe, that is, only when the cost of the public’s informing is lower than the reward for informing, and the extra cost of strict supervision by the government is low, there will be only one stable point E40,1,1 in the dynamic replication system, which means the government and the public will stabilize their strategy choices on strict supervision and informing against social organizations respectively. In this case, even if government practices strict supervision with the help of blockchain platform and punishes social organizations for their passive allocation, social organizations still choose passive allocation in order to seek high profits.
In summary, the co-governance of emergency supply allocation can be divided into three stages: the ineffective stage, the intermediate stage, and the useless stage. The ineffective stage corresponds to Scenario 3, and in this case, no matter whether the government practices strict supervision with the help of blockchain platform, social organizations will choose passive allocation as the optimum strategy, and the emergency supply allocation management system is extremely deteriorating. The useless stage corresponds to Scenario 2, and in this case, social organizations will practice active allocation, and the government’s blockchain platform will be useless. The emergency supply allocation management system is in a complete stage. The intermediate stage is the transition from the ineffective stage to the useless stage. At this stage, there are few evolutionary stable points in the system, and the strategies of social organizations are constantly adjusted according to the strategies of the public and the government. Therefore, it is necessary to build the blockchain platform to promote the optimization and adjustment of relevant parameters and realize the co-governance of emergency supply allocation from ineffective stage to useless stage [24].


## 5. Simulation Analysis

In order to observe the stable equilibrium strategies of tripartite participants and their sensitivity to parameters in evolutionary game, and verify the validity of the stability analysis, we use MATLAB R2021a to simulate the game. DefineRn=4, Nn=4, Cp=3, Ca=6, Yp=4, Fe=1, Rp=4, Cr=2, Rg=2, Ng=4, Cy=13, and λ=1.5, which satisfies the condition of Scenario 2. Suppose the probabilities of initial game strategy choices of tripartite participants are all 0.5, and on this basis, in the following we discuss the impact of initial strategy choice, the government penalty intensity, social organizations’ positive and negative effects, the effect’s increasing multiple, and the changes of public’ informing cost on evolutionary process and results.


### 5.1. The Impact of Initial Strategy Choice on the Stability of Game Strategy

According to replication dynamic equations, it can be seen that the evolutionary stable state of a single game participant will be affected by the initial strategy choices of other subjects. Based on this premise, this paper verifies the results of strategies evolution by adjusting the initial values. When examining the sensitivity of each game participant to the initial strategy choice, the initial values of other game subjects are set as 0.5. Respectively suppose the initial state of the social organizations isx0  = 0.2, 0.5, 0.7, the initial state of the public is y0  = 0.2, 0.5, 0.7, and the initial state of the government is z0  = 0.2, 0.5, 0.7, and the other parameters keep unchanged. Then, the simulation results can be shown by Figures 5 to 7.Figure 5
The evolution result of the change of social organizations’ initial strategies.Figure 6
The evolution result of the change of public’s initial strategies.Figure 7
The evolution result of the change of government’s initial strategies.As shown in these figures, no matter what the initial strategy choice of tripartite participants is, with the probability of social organizations choosing active allocation strategies tends to 1, the public and the government will adopt the strategies of tolerance and relaxing supervision, respectively, which means that (1, 0, 0) is the evolutionary stability point.As shown in Figure5, with the increase of x, y and z will quickly converge to 0, which further verifies Propositions 4 and 6. This is because the increased awareness of social organizations in allocating emergency supplies has accelerated the process of emergencies prevention and control, and both the government and the public can obtain positive effects without paying extra costs for supervision. Therefore, the government tends to relaxing supervision and the public tends to tolerance.As shown in Figure7, with the increase of z, the speeds of x converging to 1 are accelerated, which further verifies Proposition 2. When the government practices strict supervision with the help of blockchain platform, the information of social organizations’ allocating emergency supplies will be recorded in the blockchain and be open to all of authorized participants; in this condition, the profits of passive allocation gradually cannot compensate the loss of fine by the government, the loss of social reputation, and so on, which promotes social organizations’ active allocation.From Figure5 to Figure 7, it can be seen that no matter what the initial strategy choice is, the speed of x converging to 1 is less than the speed of y and z converging to 0. It means that guiding social organizations to practice active allocation needs a long-term process. The process requires the government actively to construct blockchain platform of emergency supplies allocation and build the reward and punishment mechanism to mobilize the participating enthusiasm of social organizations.


### 5.2. The Impact of Government Penalty Intensity on the Stability of Game Strategy

To analyse the impact of government penalties on the evolutionary game, we keep the remaining parameters unchanged, and set the values ofFa as follows: Fa=0; Fa=4; and Fa=8. The simulation result is shown in Figure 8.Figure 8
Evolution path under different penalties.The figure indicates that in the evolution process, with the increment of the penalty imposed by the government on the passive allocation of social organizations, the probability of social organizations actively performing their duties increases, and at the same time the speed that the government evolves to strict supervision accelerates, which further verifies Propositions1 and 5. In the condition of strict supervision, the government will supervise social organizations at a lower cost with the help of blockchain platform. And when the government’s profits from penalties exceed the cost of strict supervision, the probability that the government enhances supervision by improving blockchain platform will increase, which will promote social organizations’ active allocation.


### 5.3. The Impact of Social Organizations’ Positive and Negative Effects on the Stability of Game Strategy

To analyse the impact of social organizations’ positive and negative effects on the strategy stability, we keep the remaining parameters unchanged, and set the values ofRn and Nn as follows: Rn=0, Nn=0; Rn=5, Nn=5; and Rn=10, Nn=10. The simulation result is shown in Figure 9.Figure 9
Evolution path under different positive and negative effects.Figure9 indicates that in the process of evolution, with the increase of the positive effect of active allocation and the negative effect of passive allocation, the probability of social organizations choosing active allocation increases. When the positive and negative effects gradually increase and exceed the threshold, social organizations change from passive allocation to active allocation, which further verifies Proposition 1. It can be seen that the positive and negative effects have a great impact on emergency supply allocation. When the government uses blockchain platform to practice supervision, the transparency of information will increase, and the flowing speed of information will be accelerated [22]; social organizations will evolve forward active allocation to maintain the reputation and decrease the negative effect.


### 5.4. The Impact of Effect’s Increasing Multiple on the Stability of Game Strategy

To analyse the impact of effect’s increasing multiple on the strategy stability, we keep the remaining parameters unchanged, and set the values ofλ as follows: λ=1.1; λ=1.5; and λ=1.9 (corresponding the application levels of blockchain platform from low to high). The simulation result is shown in Figure 10.Figure 10
Evolution path under different effect’s increasing multiples.The figure indicates that as the increasing multipleλ of positive and negative effects increases, social organizations will accelerate forward active allocation, which further verifies Proposition 1. Social organizations’ strategy will vary with the different application levels of blockchain platform. That is because when the application level of blockchain platform is lower, the blockchain platform does not practice effective supervision on social organizations, and with the application level increasing, it can decrease the information asymmetry and improve supervision efficiency.


### 5.5. The Impact of the Public’ Informing Cost on the Stability of Game Strategy

To analyse the impact of the public’ informing cost on the strategy stability, we keep the remaining parameters unchanged, and set the values ofCr as follows: Cr=0; Cr=2; and Cr=5. The simulation result is shown by Figure 11.Figure 11
Evolution path under different costs of informing.The figure indicates that in the evolutionary process, the probability of the public choosing tolerance will accelerate with the increase of the public’ informing costCr, which further verifies Proposition 3. It can be seen that the public’ informing cost is an important factor affecting the allocation management of emergency supplies. In the absence of blockchain platform, due to the existence of information islands, the public have higher cost of collecting information to conduct supervision, which reduces their enthusiasm for participating.


## 5.1. The Impact of Initial Strategy Choice on the Stability of Game Strategy

According to replication dynamic equations, it can be seen that the evolutionary stable state of a single game participant will be affected by the initial strategy choices of other subjects. Based on this premise, this paper verifies the results of strategies evolution by adjusting the initial values. When examining the sensitivity of each game participant to the initial strategy choice, the initial values of other game subjects are set as 0.5. Respectively suppose the initial state of the social organizations isx0  = 0.2, 0.5, 0.7, the initial state of the public is y0  = 0.2, 0.5, 0.7, and the initial state of the government is z0  = 0.2, 0.5, 0.7, and the other parameters keep unchanged. Then, the simulation results can be shown by Figures 5 to 7.Figure 5
The evolution result of the change of social organizations’ initial strategies.Figure 6
The evolution result of the change of public’s initial strategies.Figure 7
The evolution result of the change of government’s initial strategies.As shown in these figures, no matter what the initial strategy choice of tripartite participants is, with the probability of social organizations choosing active allocation strategies tends to 1, the public and the government will adopt the strategies of tolerance and relaxing supervision, respectively, which means that (1, 0, 0) is the evolutionary stability point.As shown in Figure5, with the increase of x, y and z will quickly converge to 0, which further verifies Propositions 4 and 6. This is because the increased awareness of social organizations in allocating emergency supplies has accelerated the process of emergencies prevention and control, and both the government and the public can obtain positive effects without paying extra costs for supervision. Therefore, the government tends to relaxing supervision and the public tends to tolerance.As shown in Figure7, with the increase of z, the speeds of x converging to 1 are accelerated, which further verifies Proposition 2. When the government practices strict supervision with the help of blockchain platform, the information of social organizations’ allocating emergency supplies will be recorded in the blockchain and be open to all of authorized participants; in this condition, the profits of passive allocation gradually cannot compensate the loss of fine by the government, the loss of social reputation, and so on, which promotes social organizations’ active allocation.From Figure5 to Figure 7, it can be seen that no matter what the initial strategy choice is, the speed of x converging to 1 is less than the speed of y and z converging to 0. It means that guiding social organizations to practice active allocation needs a long-term process. The process requires the government actively to construct blockchain platform of emergency supplies allocation and build the reward and punishment mechanism to mobilize the participating enthusiasm of social organizations.


## 5.2. The Impact of Government Penalty Intensity on the Stability of Game Strategy

To analyse the impact of government penalties on the evolutionary game, we keep the remaining parameters unchanged, and set the values ofFa as follows: Fa=0; Fa=4; and Fa=8. The simulation result is shown in Figure 8.Figure 8
Evolution path under different penalties.The figure indicates that in the evolution process, with the increment of the penalty imposed by the government on the passive allocation of social organizations, the probability of social organizations actively performing their duties increases, and at the same time the speed that the government evolves to strict supervision accelerates, which further verifies Propositions1 and 5. In the condition of strict supervision, the government will supervise social organizations at a lower cost with the help of blockchain platform. And when the government’s profits from penalties exceed the cost of strict supervision, the probability that the government enhances supervision by improving blockchain platform will increase, which will promote social organizations’ active allocation.


## 5.3. The Impact of Social Organizations’ Positive and Negative Effects on the Stability of Game Strategy

To analyse the impact of social organizations’ positive and negative effects on the strategy stability, we keep the remaining parameters unchanged, and set the values ofRn and Nn as follows: Rn=0, Nn=0; Rn=5, Nn=5; and Rn=10, Nn=10. The simulation result is shown in Figure 9.Figure 9
Evolution path under different positive and negative effects.Figure9 indicates that in the process of evolution, with the increase of the positive effect of active allocation and the negative effect of passive allocation, the probability of social organizations choosing active allocation increases. When the positive and negative effects gradually increase and exceed the threshold, social organizations change from passive allocation to active allocation, which further verifies Proposition 1. It can be seen that the positive and negative effects have a great impact on emergency supply allocation. When the government uses blockchain platform to practice supervision, the transparency of information will increase, and the flowing speed of information will be accelerated [22]; social organizations will evolve forward active allocation to maintain the reputation and decrease the negative effect.


## 5.4. The Impact of Effect’s Increasing Multiple on the Stability of Game Strategy

To analyse the impact of effect’s increasing multiple on the strategy stability, we keep the remaining parameters unchanged, and set the values ofλ as follows: λ=1.1; λ=1.5; and λ=1.9 (corresponding the application levels of blockchain platform from low to high). The simulation result is shown in Figure 10.Figure 10
Evolution path under different effect’s increasing multiples.The figure indicates that as the increasing multipleλ of positive and negative effects increases, social organizations will accelerate forward active allocation, which further verifies Proposition 1. Social organizations’ strategy will vary with the different application levels of blockchain platform. That is because when the application level of blockchain platform is lower, the blockchain platform does not practice effective supervision on social organizations, and with the application level increasing, it can decrease the information asymmetry and improve supervision efficiency.


## 5.5. The Impact of the Public’ Informing Cost on the Stability of Game Strategy

To analyse the impact of the public’ informing cost on the strategy stability, we keep the remaining parameters unchanged, and set the values ofCr as follows: Cr=0; Cr=2; and Cr=5. The simulation result is shown by Figure 11.Figure 11
Evolution path under different costs of informing.The figure indicates that in the evolutionary process, the probability of the public choosing tolerance will accelerate with the increase of the public’ informing costCr, which further verifies Proposition 3. It can be seen that the public’ informing cost is an important factor affecting the allocation management of emergency supplies. In the absence of blockchain platform, due to the existence of information islands, the public have higher cost of collecting information to conduct supervision, which reduces their enthusiasm for participating.


## 6. Results and Discussion

The paper concentrates the problems of emergency supply allocation and builds a tripartite evolutionary game model among the government, social organizations, and the public to analyse the impact of blockchain platform on emergency supply allocation. The results show that the initial strategy choices, penalty intensity, positive and negative effects, effect’s increasing multiple, and public’ informing cost have different influences on the governance of emergency supply allocation.(1)
From the perspective of initial strategy choices, the strategy choices of the government have a great impact on the evolution and stability of social organizations. It needs a long term to guide social organizations to actively take part in the emergency supply allocation, and the government should speed up the construction of blockchain platform to promote this process (different from [25, 26]).(2)
With the help of blockchain platform, increasing penalty intensity for social organizations’ passive allocation will increase the probabilities that social organizations’ active allocation and the government’s strict supervision.(3)
The blockchain platform has a significant impact on social organizations’ positive and negative effects, effect’s increasing multiple, and public’ informing cost, and improving the blockchain platform is of great significance to improve the robustness of social organizations’ active allocation.Based on the above research conclusions, we construct an emergency supply allocation governance system based on blockchain, which includes coordination mechanism, trust mechanism, supervision mechanism, and incentive mechanism, as shown in Figure12.(1)
Coordination Mechanism. Based on the distributed consensus technology of blockchain, all nodes can participate in governance equally. After social organizations and the public join blockchain, the information of supply allocation will be shared among multiple subjects, which will increase the positive and negative effects and effectively promote the collaboration among subjects.(2)
Trust Mechanism. The traceability mechanism and tamper-proofing mechanism of blockchain technology can ensure the authenticity of information, facilitate the public’s evidence collection and rights protection, and realize penetrating supervision in the whole process. In addition, asymmetric encryption technology will ensure the security of information. These all reduce the public’s informing cost and the government’s supervision cost.(3)
Supervision Mechanism. Through the smart contract mechanism, the rights and responsibilities of participants are clearly defined in the form of codes. Once the trigger conditions are satisfied, the smart contract will be enforced, which will improve the self-discipline consciousness of each node. At the same time, intelligent matching of supply and demand information of supplies can be realized through smart contract technology, which avoids human interference and improves the accuracy and efficiency of emergency supply allocation.(4)
Incentive Mechanism. The foothold of promoting sustainable emergency management lies in incentive mechanism. By issuing tokens using blockchain and using tokens as rewards, the system will arouse the enthusiasm of multiple subjects [22].Figure 12
Emergency supply allocation governance system based on blockchain.Based on the above conclusions and mechanism design, this paper puts forward the following suggestions to promote the process of emergency supply allocation governance.(1)
In the emergency supply allocation, social organizations hardly can practice active allocation consciously. And in order to guide social organizations allocating supplies actively, the government should speed up the construction of information communication platform based on blockchain, practice real-time supervision based on coordination mechanism, trust mechanism, supervision mechanism and incentive mechanism, and provide according supports in terms of policies, regulations, talents, and funds [4].(2)
The government should set reward and penalty mechanism through smart contracts to increase the punishment for illegal activities of social organizations seeking extra income and increase incentives for the public who informs in compliance and social organizations that practice active allocation, so as to improve the efficiency of government supervision.(3)
In emergency supply allocation, even if there is a blockchain platform, social organizations may still allocate emergency supplies passively. Therefore, the public should be guided to actively supervise the allocation of emergency supplies and timely feedback the problems of social organizations, which is conductive to safeguard their own legitimate rights and interests [22].Emergency supply allocation has a great significant on dealing with emergent events and ensuring the people’s wellbeing, and the government should take full advantage of blockchain technology to build a co-governance system to guide all parts taking part in the emergency supply allocation management actively. This paper combines the evolutionary game theory and simulation method to analyse the participants strategies in emergency supply allocation; it is a new try and will enrich the co-governance theory on the realm of emergency management.



---

*Source: 7309945-2022-04-18.xml*