A Tripartite Analysis of Online Healthcare Platforms: Evidence from Spring Rain Doctor in China

Background: Online healthcare platform (OHP) is a new form of medical treatment, which solves the problems of unbalanced distribution of medical resources and expensive medical treatment in China. Especially under the epidemic of COVID-19, OHP has greatly reduced the medical pressure of the hospital and the risk of cross infection. Methods: This paper uses evolutionary game theory to analyze behavioral strategies and their dynamic evolution in the promotion of OHP, and then numerical simulations are carried out with the help of program compilation. Results: The results demonstrate that: (1) both the stricter qualification inspection of doctors and the more investment in information protection promote the participation of doctors and the use of patients; (2) with a higher initial probability of doctors joining, the possibility for patients in using OHP and platforms to provide standardized online healthcare services becomes higher; (3) if the initial probability of patients using is higher, the possibility for doctors to participate OHP and platforms to provide standardized online healthcare services raises; (4) the trend of doctors joining the platform is affected by factors, such as registration cost, time cost, reputation loss and so on; (5) the tendency of patients in using online healthcare is mainly decided by the cost. Conclusions: Based on theoretical analysis, this article takes the Spring Rain Doctor OHP as an example to verify the game results. Therefore, OHP should attach importance to the inspection of doctors and the protection of privacy information, and strengthen the publicity in remote places. At the same time OHP can promote the active participation of grassroots doctors, and set a reasonable evaluation mechanism, so as to popularize online medical treatment among patients further.

become the focus of scholars' research. Ba established a motivation mechanism for users to accept OHP services [14]. Rita used a combination of sociology and communication theory to verify the positive role of social media in promoting the effectiveness of online healthcare services [15]. Deng designed models with influencing factors of perceived value, social impact and attitude, further to explore user adoption behaviors for specific situations of mobile healthcare [16]. Chang used SEM to verify that distributional fairness, procedural fairness and interpersonal fairness in OHP exert significant direct effects on patients' trust. Regarding the influences of patients' trust, it has significant effects on continuance consulting willingness and satisfaction [17]. Lu and Wu researched and confirmed the positive impact of other patients' online service quality assessment on patients' choices [18]. Gu demonstrated through empirical research that patient satisfaction with OHP is positively affected by perceived usefulness and OHP performance expectations [19]. Based on the unified theory of technology acceptance and use, Sun and Lu used SEM to verify the performance expectations, social influence and credibility of network health information are the key factors that affect users' acceptance and use of OHP [20]. Veer analyzed the factors that affect the willingness and use behavior of electronic health behaviors of the elderly [21]. Wu combined with web mining and SEM to verify that social support, information quality, and service quality exert significant direct effects on perceived usefulness and patient satisfaction. Regarding the influences of perceived usefulness and patient satisfaction, both have significant effects on continuance use of OHP patients [22]. Wu and Lu verified through empirical analysis that service quality positively affects patient satisfaction, and service prices and satisfaction show an inverted U-shaped relationship [7]. Yang founded that the response time, the depth of interaction and the service content of the first consultation have a significant impact on the patients' follow-up consultation behavior [4]. Amin believed that the hospital information system (HIS) can improve the efficiency of doctors, reduce the waiting time of patients, provide patients with convenient services and useful information and improve the patients' satisfaction [23].
Most studies have been conducted from the perspective of patients. While it is imperative to understand how patients benefit from OHP, OHP will be viable only when participating doctors also gain returns from OHP [24]. Therefore, some scholars concerned about the influencing factors of doctors joining OHP. Guo studied the impact of status capital and decision capital on the social and economic returns of different doctor groups. The results show that doctor's decision capital is a professional component which is important to platform maintaining exchange returns [24]. Chen combined the expectancy theory and the Bagozzi, Dholakia, and Basuroy (BDB) model, the results show that extrinsic motivations(i.e., extrinsic rewards, expected relationships, and image) and intrinsic motivation (i.e., a sense of self-worth) significantly influence the desire to serve patients well, which in turn positively affects the willingness to offer free services and the willingness to offer paid services [25]. Ma founded that performance expectations, effort expectations, social impact and convenience conditions have a positive impact on doctors' willingness to use and the usage behavior [26]. Through empirical research, Han founded that in OHP, the economic return, reputation return and offline identity of doctors have a positive impact on doctors' contribution behavior [27].
Some scholars have also done corresponding research from the perspective of online healthcare development trends and social influence. Mcgeady studied the information transfer between patients and doctors and founded that the OHP can increase the communication between patients and doctors and improve the quality of care [28]. Goh studied the social value of OHP services. He believed that the OHP can make medical information break through geographical boundaries and pass from the city to the countryside, which greatly improve the rural medical environment and achieved social value [29].
Venkatesh founded that the emergence of Internet medical services could help rural pregnant women obtain online healthcare information. It can alleviate the problem of uneven distribution of medical resources in urban and rural areas and greatly reduce the infant mortality rate [30]. Wu founded that the OHP can use the Internet to promote the flow of high-quality doctor resources and medical information services across regions, which is beneficial to improve the uneven distribution of medical resources in China [31].
In existing research, online healthcare research focuses on the willingness and motivation of patients and doctors. However, in fact, participating entities often compare their own benefits and costs from an economic perspective and make decisions. Few studies have focused on the dynamic evolution and mutual influence of the behaviors of different subjects in online healthcare. In order to promote the dissemination and development of online medicine, we should balance the interests of each side of OHP.
It is appropriate to analyze the behavior of stakeholders in the online healthcare to improve the promotion of online healthcare. This paper builds an evolutionary game model, analyzes the evolutionary stabilization strategy of online healthcare stakeholders, and uses program compilation for numerical simulation. Finally, we put forward feasible suggestions to the promotion of online medical treatment.
This work is of great importance to improving the imbalance of medical resources.

Evolutionary Game Theory in Healthcare
Evolutionary game theory is derived from the concept of evolutionary stability strategy [32]. It was originally developed in the economics field to study the social interactions [33]. This method takes the group of participants with limited rationality as the research object, and examines the evolution trend of group behavior from the point of view of system theory. Over the last few decades, the evolutionary game theory has been widely adopted by economists, sociologists, social scientists, as well as the philosophers [34].
The concept of evolutionary game theory also has been used among the access to the healthcare.
Chen et al. leveraged the evolutionary game theory to build a novel model to capture the behaviors of hospitals and patients in mHealth, then they analyzed the payoff matrix between hospitals and patients such that a replicator dynamic system can be built [35]. Li  characteristics and on the recent choices of nearby peers-either because there are local knowledge spillovers or because physicians want to conform to local practice patterns [38]. Yu used evolutionary game theory to analyze behavioral strategies and their dynamic evolution in the implementation and operation of telemedicine [39]. Through these studies, game theory has the possibility to provide a new theoretical basis for future research on the healthcare.

Evolutionary stable strategy
Maynard Smith formulated a central concept of evolutionary game theory called the evolutionary stable strategy (ESS) [40]. ESS is the strategy when game players continuously learn and imitate successful strategies in the evolution process and finally reach a stable state after improving their own strategies. The replication dynamic equation is a dynamic differential equation, which is used to express the frequency that a particular strategy is selected by a class of groups. It can be expressed by formula: where xi denotes the frequency of strategy si, usi denotes the expected return of strategy si selected by this group, u denotes the average expected return of this group. When interference factors make x smaller than x * , dd xt needs to be bigger than 0. And when x is bigger than x * , dd xt needs to be smaller than 0, so as to achieve a stable state.
In summary, evolutionary game theory based on the assumption of bounded rationality, considering the interaction between game players. Through multiple games, players constantly learn and improve their strategies, and finally reach an evolutionary stable state.

The Hypothesis of the Tripartite Evolutionary Game Model
In China, the enterprise-based mode is the main mode of online healthcare, accounting for 70% of the total. Internet companies build OHP and cooperate with doctors. The platforms need to contact doctors and inspect the qualifications of doctors. During this time, the platforms need to pay more costs.
Also, the platform needs to invest in information protection. The higher platforms invest, the higher the risk of cost recovery that platforms confront.
From the perspective of doctors, doctors can obtain economic and social benefits by joining OHP [24]. Specifically, doctors can obtain additional income and build a reputation by providing good online healthcare services [17] [25]. At the same time, doctors need to pay the time costs and registration costs.
When the platforms don't strictly inspect doctors, doctors will face reputation loss due to misdiagnosis and low patient satisfaction. When the platforms' investment in information protection is insufficient, doctors will face the risk of leakage of private information.
From the patients' perspective, patients can save time and money by using OHP. However, patients may face the risk of being misdiagnosed and divulged of privacy.
The following hypotheses were tested in this study: (1) The promotion of OHP is influenced by three groups: doctors, patients and online healthcare platforms. All the groups with bounded rationality can alter their own strategies by imitating and learning proven behaviors to obtain maximum revenues.
(2) Doctors take two courses of action: One strategy is to join OHP (join), while the other is not to join OHP (not join). Thus, the strategy space of doctors is S1{join, not join}. Patients take two courses of action: One strategy is to use OHP, while the other is not to use OHP. Thus, the strategy space of patients is S2{use, not use}. Online healthcare platforms take two courses of action: One strategy is to provide standardized online healthcare services, while the other is not to provide standardized online healthcare services. Thus, the strategy space of platforms is S3{provide, not provide}.
(3) The assumptions are that doctors may with x probability adopt the 'join' strategy, and with (1-x) probability adopt the 'not join' strategy. Patients may with y probability adopt the 'use' strategy, and with (1-y) probability adopt the 'not use' strategy. Platforms may with z probability adopt the 'provide' strategy, and with (1-z) probability adopt the 'not provide' strategy, in which 0 < x < 1, 0 < y < 1, and 0 < z < 1, respectively.

Payoff Matrix of the tripartite Evolutionary Game in OHP
Based on the above assumptions, a tripartite evolutionary game model including doctors, patients, and platforms under bounded rationality was constructed. The payoff matrix of the three groups is shown in Table 1 and Table 2. Table 1. Payoff matrix when the platforms provide standardized healthcare services (z) Table 2. Payoff matrix when the platforms don't provide standardized healthcare services (1-z)

Replicator Dynamics Equation of the Tripartite Evolutionary Game
Under the aforementioned assumption, the marginal expected revenue when doctors implement the 'join' strategy is P11: The marginal expected revenue when doctors implement the 'not join' strategy is P12: The expected revenue of the doctors is P1: Thus, the replicator dynamics equation of doctors can be written as (1) The marginal expected revenue when patients implement the 'use' strategy is P21: The marginal expected revenue when patients implement the 'not use' strategy is P22: The expected revenue of the patients is P2:  (2): The marginal expected revenue when platforms implement the 'provide' strategy is P31: The marginal expected revenue when platforms implement the 'not provide' strategy is P32: The expected revenue of the platforms is P3:

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Thus, the replicator dynamics equation of platforms can be written as ( ) 3 Pz in Formula (3):

Stability Analysis
The above three replication dynamic equations describe the dynamic adjustment process of the strategy selection of doctors, patients and platforms. When the three groups continue to learn and imitate to reach the Nash equilibrium, it shows that the game system has reached a stable state. In order to find the stability point of the evolutionary game among the three stakeholders, we assume: ,, E x y z is also in the above solution domain and satisfies: Differentiate the three equations above to get: . According to the stability theorem of the evolutionary game, when Pz   in the above three formulas, x * , y * , and z * represent the stable strategies that doctors, patients, and platforms should adopt in the evolution process.
According to equation (4) This equation represents the boundary of the steady state. When the following conditions are met: Then, we get: This indicates that joining OHP is stable, and not joining OHP is unstable.
In contrast, when the following conditions are met: Then, we get: This indicates that not joining OHP is stable, and joining OHP is unstable. When . The phase evolution diagram of its stability depends on the shape of the quadratic curve of equation (4).
This equation represents the boundary of the steady state. When the following conditions are met: This indicates that using online medical treatment is stable, and not using online medical treatment is unstable.
In contrast, when the following conditions are met: Then, we get: This indicates that not joining online medical treatment is stable, and joining online medical treatment is unstable. When Px . The phase evolution diagram of its stability depends on the shape of the quadratic curve of equation (5).
According to equation (6) This equation represents the boundary of the steady state. When the following conditions are met: Then, we get: This indicates that using OHP is stable, and not using OHP is unstable.
In contrast, when the following conditions are met: Then, we get: This indicates that not joining OHP is stable, and joining OHP is unstable. When Px . The phase evolution diagram of its stability depends on the shape of the quadratic curve of equation (6).

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In order to explore the evolution of OHP under different parameter values, based on the established evolutionary game model, the platforms' QISC, IPISC, the initial state of doctors and patients, and the doctor's registration costs, time costs, reputation loss, and online healthcare costs of patients.
The Influence of QISC α on the OHP Evolutionary Game Behavior α takes 0.1, 0.5 and 0.9 respectively for low QISC, medium QISC and high QISC.
As shown in Figure 1, due to the platforms' QISC is medium and low, doctors doubt the credibility of the platform. Finally, doctors will tend to the strategy of not joining OHP, and the lower the QISC, the faster the rate of evolution to the strategy of not joining. When the platform has a higher degree of QISC, doctors tend to believe the operation level of the platform. Therefore, OHP can improve the healthcare efficiency of doctors and their additional income. At last, doctors will tend to join OHP.   Figure 2, when the platforms' QISC is low, patients doubt the healthcare level of the doctors on the platform and the reliability of the platform based on the doctors' information on the platform. Due to the fear of misdiagnosis, the patients' behavior will tend to the strategy of not using OHP. When the platforms' QISC is moderate, the patients will initially tend to not using OHP due to the psychology of observation. After that, patients can accurately judge the qualifications of doctors through the patient and peer evaluation mechanism on the platform, and tend to use OHP.

Figure 3. The evolution path of platforms' strategy under different QISC
When the platforms' QISC is high, patients can learn about the doctors' healthcare level through the doctor-related information published on the platform, such as the medical institution, region, and professional title. Because patients can save time and money by using OHP, at the same time, they can enjoy healthcare resources that were not previously available due to factors such as region and income level. Therefore, patients will tend to use OHP. Figure 3, when the platforms' QISC is low, the platforms' inspection of doctors and the construction of the platform are relatively negative. Finally, the platform will tend to the strategy of not providing standardized online healthcare services.

As shown in
When the platforms' QISC is moderate, because the platforms consider reputation, they will invest part of the funds to build the platforms' qualification inspection and information protection mechanism. However, over time the platforms' revenue is not as expected, and the platforms don't pay much attention to the brand and popularity. At last, platforms tend to the strategy of not providing standardized online healthcare services.
When platforms have a high degree of QISC, they pay more attention to its own construction, social reputation and long-term development. They invest heavily in doctor qualification inspection and information protection, and they are willing to take certain risks. Thus, the platforms eventually tend to provide standardized online healthcare services. As shown in Figure 4, when the platforms' IPISC is low, doctors concern about their own information security, which will lead to the evolution of not joining OHP.

The Influence of IPISC β on OHP Evolutionary Game Behavior
When the platforms' IPISC is moderate, doctors will choose to join OHP for a period of time to observe the quality of the platforms' operation. However, the platforms' investment in information protection cannot meet the needs of doctors for their information security protection. Thus, the doctors finally choose not to join the OHP.
When the platforms invest heavily in information protection, doctors elect to trust the platforms' information protection mechanism and join OHP. And the greater the IPISC, the faster doctors elect to join OHP.
As shown in Figure 5, when the IPISC is low, patients concern about the leakage of private information and identity information, and they tend to elect not using OHP. The lower the platforms' IPISC, the faster the patients choose not to use it. When the platforms' IPISC is moderate or high, patients elect to trust the platforms' information protection mechanism and choose to use OHP. When the platforms' IPISC is high, they pay more attention to the protection of doctors' and patients' privacy information and invest more funds to protect it. At this time, the platforms care more about long-term interests, so they choose to provide standardized online healthcare services. The higher the platforms' IPISC, the faster they choose to provide standardized online healthcare services.

The Influence of Different Initial States of Doctors on the OHP Evolution Game Behavior
As shown in Figure 7, when the probability that the doctors initially choose to join the OHP is 0.2, doctors' attitude towards joining the OHP is negative. Therefore, patients concern about OHP and doubt the reliability of the platform. Eventually the patients elect not to use OHP. Because doctors don't join OHP, platforms cannot attract patients, and they quickly choose not to provide standardized online healthcare services.
When the probability that the doctors initially choose to join OHP is 0.9, the doctors' willingness to join OHP is relatively strong, and there are a lot of doctors signing contracts with the platform at this time. The platform has very rich medical resources. These resources enable patients to trust the platforms, so they choose to use OHP. At this time the platform has a good thinking and they choose to provide standardized online healthcare services much faster than patients choose to use OHP.
x (1) = 0.2 x (1) = 0.9 At this time, the platform is reluctant to spend too much cost on operating online healthcare services and tend to not provide standardized online healthcare services.
When the probability that patients initially choose to use OHP is 0.9, most patients choose to use OHP. This form of OHP is popular among the public. At this time, a large amount of online medical resources is required. When a large number of patients choose to use OHP, the medical efficiency of doctors will be improved, and the pressure on hospitals will be reduced. Doctors can also obtain additional income. Therefore, doctors choose to join OHP. When a large number of users are registered on the platform, the platforms have the opportunity to obtain huge profits. They further improve the quality of platform services for their reputation and patients, strictly inspect the qualifications of doctors and actively protect the safety of patient information. At last, platforms tend to provide standardized online healthcare services.

The Influence of Different Reputation Loss on the Evolutionary Behavior of Doctors
As shown in Figure 11, when the reputation loss of doctors among patients is small, it is because the evaluation mechanism of patients on doctors set by the platforms is more reasonable and objective, and the professional level and working attitude of doctors can be fairly evaluated. At this time, the doctor has a greater willingness to join OHP. When the doctors' reputation is greatly lost, in addition to the medical level, the patients' requirements for the doctors' service level are also higher, and the doctor is more likely to receive negative evaluations about communication skills, timeliness and service attitudes. For example, the experience mechanism of doctors will be questioned by patients; patients are more willing to trust the opinions of doctors in offline hospitals than OHP; due to the availability of online knowledge, patients' psychological expectations for OHP are too high, which will lead to patients giving negative comments. Initially, doctors choose to join OHP. Over time, negative online reviews will put pressure on doctors, and they ultimately choose not to join OHP. Doctors could converse with patients through the website, pictures, mobile phones, and even video format. In addition, doctors could observe timely feedback and service assessments of patients [25].
Online healthcare services are one of the "standard configurations" of various mobile medical enterprises. This is also one of the most competitive areas. However, only the most reliable and reliable In terms of doctor qualifications, Spring Rain Doctor has a strict inspect mechanism. First, it requires four cards, namely real-name information such as a doctor's qualification certificate, a practicing qualification certificate, an ID card, and a bank card. Then there will be staff to confirm the doctor's work by phone or offline to confirm that the doctor is indeed a working doctor. In addition, when the doctor serves online, there will also be a strict evaluation mechanism. This shows that the platform's inspection of doctor qualifications is an important factor affecting the platform's online healthcare competitiveness.
On is also a way for the platform to attract doctors to join.
The most important purpose for doctors to join OHP is to increase economic and reputational benefits. Through research, the doctors on the platform of Spring Rain Doctor report that the platform arbitration is biased towards users when disputes occur between doctors and patients; Spring Rain Doctor's doctor evaluation system drop more points than other platforms; It is often the case that doctors didn't respond in time and receive bad reviews. These problems have dampened the enthusiasm of doctors. The common point of these problems is that they damage the reputation of doctors. Therefore, the loss of the reputation of doctors is an important factor for doctors to consider whether to join OHP.

Discussion
This paper establishes a game model for the evolution of the players in the online medical field based on the premise of the bounded rationality of the game party. Through the analysis of the threeparty evolution game model and the numerical simulation analysis of the evolutionary behavior of doctors, patients and platforms, we found that the higher the platforms' inspection of doctor qualifications, the more it can strengthen the trust of doctors and patients to the platform, and promote the participation and use of doctors and patients. Low and medium intensity scrutiny will cause doctors and patients to choose not to join or use it because of fear of misdiagnosis. In the existing literatures, some scholars have mentioned that OHP employ doctors to answer patient questions, and high quality OHP are more likely to be acknowledged by patients [24]. Therefore, for patients, they can easily and quickly obtain high-quality medical resources such as doctors in the third-class hospital by using OHP.
The lack of medical resources and the uneven distribution are important reasons for patients to use OHP.
The greater the platforms' inspection of medical resources, the better the quality of doctors can be guaranteed, which improves the patients' trust in the platforms, avoids misdiagnosis and other issues, and improves the platforms' credibility, thereby forming a benign circulatory system. In addition, the high inspection strength of the platform also has an incentive effect on the platform itself, making the platform unwilling to give up sunk costs and promoting the high-quality development of the platform.
When the platforms' privacy information protection is moderate or low, doctors and patients tend to choose not to join or use OHP. The greater the protection of the platforms' information, the more able to promote doctors and patients to join and use OHP. Indeed, there has been evidence in the literature indicating that patients may hesitate to disclose their personal information online so they switch doctors frequently or switch to an offline hospital visit [4]. Thus, the platforms' information protection mechanism is an important factor in whether the doctors and patients choose OHP. The competent government department should clarify the entry threshold for OHP as soon as possible, improve the information security management system, ensure user information security and privacy, and better play the role of OHP.
For doctors, the stronger the patients' willingness to use OHP, the more inclined the doctors to join OHP, thereby obtaining more benefits. At the same time, registration costs, time costs, and reputation loss all affect whether doctors join OHP. It is proved that if a doctor provides a satisfactory service online, it may help his/her simultaneously gain reputation from both online and offline channels through word of mouth communication [25]. Rather, when doctors decide to offer online counseling services in their free time, the number of consultations and extra devoted time are considered to be negative factors affecting doctors' initiatives [25]. For patients, the richer the medical resources and the higher the quality of the platforms, and the lower the costs of OHP, the more they can encourage patients to use OHP, saving more time and money costs. Previous studies have confirmed that online consultation can provide patients with convenient access to physicians at low cost [8]. Therefore, the platforms should vigorously promote OHP, so that more doctors can actively join in, thereby attracting more patients. There are many ways to promote OHP, but grassroots doctors are the entrance with the highest conversion rate.
Grassroots doctors can connect medical resources and patients to a certain extent, which will be a key part of the cross-border integration of the Internet and the medical industry. The platform should concentrate high-quality resources on grassroots doctors, provide them with certain training opportunities and room to learn, and increase the income of grassroots doctors. At the same time, the platform should improve the doctors' review and evaluation mechanism, such as simplifying the review and registration process, making the process more user-friendly and more convenient; optimizing the operation process function, and adding online and offline to the doctor in the graphical consultation interface Status setting function, so that patients will not give bad reviews to doctors because of the long waiting time; adding the functions of message withdrawal, message copy, sending small video, voice to text, service end countdown, remaining number of conversations, and the other party's reply status in the dialog box between the two parties, so that the upper limit of the number of conversations in the service time limit can be reduced; using technology to improve the communication efficiency of doctors and patients, reduce the reputation loss and time cost of doctors, and make reasonable use of limited and precious medical resources. In addition, the core of OHP promotion is the patient. For China, remote cities and township residents are the largest customer groups of OHP. The OHP is just a new form of service in the medical industry. Promoting the popularization of OHP in remote and township residents can make the value of OHP form truly reflected, thus promoting the development of the entire mobile medical industry.
Therefore, the platforms should increase publicity and advertising in remote cities and rural township residents to attract more medical workers to join the OHP field.
Although we found some implication of OHP promotion, there still work need to do in the future.
For example, we can study the behavior of OHP subjects from the perspective of government regulation, and whether free consultation will affect the enthusiasm of doctors. In the future, we need to include the government into the scope of OHP subjects to further study the promotion of OHP.

Conclusion
In this paper, through the establishment of an evolutionary game model of OHP stakeholders, we found that the platforms' qualification inspection of doctors, investment in information protection, initial probability of doctors joining, initial probability of patients using, doctors' registration costs, time costs, reputation loss, and the online healthcare costs of patients have an impact on the three parties' strategic choices. The three stakeholders influence each other's behavior. Therefore, the platforms should pay attention to doctor qualification and information protection, improve the platform function and patient evaluation mechanism, and set reasonable prices of online healthcare treatment. At the same time, the government should increase supervision, regulate the behavior of the platform, clarify the distribution of responsibility for online healthcare legal issues, and promote the healthy development of OHP.