Research on Value Co-Creation Strategies for Stakeholders of Takeaway Platforms Based on Tripartite Evolutionary Game

Abstract

As the digitization of the supply side continues to advance, the takeaway industry has made a significant contribution to economic growth. However, the rapid expansion of the scale has also brought many social problems, merchants provide low-quality goods out of the psychology of opportunity, and the uneven quality of goods and asymmetric information not only bring great regulatory problems for the takeaway platform, but also make it difficult for consumers to identify the platform, merchants, and consumers as takeaway platform stakeholders, it is difficult to integrate resources to achieve value co-creation. Therefore, in order to realize the value co-creation among the stakeholders of the takeaway platform, a three-party evolutionary game model was constructed to analyze and simulate the strategic choices of stakeholders under different situations through simulation experiments and to explore the sensitive influence of each factor. The results of the study show the following: shaping a scientific reward and punishment system and setting reasonable rewards and punishments within a limited threshold; platforms, consumers using word-of-mouth effects to amplify the loss of network externalities that merchants have to bear when they provide low-quality services, and improving the consumer feedback mechanism to reduce the cost of feedback are all effective measures to promote the active participation of takeaway platform stakeholders in value co-creation and promote the sustainable and healthy development of the takeaway industry.

1. Introduction

The convenience of takeaway has enabled it to ride on the growth of the “home economy” against the odds [1], achieving rapid growth in market scale and a rapid increase in stakeholder numbers [2]. According to iiMedia Data, by December $2022$, the takeaway market has grown at a rate of $19.8\%$, with $521$ million users, accounting for $48.8\%$ of the country’s total Internet users, making takeaway an integral part of people’s daily lives. Although the market is growing in size, the corresponding regulatory approach has not kept pace [3], with problems ranging from takeaway shops shamming doors to zombie cooking kits. According to a survey conducted by the Shanghai Quality Association, $78.8\%$ of consumers are most concerned about food safety when buying takeaways, so frequent food safety problems will reduce consumer trust and need to be effectively regulated.

The “Provisions of the Supreme People’s Court on Several Issues Concerning the Application of Law in Hearing Cases of Online Consumer Disputes (I)”, which came into force on $15$ March $2022$, proposes to strengthen the awareness of rights and responsibilities of takeaway platforms and merchants, protect the rights and interests of consumers, rectify the chaos of takeaway services, and eliminate food safety hazards. However, the low barrier to entry and the serious information asymmetry that exists in the regulatory and consumer processes have led merchants to cut corners and use substandard goods for noncompliant services out of opportunism, and some compliant merchants imitate them out of a follow-the-leader mentality. According to statistics from the Black Cat platform, the number of complaints against the takeaway industry reached $40,000$ in May $2023$, an increase of $16.48\%$ compared to the previous year, with jerry-built, spoiled meals and mixed foreign substances occurring frequently. Such shortsighted behavior has greatly reduced consumer trust, damaged the reputation of the platform, caused poor-quality service providers to drive out quality service providers in the takeaway market, and hindered the sustainable development of the takeaway industry.

Therefore, this paper analyzes the factors affecting stakeholders’ strategic choices by means of an evolutionary game and uses the platform to reward the best and punish the worst to motivate merchants to provide compliant products and improve service quality. On the one hand, the platform uses the adoption of appropriate incentives and penalties to encourage merchants to provide compliant products and improve service quality. On the other hand, it motivates consumers to give positive feedback, provides references for other consumers, gives full play to the consumer word-of-mouth effect, and enables consumers and takeaway platforms to collaborate to regulate merchants’ illegal behaviors, realizing the value co-creation of stakeholders. It is of practical significance to promote the sustainable and healthy development of the takeaway industry.

2. Literature Review

2.1. Takeaway Platform Stakeholders

The stakeholders of the takeaway platform include the platform, merchants, deliverers, and consumers. Consumers order goods on the online platform, merchants provide products and services, and then the platform assigns deliverers to complete the corresponding delivery tasks [4], and the quality of task completion and consumers’ perceived value will significantly affect the development of the takeaway platform [5].

The takeaway platform is regarded as an O2O application model for the food industry [6], bringing more choices and providing more convenient services [7]. Kang, J.W. [8] constructed a scale to measure service quality from the perspective of service quality of the takeaway platform in seven dimensions, including information quality, delivery quality, and problem solving. At the level of research on the service quality of goods provided by merchants, Shi, C. [9] combined big data analysis with rooting theory to deeply analyze negative consumer reviews on the Meituan platform and obtained that merchant service quality has a significant impact on consumers’ user experience. Zhang, L. [10] introduced blockchain smart contracts to the phenomenon of inflated ratings of takeaway merchants, many false reviews, and low consumer satisfaction to takeaway platform to motivate merchants to transact with integrity. In terms of the quality of delivery services provided by delivery personnel, Guo, J. [11] adds social responsibility to the platform’s objective function and uses it as a basis to reconstruct the revenue distribution contract between the platform and delivery personnel, so as to improve delivery violations by delivery personnel and enhance service quality. The role of consumers as stakeholders in the regulation of takeaway service quality has become increasingly important [12], and Liang, D. [13] suggests that consumers express their evaluation and satisfaction with takeaway services through online reviews, and that consumer satisfaction can guide takeaway platforms and merchants to improve their products and services.

2.2. Stakeholder Value Co-Creation

Stakeholder value co-creation is the act of sharing information, interacting and taking responsibility between subjects with an interest in a platform that acts as a mediator between the merchant providing the service and the consumer receiving it [14].

In terms of influencing factors, Cheng, H. [15] suggests that economic, psychological and social motivations work together to influence stakeholders’ willingness to engage in value co-creation. García-Magro, C. [16] puts consumer emotions at the heart of the value co-creation research paradigm, revealing the positive influence of emotional mechanisms on the elements of value co-creation. Ebrahimi, P. [17] adopted the ISM to further extract the variables influencing consumer purchase behavior obtained by the Delphi method and found that factors such as consumer value perception and consumer engagement were positively associated with consumers’ willingness to co-create value in social e-commerce platforms.

Chen, L. [18] believes that modeling through games can optimize platform services to a great extent, and evolutionary game, as an important branch of game theory, represents a dynamic equilibrium achieved by finite rational participants in the process of continuous game [19], which can reflect the evolutionary stable strategies of the system under different influencing factors [20] and provide a basis for the choice of stakeholders’ value co-creation strategies [21,22,23,24]. Zou, X. [25] constructed an evolutionary game model for value co-creation based on the perspective of platform network effects, considering the different perceived interests of supply chain platforms and manufacturers, and sought boundary conditions for both parties to actively participate in value co-creation. Guo, H. [26] further constructed a three-party evolutionary game model for regulating counterfeit goods on e-commerce platforms and obtains that platform regulation and consumer evaluation can effectively promote merchants’ choice of value co-creation strategies. He, H. [27] introduced a consumer feedback mechanism with regulators, sellers and e-commerce platforms as stakeholders and obtained that consumer complaints play an indirect regulatory role for sellers and strengthen the loss-sharing relationship between sellers and platforms, which can effectively promote collaborative co-creation of value. Fan, J. [28] studied stakeholder behavioral choices involving traffic safety value co-creation in the takeaway industry, identified relevant influencing factors such as penalties for noncompliance, opportunity costs of compliance and cost–benefit incentives, and proposed that platforms should set up appropriate reward and punishment mechanisms to create a safe delivery environment. Zhang, Y. [29] constructed a tripartite evolutionary game model of the takeaway platform, merchants and delivery workers, showing that rectification costs and incentive coefficients will influence the choice of stakeholder value co-creation strategies, providing a reference for safety management in the delivery process of takeaway food. Information on the application of evolutionary games to platform stakeholder value co-creation is summarized in

Table 1. Overview of the application of evolutionary games in platform stakeholder value co-creation.

Authors	Research Issue	Research Methodology	Research Result
Zou, X. et.al. [25]	Value co-creation between the platform and suppliers in actively engaging in shared issues.	Two-sided evolutionary game model	From the perspective of platform network effect, we explore the boundary conditions for platforms and suppliers to actively participate in value co-creation, and we argue that the costs and benefits under the network effect will significantly affect their value co-creation behaviors.
Guo, H. et.al. [26]	Co-creation of the value of e-commerce platform stakeholders in remediating the problem of counterfeit and substandard products.	Tripartite evolutionary game model	Exploring the influence of platform regulation and consumer returns on merchants’ counterfeiting strategies, it is argued that platform regulation and consumer returns to protect their own rights and interests will effectively inhibit merchants’ counterfeiting behaviors.
He, H. et.al. [27]	Value co-creation of e-commerce platform stakeholders in safeguarding merchant service quality issues.	Tripartite evolutionary game model	Taking government regulators, sellers and platforms as the three parties involved in e-commerce platforms, it is believed that consumer complaints will indirectly regulate merchants, and that appropriate rewards and punishments can promote the active creation of value by the participating parties.
Fan, J. et.al. [28]	Value co-creation among takeaway platform stakeholders in delivery safety issues.	Two-sided evolutionary game model	Taking the stakeholder takeout platform and couriers as the participating subjects and the local government’s control initiatives as the external variables, it analyzes the interaction behaviors of the platform and the deliverers in different situations, and puts forward targeted suggestions for improving delivery safety based on the simulation results.
Zhang, Y. et.al. [29]	Value co-creation among takeaway platform stakeholders in delivery safety issues.	Tripartite evolutionary game model	Taking the stakeholder takeaway platform, merchants and couriers as the participant subjects, the numerical simulation experiment simulates the evolution paths under different strategy choices of the participants, and proposes that controlling the coefficient of expenditure ratio and strengthening publicity and education can effectively improve the hygiene problem of takeaway delivery.

below.

Through combing the abovementioned scholars’ studies, we found that most of the existing studies on the stakeholders of takeaway platforms have been analyzed from the perspective of a single participant, and there is a lack of in-depth research on the interactive behavior of the stakeholders. In the study of stakeholder value co-creation, on the one hand, the existing tripartite evolutionary game mostly takes the regulator, the platform and the merchant as the game subjects and lacks consideration of the participation behavior of consumers who actually enjoy the goods and services. On the other hand, there are few studies on value co-creation among stakeholders of takeaway platforms, and most of them study the quality of delivery services, without analyzing the impact of the quality of products and services provided by merchants on value co-creation.

Therefore, this paper takes platforms, merchants, and consumers as stakeholders, further opens the black box of consumer participation, and combines the tripartite evolutionary game to study in depth the interaction behaviors and strategy choices among the stakeholders of takeaway platforms in different contexts, and explore how to promote active participation of stakeholders, and then improve the quality of products and services in takeaway platforms. Numerical simulations are conducted through simulation experiments to verify the validity of the conclusions drawn from the reasoning, as well as to reflect more intuitively the impact of the sensitivity of different factors. The results are also used to suggest countermeasures to promote value co-creation among takeaway platform stakeholders’ choices. The research process is shown in Figure 1 below:

3. Basic Assumptions and Model Construction

3.1. Description of the Problem

The takeaway platform acts as an intermediary bridge between the supply side (merchants) and the demand side (consumers) of the product service, and takes a certain commission to make a profit, and the interests of the three parties are closely related to each other [30]. If the platform actively regulates and fulfils its social responsibility, merchants provide quality services, consumers provide positive feedback, and the three stakeholders effectively use their own resources to achieve value co-creation, it can improve the platform’s reputation and cascade to expand the network externalities of merchants, maximize the protection of consumers’ legitimate rights and interests, create a good market environment, and promote the sustainable and healthy development of the takeaway industry. The game relationship between the three stakeholders of the takeaway platform is shown in Figure 2 below:

3.2. Basic Assumptions

In order to fully analyze the value co-creation strategy choices of the takeaway platform stakeholders, the three parties of limited rational platform, merchant, and consumer stakeholders are taken as the subjects involved in the evolutionary game. Based on the purpose of solving the benefits under different strategy choices and the influence of different decision variables on each stakeholder’s strategy choice, the following hypotheses are made:

Hypothesis 1.

The choice of value co-creation strategies for takeaway platforms is $X_{TP}=(x,1-x)$ $=$ (active regulation, passive regulation). Merchants’ value co-creation strategy choice space is $Y_M=(y,1-y)$ $=$ (provide quality service, provide low-quality service). Consumers’ value co-creation strategy choice space is $Z_C=(z,1-z)$ $=$ (positive feedback, negative feedback).

Hypothesis 2.

The takeaway platform’s percentage of sales draw on the resident merchants is $\gamma$ [31]. If the platform chooses to actively regulate the strategy, it will create the value of standardized management, continued healthy development of the industry, and create a good market environment, at which time the cost of regulation is $C_{P1}$. If the platform actively regulates and consumers provide feedback, the platform will receive a reputation boost $R_P$ and will reward consumers for their positive feedback $S$. When there is no feedback from consumers and the platform only actively regulates, the probability of finding a merchant providing low-quality services is $\beta$. If a merchant is found to be providing low-quality services, it will be required to compensate consumers for their losses $D$ and be fined $F$ as a penalty for disrupting the market environment. When a platform colludes with a merchant to passively regulate its low-quality behavior, it will bear the cost of network externalities resulting from a poor market environment $L_{P1}$; if consumers provide positive feedback at this point, it will result in additional network externalities resulting from a decline in the platform’s reputation and the horse-trading effect $\Delta L_P$.

Hypothesis 3.

The merchant’s revenue from sales on the takeaway platform is $R_M$. When a merchant provides a low-quality service, the cost is $C_M$. If a merchant provides a high-quality service, the additional cost of human and material resources required to use fresh, clean raw materials is $\Delta C$. If a merchant is found to be providing a low-quality service, they will suffer from the network externalities $L_M$ of reduced weighting on the takeaway platform and reduced consumer trust.

Hypothesis 4.

The cost of time and effort required for positive consumer feedback is $C_C$. If the business provides quality service, the consumer receives a product and service that meets or exceeds expectations, and the benefit is $R_C$. If the business provides low-quality service, not only does the consumer receive a product and service that is lower than expected, but also the consumer’s life and health may be jeopardized because of the excessive pursuit of profit, neglect of food safety, and reduced raw material and labor costs. The loss is recorded as $L_C$. Referring to the consumers’ sensitivity to logistics services set by Chen, L. [32], the consumer’s sensitivity to the quality of the product and service provided by the merchant is $\alpha$, the probability of finding out that the merchant is providing a low-quality service.

3.3. Model Construction

Based on the above assumptions, the payoff matrix of the tripartite evolutionary game model is constructed as shown in

Table 2. Matrix of payoffs for the three-party evolutionary game.

Takeaway Platforms	Merchants	Consumers
		Positive Feedback z	Negative Feedback 1 − z
Active regulation x	Providing quality services y	$\gamma R_M-C_{p1}+R_P-S$	$\gamma R_M-C_{p1}$
		$(1-\gamma )R_M-C_M-\Delta C$	$(1-\gamma )R_M-C_M-\Delta C$
		$R_C-C_C+S$	$R_C$
	Providing low-quality services 1 − y	$\gamma R_M-C_{p1}+R_P-S+F$	$\gamma R_M-C_{p1}+\beta \mathrm{F}$
		$(1-\gamma )R_M-C_M-F-D-L_M$	$(1-\gamma )R_M-C_M-\beta (F+D+L_M)$
		$D-C_C+S-L_C$	$\beta D-L_C$
Negative regulation 1 − x	Providing quality services y	$\gamma R_M$	$\gamma R_M$
		$(1-\gamma )R_M-C_M-\Delta C$	$(1-\gamma )R_M-C_M-\Delta C$
		$R_C-C_C$	$R_C$
	Providing low-quality services 1 − y	$\gamma R_M-L_{P1}-\Delta L_P$	$\gamma R_M-L_{P1}$
		$(1-\gamma )R_M-C_M-\alpha L_M$	$(1-\gamma )R_M-C_M$
		$-L_C-C_C$	$-L_C$

:

Based on the above payoff matrix, the expected payoff and replication dynamics equations for the three stakeholders under different strategy choices can be derived as follows:

The expected return when the takeaway platform is actively regulated $U_{TP1}$, the expected return when it is negatively regulated $U_{TP2}$, and the average expected return $\overline{U_{TP}}$ are shown in the following equations, respectively:

$$\begin{array}{c}{U}_{TP1}=yz(\gamma R_M-C_{P1}+R_P-S)+y(1-z)(\gamma R_M-C_{P1})\\ +(1-y)z(\gamma R_M-C_{P1}+R_P-S+F)+(1-y)(1-z)(\gamma R_M-C_{P1}+\beta F)\end{array}$$

(1)

$$\begin{array}{c}{U}_{TP2}=yz(\gamma R_M)+y(1-z)(\gamma R_M)\\ +(1-y)z(\gamma R_M-L_{P1}-\Delta L_P)+(1-y)(1-z)(\gamma R_M-L_{P1})\end{array}$$

(2)

$$\overline{U_{TP}}=x{U}_{TP1}+(1-x)U_{TP2}$$

(3)

The replication dynamic equation for the takeaway platform can be found as:

$$\begin{array}{c}F(x)=\frac{dx}{dt}=x(U_{TP1}-\overline{U_{TP}})\\ =x(1-x)\left\{\mathrm{y}\right[z(-(1-\beta )F-\Delta L_P)-\beta F-L_{P1})]\\ +z(R_P-S+(1-\beta )F+\Delta L_P)+\beta F+L_{P1}-C_{P1}\}\end{array}$$

(4)

The expected return $U_{M1}$ when a merchant provides a high-quality service, the expected return $U_{M2}$ when a low-quality service is provided, and the average expected return $\overline{U_M}$ are shown in the following equations, respectively:

$$\begin{array}{c}{U}_{M1}=xz((1-\gamma )R_M-C_M-\Delta C)+\mathrm{x}(1-z)((1-\gamma )R_M-C_M-\Delta C)\\ +(1-x)z((1-\gamma )R_M-C_M-\Delta C)+(1-x)(1-z)((1-\gamma )R_M-C_M-\Delta C)\end{array}$$

(5)

$$\begin{array}{c}{U}_{M2}=xz((1-\gamma )R_M-C_M-F-D-L_M)+(1-x)z((1-\gamma )R_M-C_M-\alpha L_M)\\ +\mathrm{x}(1-z)((1-\gamma )R_M-C_M-\beta (F+D+L_M))+(1-x)(1-z)((1-\gamma )R_M-C_M)\end{array}$$

(6)

$$\overline{U_M}=y{U}_{M1}+(1-y)U_{M2}$$

(7)

The replication dynamic equation for the merchant can be found as:

$$\begin{array}{c}F(y)=\frac{dy}{dt}=y(U_{M1}-\overline{U_M})\\ =y(1-y)\left\{x\left[z((1-\beta )(F+D)+(1-\alpha -\beta )L_M)+\beta (F+D+L_M)\right]+\mathrm{z}\alpha L_M-\Delta C\right\}\end{array}$$

(8)

The expected benefit when consumers give positive feedback $U_{C1}$, the expected benefit when they give negative feedback $U_{C2}$, and the average expected benefit $\overline{U_C}$ are shown in the following equations, respectively:

$$\begin{array}{c}{U}_{C1}=xy(R_C-C_C+S)+x(1-y)(D-C_C+S-L_C)\\ +(1-x)y(R_C-C_C)+(1-x)(1-y)(-C_C-L_C)\end{array}$$

(9)

$$U_{C2}=xy{R}_C+x(1-y)(-L_C)+(1-x)y{R}_C+(1-x)(1-y)(-L_C)$$

(10)

$$\overline{U_C}=z{U}_{C1}+(1-z)U_{C2}$$

(11)

The replication dynamic equation for the consumer can be found as:

$$\begin{array}{c}F(z)=\frac{dz}{dt}=z(U_{C1}-\overline{U_C})\\ =z(1-z)\left\{x\left[-y(1-\beta )D+(1-\beta )D+S\right]-C_C\right\}\end{array}$$

(12)

4. Analysis of the Evolutionary Stabilization Strategy of Value Co-Creation among the Three Stakeholders of a Takeaway Platform

The stability theorem of the differential equation shows that if $\frac{dF(x)}{dx}<0$, $\frac{dF(y)}{dy}<0$, $\frac{dF(z)}{dz}<0$, which is the evolutionary stability strategy of the three parties involved in the takeaway platform, is analyzed as follows:

4.1. Analysis of the Takeaway Platforms’ Evolutionary Stabilization Strategy

A first-order derivative of the replication dynamic equation for the takeaway platforms obtains:

$$\begin{array}{c}\frac{dF(x)}{dx}=(1-2x)\{y[z(-(1-\beta )F-\Delta L_P)-\beta F-L_{P1})]\\ +z(R_P-S+(1-\beta )F+\Delta L_P)+\beta F+L_{P1}-C_{P1}\}\end{array}$$

(13)

Noting the threshold ${\mathsf{\Omega }}_1=\frac{y(\beta F+L_{P1})-C_{P1}+\beta F+L_{P1}}{-y((1-\beta )F+\Delta L_P)+R_P-S+(1-\beta )F+\Delta L_P}$, and $0<{\mathsf{\Omega }}_1<1$, when $z={\mathsf{\Omega }}_1$, $\frac{dF(x)}{dx}\equiv 0$, then the takeaway platform will be in a constant stable strategy regardless of how its initial probability changes. When the reward $S$ given by the platform to consumers for positive feedback is less than the reputation $R_P$ gained, if $0<z<{\mathsf{\Omega }}_1$, then $x=1$, then the platform as a stakeholder will actively create regulatory value. If ${\mathsf{\Omega }}_1<z<1$, then $x=0$, then the takeaway platform chooses a negative regulatory strategy, which may lead to merchants waiting for an opportunity to engage in shortsighted behavior of cutting corners.

In summary, the response function for the probability $x$ of the takeaway platform creating regulatory value as a stakeholder is:

$$x=\left\{\begin{array}{cc}0& \mathrm{if} {\mathsf{\Omega }}_1<\mathrm{z}<1\hfill \\ (0,1)& \mathrm{if} \mathrm{z}={\mathsf{\Omega }}_1\hfill \\ 1& \mathrm{if} 0<\mathrm{z}<{\mathsf{\Omega }}_1\hfill \end{array}\right.$$

(14)

The phase diagram of the evolution of the strategy space for the takeaway platform is shown in Figure 3.

4.2. Analysis of the Merchants’ Evolutionary Stabilization Strategy

A first-order derivative of the replication dynamic equation for the merchants obtains:

$$\begin{array}{c}\frac{dF(y)}{dy}=(1-2y)\{x[z((1-\beta )(F+D)+(1-\alpha -\beta )L_M)\\ +\beta (F+D+L_M)]+\mathrm{z}\alpha L_M-\Delta C\}\end{array}$$

(15)

Noting the threshold ${\mathsf{\Omega }}_2=\frac{\Delta C-z\alpha L_M}{z((1-\beta )(F+D)+(1-\alpha -\beta )L_M)+\beta (F+D+L_M)}$, and $0<{\mathsf{\Omega }}_2<1$, when $x={\mathsf{\Omega }}_2$, $\frac{dF(y)}{dy}\equiv 0$, then no matter how the initial probability of the merchants changes, it will be constant in a stable strategy. If $0<x<{\mathsf{\Omega }}_2$, then $y=1$, when the merchants as a stakeholder will actively create quality products and services value. If ${\mathsf{\Omega }}_2<x<1$, then $y=0$, that is, the merchants choose to provide a low-quality service strategy, which is detrimental to the image of the platform and endangers the rights and interests of consumers.

In summary, the response function for the probability $y$ of a merchant creating the value for a quality product service as a stakeholder is:

$$y=\left\{\begin{array}{cc}0& \mathrm{if} {\mathsf{\Omega }}_2<\mathrm{x}<1\hfill \\ (0,1)& \mathrm{if} \mathrm{x}={\mathsf{\Omega }}_2\hfill \\ 1& \mathrm{if} 0<\mathrm{x}<{\mathsf{\Omega }}_2\hfill \end{array}\right.$$

(16)

The phase diagram of the evolution of the strategy space for the merchant is shown in Figure 4.

4.3. Analysis of the Consumers’ Evolutionary Stabilization Strategy

A first-order derivative of the replication dynamic equation for the consumers obtains:

$$\frac{dF(z)}{dz}=(1-2z)\left\{x\left[-y(1-\beta )D+(1-\beta )D+S\right]-C_C\right\}$$

(17)

Noting the threshold ${\mathsf{\Omega }}_3=\frac{C_C}{-y(1-\beta )D+(1-\beta )D+S}$,and, when $x={\mathsf{\Omega }}_2$, $\frac{dF(y)}{dy}\equiv 0$, then no matter how the initial probability of $0<{\mathsf{\Omega }}_2<1$ the consumers changes, it will be constant in a stable strategy. If $0<x<{\mathsf{\Omega }}_3$, then $z=1$; at this time the consumer as a stakeholder will actively create word-of-mouth, collaborative regulatory value. If ${\mathsf{\Omega }}_3<x<1$, then $z=0$, that is, consumers choose a negative feedback strategy, when the platform regulation is more difficult, not conducive to the sustainable development of the takeaway industry.

In summary, the response function for the probability $z$ of consumers actively creating word-of-mouth and coregulatory value as stakeholders is:

$$z=\left\{\begin{array}{cc}0& \mathrm{if} {\mathsf{\Omega }}_3<\mathrm{x}<1\hfill \\ (0,1)& \mathrm{if} \mathrm{x}={\mathsf{\Omega }}_3\hfill \\ 1& \mathrm{if} 0<\mathrm{x}<{\mathsf{\Omega }}_3\hfill \end{array}\right.$$

(18)

The phase diagram of the evolution of the strategy space for the consumer is shown in Figure 5.

4.4. Stability Analysis of a Three-Stakeholder Evolutionary Game System

Equations $(4)$,$(8)$ and $(12)$ constitute the evolutionary game system of the three stakeholders, take $F(x)=F(y)=F(z)=0$, and the strategy choice space of the three stakeholders are located in the interval $[0,1]$. At this time, the equilibrium strategy in the system is $E_1(0,0,0)$, $E_2(0,1,0)$, $E_3(0,0,1)$, $E_4(0,1,1)$, $E_5(1,0,0)$, $E_6(1,1,0)$, $E_7(1,0,1)$, $E_8(1,1,1)$, and $E_9({\mathsf{\Omega }}_1,{\mathsf{\Omega }}_2,{\mathsf{\Omega }}_3)$.

Separate partial derivatives of $x$, $y$, $z$ for the replicated dynamic system of equations give the following Jacobian matrix:

$$J=\left[\begin{array}{ccc}\frac{\partial F(x)}{\partial x}& \frac{\partial F(x)}{\partial y}& \frac{\partial F(x)}{\partial z}\\ \frac{\partial F(y)}{\partial x}& \frac{\partial F(y)}{\partial y}& \frac{\partial F(y)}{\partial z}\\ \frac{\partial F(z)}{\partial x}& \frac{\partial F(z)}{\partial y}& \frac{\partial F(z)}{\partial z}\end{array}\right]$$

(19)

Of these:

$$\begin{array}{c}\frac{\partial F(x)}{\partial x}=(1-2x)\left\{\mathrm{y}\right[z(-(1-\beta )F-\Delta L_P)-\beta F-L_{P1})]+z(R_P-S+(1-\beta )F\\ +\Delta L_P)+\beta F+L_{P1}-C_{P1}\};\\ \frac{\partial F(x)}{\partial y}=x(1-x)[z(-(1-\beta )F-\Delta L_P)-\beta F-L_{P1})];\\ \frac{\partial F(x)}{\partial z}=x(1-x)\{y(-(1-\beta )F-\Delta L_P)+R_P-S+(1-\beta )F+\Delta L_P\};\\ \frac{\partial F(y)}{\partial x}=y(1-y)\{z[(1-\beta )(F+D)+(1-\alpha -\beta )L_M]+\beta (F+D+L_M)\};\\ \frac{\partial F(y)}{\partial y}=(1-2y)\{x[z((1-\beta )(F+D)+(1-\alpha -\beta )L_M)+\beta (F+D+L_M)]+\mathrm{z}\alpha L_M-\Delta C\};\\ \frac{\partial F(y)}{\partial z}=y(1-y)\{x[(1-\beta )(F+D)+(1-\alpha -\beta )L_M]+\alpha L_M\};\\ \frac{\partial F(z)}{\partial x}=z(1-z)[-y(1-\beta )D+(1-\beta )D+S];\\ \frac{\partial F(z)}{\partial y}=z(1-z)[-x(1-\beta )D];\\ \frac{\partial F(z)}{\partial z}=(1-2z)\left\{x\left[-y(1-\beta )D+(1-\beta )D+S\right]-C_C\right\};\end{array}$$

When the takeaway platform, merchants, and consumers make positive choices, the probability of achieving value co-creation is ${\mathsf{\Omega }}_1$, ${\mathsf{\Omega }}_2$, and ${\mathsf{\Omega }}_3$ respectively, namely, $E_9$ is the mixed strategy equilibrium point. In contrast, subjects in asymmetric evolutionary games are in a strict Nash equilibrium, which is the pure strategy equilibrium, when their strategy choice combinations are asymptotically stable [33], so only the stability of the $E_1-E_8$ pure strategy asymptotic equilibrium point is considered. According to the Lyapunov first discriminant rule, the system evolves to an asymptotically stable state when the equilibrium point corresponding to $\lambda <0$ in the Jacobian matrix is stable. When the corresponding equilibrium points of $\lambda$ are greater than $0$, the system cannot reach a stable state, and it is an unstable point; if the corresponding equilibrium points of $\lambda >0$ and $\lambda <0$ exist at the same time, it is a saddle point. The resulting eigenvalues for each equilibrium point are shown in

Table 3. Eigenvalues corresponding to each equilibrium.

Equalization Points	${\lambda }_1$	${\lambda }_2$	${\lambda }_3$
$E_1(0,0,0)$	$L_{P1}-C_{P1}+\beta F$	$-\Delta C$	$-C_C$
$E_2(0,1,0)$	$-C_{P1}$	$\Delta C$	$-C_C$
$E_3(0,0,1)$	$F-C_{P1}+L_{P1}+\Delta L_P+R_P-S$	$\alpha L_M-\Delta C$	$C_C$
$E_4(0,1,1)$	$R_P-C_{P1}-S$	$\Delta C-\alpha L_M$	$C_C$
$E_5(1,0,0)$	$C_{P1}-L_{P1}-\beta F$	$\beta D-\Delta C+\beta F+\beta L_M$	$D-C_C+S-\beta D$
$E_6(1,1,0)$	$C_{P1}$	$\Delta C-\beta D-\beta F-\beta L_M$	$S-C_C$
$E_7(1,0,1)$	$C_{P1}-F-\Delta L_P-L_{P1}-R_P+S$	$D-\Delta C+F+L_M$	$C_C-D-S+\beta D$
$E_8(1,1,1)$	$C_{P1}-R_P+S$	$\Delta C-L_M-D-F$	$C_C-S$

below:

Of these, $E_2$, $E_3$, $E_4$, and $E_6$ all have a positive value of $\lambda$, which is an unstable point. The stability scenarios for the remaining equilibrium points are analyzed as follows:

Scenario 1.

When $\beta F-C_{P1}<-L_{P1}$, $E_1(0,0,0)$ is the asymptotic stability point of the evolutionary game system. At this point, the difference between the effective regulatory benefit of the takeaway platform and the cost of positive regulation is smaller than the loss in negative regulation, the platform does not have enough incentive to actively regulate, merchants choose to provide low-quality goods profitably, consumers can hardly afford the cost of sole regulation and choose negative feedback, and all three parties do not engage in value co-creation;

Scenario 2.

When $\beta F-C_{P1}>-L_{P1}$, $\beta D+\beta F+\beta L_M<\Delta C$, and $D-C_C+S<\beta D$, $E_5(1,0,0)$ is the asymptotic stability point of the evolutionary game system. At this point for the takeaway platform, contrary to Scenario $1$, the takeaway platform has sufficient regulatory incentive to actively regulate the platform. However, the cost of providing quality services is greater than the loss of low-quality services when only the platform regulates, and the gain from positive feedback from consumers is less than the compensation from merchants who take advantage of the platform’s regulation when negative feedback is given. Therefore, only the platform itself actively creates regulatory value; merchants and consumers do not collaborate with the platform for value co-creation;

Scenario 3.

When $\beta F-C_{P1}>-L_{P1}$, $-\Delta L_P-L_{P1}<R_P-S-C_{P1}+F$, $\Delta C>L_M+D+F$, and $D-C_C+S>\beta D$, $E_7(1,0,1)$ is the asymptotic stability point of the evolutionary game system. At this point, the network externality loss suffered by the negative regulation of the takeaway platform is less than the difference between the reputation, the gain in fines and the cost of regulation, and the bonus to active consumers in case of positive regulation. The penalties and network externality losses when merchants provide low-quality service do not offset the additional costs of quality service. The benefits of positive consumer feedback can cover the compensation of merchants who ride on the coattails of platform regulation. Thus, the platform actively collaborates with consumers for value co-creation, while merchants take shortsighted actions of low-quality services;

Scenario 4.

When $\beta F-C_{P1}>-L_{P1}$, $C_{P1}+S<R_P$, $\Delta C<L_M+D+F$, and $C_C<S$, $E_8(1,1,1)$ is the asymptotic stability point of the evolutionary game system. At this point, the reputation gain from active regulation of the takeaway platform can cover the cost of regulation and the bonus given to consumers. The additional cost to the merchant of providing quality service is less than the penalty and network externality loss for providing low-quality service. The cost of positive feedback from consumers is offset by the bonuses given by the platform. Thus, the platform, merchants, and consumers all actively use their resources to create a good environment for takeaway development and achieve value co-creation;

Scenario 5.

When $C_{P1}-\beta F>L_{P1}$, $C_{P1}+S<R_P$, $\Delta C<L_M+D+F$, and $C_C<S$, $E_1(0,0,0)$ and $E_8(1,1,1)$ are the asymptotic stability points of the evolutionary game system, while satisfying the condition of Scenario $4$, if the difference between the benefit of effective regulation and the cost of positive regulation of the takeaway platform is less than the loss in case of negative regulation. Thus, in this case, there are two strategic choices for the takeaway platform, merchants, and consumers, which are co-opting the nonvalue co-creation strategy or co-opting the value co-creation strategy.

5. Numerical Simulation and Influencing Factors of Value Co-Creation among Stakeholders of Takeaway Platforms

5.1. Numerical Simulation

In order to fully verify the correctness of the above evolutionary game system analysis, the value co-creation strategy of the stakeholders of the takeaway platform is reflected more intuitively by using simulation experiments through $Matlab R2021 b$ simulation values. The parameter values are set according to the constraints in different scenarios, as shown in

Table 4. Setting of parameter values in different scenarios.

Scenario	${\mathit{C}}_{\mathit{P}\mathbf{1}}$	$\mathit{\beta }$	$\mathit{D}$	$\mathit{F}$	${\mathit{R}}_{\mathit{P}}$	$\mathit{S}$	${\mathit{L}}_{\mathit{P}\mathbf{1}}$	$\mathit{\Delta }{\mathit{L}}_{\mathit{P}}$	$\mathit{\Delta }\mathit{C}$	${\mathit{L}}_{\mathit{M}}$	${\mathit{C}}_{\mathit{C}}$	$\mathit{\alpha }$
$1$	$8$	$0.5$	$8$	$8$	$15$	$8$	$1$	$1$	$25$	$6$	$15$	$0.7$
$2$	$4$	$0.5$	$8$	$8$	$15$	$8$	$1$	$1$	$25$	$6$	$15$	$0.7$
$3$	$4$	$0.5$	$8$	$8$	$15$	$8$	$1$	$1$	$25$	$6$	$5$	$0.7$
$4$	$4$	$0.5$	$8$	$8$	$15$	$8$	$1$	$1$	$10$	$6$	$5$	$0.7$
$5$	$6$	$0.5$	$8$	$8$	$15$	$8$	$1$	$1$	$10$	$6$	$5$	$0.7$

below:

The values of the parameters in the above table are brought into the evolutionary game system of the three stakeholders of the takeaway platform. To ensure that the results are not affected by the initial willingness of the participants, set the step size to $0.2$ and values of $x$, $y$, and z, the range of values is $(0,1)$, $t$ is $50$ loop function. The different colors in the figure represent the evolutionary paths of stakeholders’ strategy choices under different initial states. The results are shown in Figure 6a–e below, which correspond to the above five scenarios and effectively verify the correctness of the above inference of the value co-creation strategy choice of the three stakeholders of the takeaway platform. In addition, it can be seen from Figure 6a–d that, in scenarios 1–4, the initial willingness of the takeaway platform stakeholders only affects the rate of evolution to a stable strategy, but it does not change their final stable strategy choice. In contrast, in Figure 6e, namely, Scenario $5$, the initial willingness of the takeaway platform stakeholders not only affects the rate of evolution to a stable strategy, but also changes the final stable strategy choice. When the initial willingness level is low, it will evolve to the point that all three stakeholders do not choose the value co-creation strategy. When the initial willingness level gradually increases and reaches a medium-to-high level, it will evolve to the point that all three stakeholders choose the value co-creation strategy.

5.2. Sensitivity Analysis of Different Influences on System Evolutionary Stabilization Strategies

In order to achieve the ultimate ideal goal of value co-creation among takeaway platform stakeholders, the takeaway platform is actively regulated, merchants provide quality services, and consumers provide positive feedback, that is, the final system evolves to an asymptotic stabilization point of $E_8(1,1,1)$. From the numerical simulation in the previous section, it is clear that the initial willingness of stakeholder value co-creation strategy selection does not change the final evolutionary outcome under the parameter value limitation of Scenario $4$. Therefore, the initial willingness of three parties is randomly selected to be constant $0.2$, in order to eliminate the perturbation of the initial willingness, and the sensitivity of different influencing factors to evolve to a stable strategy is analyzed through comparative experiments.

5.2.1. Sensitivity Analysis of Platform Penalties for Low-Quality Service Merchants to System Evolutionary Stabilization Strategies

The punishment of the takeaway platform for low-quality service merchants is divided into low, medium and high intensity, namely, $F=\{4,8,12\}$. To avoid the remaining influencing factors from interfering with the experimental results, the remaining parameter values were taken as constant values. At this point, the evolution of the value co-creation strategy for takeaway platform stakeholders is shown in Figure 7 below. As can be seen from the figure, when the takeaway platform penalty $F$ is low, the deterrent effect is insufficient, and the price to be paid by merchants for providing low-quality services in violation is small, at which time the platform and consumers will also choose a negative strategy due to the lack of regulatory incentives, and all three stakeholders will evolve to a nonvalue co-creation strategy. When $F$ increases to a certain threshold, the benefits of active regulation by the platform can cover the cost of regulation, so it will change to an active regulatory strategy; higher penalties also make the cost of providing low-quality services rise, even more than the additional cost of providing quality services, so they will choose to provide quality services; consumers will be rewarded by the platform if they give positive feedback, and at this point, the three stakeholders will evolve to a value co-creation strategy. With the increase $F$, the rate of value co-creation strategy between the takeaway platform and merchants will also increase, but consumers are prone to the idea of hitchhiking, and the rate of positive feedback strategy tends to decrease instead of increase. Therefore, it is advisable to moderate the penalty for low-quality service merchants.

5.2.2. Sensitivity Analysis of the Reward Intensity Given by the Platform to Consumers with Positive Feedback on the Evolutionary Stabilization Strategy of the System

The intensity of rewards given to consumers with positive feedback by the platform was classified as low, medium and high, namely, $S=\{4,8,12\}$. In order to avoid the remaining influencing factors from interfering with the experimental results, the remaining parameter values are taken as constant values. At this point, the process of stakeholder value co-creation strategy evolution of the takeaway platform is shown in Figure 8 below. As can be seen from the figure, the degree of influence of $S$ on the sensitivity of the system to evolve to a steady state is stronger. When the $S$ strength is low, the benefits of positive feedback from consumers can hardly cover the cost of feedback, and their strategy choices will fluctuate, at which time the three stakeholders of the takeaway platform will continuously adjust their strategy choices according to each other’s strategy changes, combined with their own revenue situation. When the $S$ is raised to a certain threshold, moderate rewards can motivate the platform to actively monitor consumers’ positive feedback, and then effectively improve the quality of the services provided by the merchant, to achieve the value of the three stakeholders’ co-creation. However, if the $S$ strength is too high, the high cost increases the burden of active regulation of the platform, although the positive feedback will be strong from consumers, but the strategy choice of the platform and merchants will be caught in a cycle of shock, when the evolutionary system has no stable point, which is not conducive to shaping a good take-out market environment.

5.2.3. Sensitivity Analysis of the Network Externality Loss Borne by Low-Quality Service Merchants When They Are Discovered to the Evolutionary Stabilization Strategy of the System

The network externality loss borne by the low-quality service merchants when they are discovered is classified into three levels, i.e., low, medium, and high, namely, $L_M=\{1,6,11\}$. To avoid the remaining influencing factors from interfering with the experimental results, the remaining parameter values are taken as constant values. At this point, the evolution process of the value co-creation strategy of the takeaway platform stakeholders is shown in Figure 9 below. As can be seen from the figure, the level of $L_M$ value is directly proportional to the rate at which merchants tend to provide quality service strategy, and the higher the network externality loss borne when providing low-quality service is detected, the more deterrent it will be for merchants to provide quality service effectively. Meanwhile, the level of the $L_M$ value is inversely proportional to the rate at which platforms and consumers tend to be aggressive in their strategies. The higher the $L_M$ value, the more it reduces the regulatory burden on platforms and consumers. Thus, enhancing $L_M$ can effectively motivate the three stakeholders of the takeaway platform to actively choose a value co-creation strategy.

5.2.4. Sensitivity Analysis of Consumer Positive Feedback Costs to System Evolutionary Stabilization Strategies

The cost of positive consumer feedback is divided into low, medium, and high levels, namely, $C_C=\{2,5,8\}$. To avoid the remaining influencing factors from interfering with the experimental results, the remaining parameter values are taken as constant values. The evolution of the stakeholder value co-creation strategy of the takeaway platform is shown in Figure 10 below. As can be seen from the figure, when $C_C$ is within the limited threshold, consumers will spend less time and energy on positive feedback and will give positive feedback. Moreover, the smaller $C_C$ is, the more it can prevent merchants from providing low-quality services due to the emergence of a fluke mentality, which, in turn, motivates the three stakeholders of the takeaway platform to actively choose the value co-creation strategy. If the platform feedback procedure is complicated and the evaluation mechanism is not perfect, $C_C$ exceeds the limited threshold range, and at a high level, breaking the balance of consumers’ positive feedback, consumers’ strategy choice will be constantly oscillating. In addition, the platform and merchants will be caught in the cycle of oscillation. At that time, all three stakeholders have no stable strategy choice, which is not conducive to realizing the value co-creation of takeaway platform stakeholders.

6. Conclusions and Recommendations

6.1. Conclusions

Most of the existing stakeholder studies on takeaway platforms focus on the contexts in which regulators, platforms, and merchants are involved, citing consumers as exogenous variables. However, in real life, consumers are often limited in rationality, and due to their own cost–benefit, psychological preferences and other factors, there will be different value tendency in different situations, which will disturb the strategy choice of participating subjects, and require further in-depth research. In this study, we constructed an evolutionary game model of value co-creation for takeaway platform stakeholders, introduced the word-of-mouth and synergistic effects generated by consumers’ active participation into the stakeholder system, and embodied consumers’ costs and benefits as endogenous variables in the evolutionary game model, so as to open up the black box of consumers’ participation in value co-creation. It simulates the behavioral choices of platforms, merchants, and consumers as stakeholders in different situations, which, to a certain extent, broadens the research perspectives and enriches the research methods of stakeholder value co-creation on takeaway platforms, and it has certain theoretical significance. In addition, through the form of platform awards and penalties, prompting merchants to improve the quality of service and incentivizing consumers to give positive feedback and play the word-of-mouth effect is of certain practical significance for the promotion of the sustainable and healthy development of the takeaway industry.

This paper constructs a three-party evolutionary game model with platform, merchants, and consumers as takeaway platform stakeholders, and it conducts numerical simulation experiments to analyze the value co-creation strategy choices of the three stakeholders in different contexts and explore the sensitivity of different factors on the stakeholders’ evolution to a stable strategy of value co-creation. The following conclusions are obtained:

(1)

The penalty for low-quality service merchants on takeaway platforms should be within a limited threshold. If the intensity is too low, it is not enough to deter businesses. If the intensity is too high, although it increases the cost of low-quality services for merchants and effectively regulates their low-quality services, consumers are prone to free-rider mentality [34], which leads to a decrease in the efficiency of value co-creation among the three stakeholders. The time for the three stakeholders to converge on the value co-creation strategy is shortest only when the intensity is moderate. Therefore, the takeaway platform should shape a scientific regulatory punishment system, grasp the strength of punishment for low-quality service providers, and maximize the motivation of stakeholders to choose value co-creation strategies.

(2)

Similarly, the stable strategy choices of the three stakeholders will tend to be value-co-creative, that only if the rewards given by the takeaway platform to consumers with positive feedback are within a limited threshold. If the reward is too high, the cost required for the platform to actively regulate is too high to make ends meet. If the cost of rewards is too low, consumers have little incentive to give positive feedback, and all three stakeholders have no stable strategy choice, but are in a cyclical oscillation state. Therefore, takeaway platforms should improve the reward mechanism for positive feedback from consumers [35], dynamically adjust the rewards given to consumers, and set up various reward channels such as feedback points mall and rank competition rewards to give them motivation for active feedback and participation in value co-creation.

(3)

The network externality losses borne by low-quality service providers when they are discovered will affect the rate at which takeaway platform stakeholders choose value co-creation strategies. Its externality loss is positively correlated with the rate of merchants choosing premium services and negatively correlated with the rate of platforms and consumers choosing aggressive strategies. Therefore, takeaway platforms should increase the publicizing of low-quality service providers and flag those who provide noncompliant quality [36]. Consumers should also take up the “weapon” of reviews and use word of mouth to amplify the loss of network externalities that merchants bear when they provide low-quality services, causing them to think twice about doing so.

(4)

The cost of positive consumer feedback will significantly influence the choice of value co-creation strategies for the three stakeholders of the takeaway platform. The lower the cost required for consumer feedback, the more motivated the positive feedback will be, and the faster the rate of value co-creation among takeaway platforms, merchants, and consumers’ choices. Therefore, takeaway platforms should improve the consumer feedback mechanism [37], simplify the feedback process, and smooth the channels for consumers’ rights protection to effectively reduce their positive feedback costs.

6.2. Recommendations

Promoting value co-creation among the stakeholders of the takeaway platform has certain theoretical and practical significance for improving the quality of merchants’ services, increasing consumers’ loyalty, establishing the platform’s word-of-mouth image, and then expanding the network externality effect and promoting the sustainable and healthy development of the takeaway platform. Based on the findings of the above study, the following recommendations are made from the perspective of each stakeholder of the takeaway platform, respectively:

(1)

The takeaway platforms should improve the triple system of precompliance guidance, midincident reward and punishment mechanism, and postincident dynamic adjustment. First, the platform regularly conducts food safety training for merchants, emphasizing the importance of food safety, leaving samples of daily ingredients for inspection, and improving the live broadcast function of the back kitchen so that consumers can purchase goods with confidence. Secondly, we set the appropriate level of rewards and punishments within the threshold and explore diversified ways to increase the cost of low-quality services and reduce the cost of positive feedback from consumers [38]. Finally, based on the actual implementation, lessons learned and reasonable dynamic adjustments will be made to promote the sustainable and healthy development of the take-out industry.

(2)

Merchants should strengthen their own sense of social responsibility, take a long-term view, and reduce opportunistic behavior [39]. In an era where everyone is a self-publisher and word of mouth is king, merchants should strengthen their own sense of social responsibility, raise awareness of food safety, strengthen industry self-discipline, set up open kitchens, actively participate in back-of-house live streaming, use quality products as the best publicity, establish a good image, and expand their network externality.

(3)

Consumers should enhance their own food safety awareness and awareness of rights [40] in the process of providing take-out services, if you find that the business stores and online pictures do not match, the business license expired or different categories, deterioration or lack of catties and other low-quality products and services, to actively provide feedback to the platform, to assist the platform supervision, to provide reference for other consumers, to give full play to the consumer word-of-mouth effect, to reduce the cost of identification of low-quality businesses, and to create a good take-out market atmosphere.

6.3. Research Shortcomings and Future Prospects

In this paper, we only consider the deterministic factors in the value co-creation process of the stakeholders of the takeaway platform, but we do not consider the influence of the uncertainty factors that may exist in the value co-creation process on the evolutionary stabilization strategy of the system. In future research, the influence of uncertainty factors can be further considered to construct a tripartite stochastic evolutionary game containing stochastic perturbation terms.