Incentive Mechanism for Online–Offline Dual-Channel Healthcare Services While Considering Spillover Effects

Abstract

This paper investigates the incentive mechanism for dual-channel healthcare service supply chains, where doctors simultaneously undertake both offline and online medical tasks, based on the common agency theory. Considering the geographical distance between online patients and public hospitals, we construct common agency, game-theoretic models under two scenarios: without spillover effects and with spillover effects. Through analytical solutions, we derive the equilibrium outcomes for both scenarios and conduct comparative and numerical analyses. The findings reveal that as follows: (1) Compared to the scenario without spillover effects, the incentive intensity for offline healthcare increases when spillover effects are considered, and doctors exert higher effort levels in offline healthcare. (2) The incentive intensity for online healthcare may decrease, yet doctors’ effort levels in the online channel do not decline accordingly and may even increase; (3) Non-economic incentives (e.g., online reputation) exhibit a substitution effect on economic incentives; (4) Online reputation not only influences decision-making in the online healthcare channel but also affects decisions in the offline channel through spillover effects. These findings provide valuable insights for public hospitals and online healthcare platforms to optimize incentive structures and for doctors to allocate efforts effectively across dual-channel healthcare services.

1. Introduction

In China, public hospitals serve as the cornerstone of the healthcare system, with offline medical services remaining the primary channel for patient care. However, the tension between immense healthcare demand and traditionally limited medical resources remains acute. With the rapid advancement of internet technologies, online healthcare has emerged as a transformative trend in the modern medical industry. By addressing critical challenges such as capacity constraints, prolonged wait times, and geographical barriers, online healthcare has become a vital complement to offline medical services [1]. The “Internet +” era has introduced online healthcare platforms as an alternative avenue for medical consultations, significantly enhancing patient accessibility. Relative to traditional offline healthcare, online healthcare offers significant advantages across multiple dimensions. From the patient perspective, it substantially reduces waiting times and eliminates travel-related expenditures [2]. For physicians, engagement in digital healthcare platforms enhances professional visibility while generating additional revenue streams [3]. At the systemic level, online healthcare mitigates geographical disparities in medical resource distribution, thereby improving healthcare accessibility and equity [4]. Notwithstanding these benefits, the diagnostic limitations inherent in virtual care—particularly the inability to conduct physical examinations—constrain its applicability to certain patient populations and may increase misdiagnosis risks [5]. These operational constraints substantiate the necessity of developing synergistic online–offline integrated care models. Following the COVID-19 pandemic, online medical services gained substantial government support in China, ushering in unprecedented growth opportunities. Consequently, an increasing number of doctors have adopted online channels to deliver real-time medical services, transcending geographical and temporal constraints [6]. As a result, many patients have become dual-channel users (accessing both online platforms and offline public hospitals), while doctors have evolved into dual-channel service providers. Despite the rapid expansion of online healthcare, challenges persist, including low doctor engagement and imbalanced development between offline and online service provision. Two primary factors contribute to this phenomenon: First, existing platform incentive mechanisms are often inadequate, failing to sufficiently motivate doctors to actively participate in online healthcare [7]. Second, conflicts between online and offline medical services arise due to doctors’ limited time, constraining their ability to allocate effort effectively across both channels [8]. Furthermore, within dual-channel healthcare systems, the differential incentive structures across channels significantly influence physicians’ effort allocation. A doctor’s distribution of professional effort between the two channels is not only determined by the incentive intensity of each respective channel, but may also be subject to cross-channel spillover effects from the alternative channel’s incentive scheme. Thus, designing an effective incentive mechanism is crucial to encourage doctor participation in online healthcare and ensure the synergistic development of a dual-channel (offline and online) healthcare system. This study adopts a common agency perspective to explore optimal incentive strategies that align the interests of healthcare providers, platforms, and patients while mitigating spillover effects between service channels.

For doctors, the online healthcare channel offers a more dynamic reputation-building system compared to traditional offline medical services [9]. Patients can express their appreciation through various means such as thank-you letters, online reviews, and ratings on digital platforms, collectively forming the doctor’s online reputation [10]. The formation of doctors’ online reputation does not rely on traditional methods (e.g., surveys or structured interviews) but is instead derived from patient feedback on online healthcare platforms. Furthermore, patient evaluations of doctors in offline healthcare settings have also moved beyond conventional approaches. In China, even when patients seek in-person care at public hospitals, they typically complete appointments via hospital apps or WeChat mini-programs. After consultations, patients receive prompts to rate their doctors and submit evaluations through these digital platforms. Online healthcare primarily serves primary care scenarios such as common illnesses, chronic disease management, and health consultations, where service quality is difficult to quantify directly through traditional clinical metrics (e.g., postoperative survival rates and readmission rates). Consequently, the formation of online reputation relies heavily on patients’ subjective feedback—including ratings, reviews, and scores—which reflects their perceived quality of healthcare. While online medical practice enables doctors to build professional reputation, financial compensation remains an indispensable component of service provision. Monetary rewards address doctors’ fundamental economic needs, serving as direct and tangible returns for their clinical services [11]. This necessitates a paradigm shift in designing dual-channel incentive mechanisms, moving beyond purely economic models to incorporate the motivational power of non-financial incentives.

Furthermore, incentive mechanism design for dual-channel healthcare services differs fundamentally from single-channel models. Online medical services do not operate in isolation but interact synergistically with offline services. When doctors engage in multitasking across channels, the interdependencies between these tasks become a critical factor in incentive structure design. Many doctors leverage online platforms to attract patients and subsequently direct them to physical hospitals for in-person care [12]. Patient trust and satisfaction with online consultations often translate into offline visits for further diagnosis and treatment. Online platforms facilitate this channel migration by offering integrated consultation and appointment-booking services [13], effectively converting digital patients into offline ones. This cross-channel patient flow demonstrates that online medical services generate significant spillover effects on offline healthcare provision [14].

Current research on offline healthcare incentives predominantly focuses on internal incentive structures for physicians within traditional medical institutions such as public hospitals [15], while inadequately addressing incentive mechanisms for physicians operating in dual-channel healthcare environments. Studies examining online healthcare incentives primarily concentrate on identifying influencing factors, including economic and non-economic determinants [16], yet lack systematic analysis of decision-making regarding economic versus non-economic incentives. For the integration of dual-channel medical services, either the spillover effects are examined in isolation [17], or the online reputation is considered independently [18], while the research on the cross-channel reputation dissemination mechanism under the spillover effects is ignored.

Addressing these research gaps, this study focuses on the incentive problem for physicians participating in online–offline dual-channel healthcare services. Through game-theoretic modeling, we systematically analyze the strategic interactions among three key stakeholders: hospitals, platforms, and physicians. Simultaneously, our research comprehensively integrates both economic incentives and non-economic incentives (particularly online reputation), developing formal incentive models for two distinct scenarios: absence of spillover effects and presence of spillover effects. By deducing the equilibrium solution of the tripartite game among doctors, public hospitals, and online medical platforms, and conducting a comparative analysis and numerical simulation of the equilibrium results in different scenarios, we have obtained a series of theoretical and practical conclusions with substantive management significance. This provides a novel analytical framework for exploring incentive mechanisms in dual-channel healthcare. This study aims to systematically address the following core research questions:

(1)

How do public hospitals, online healthcare platforms, and physicians determine their respective optimal decisions in this multi-agent game?

(2)

How do non-economic incentives (online reputation) modulate the design of economic incentives and influence physicians’ effort allocation between dual channels?

(3)

How do spillover effects impact the setting of incentive intensity across online and offline channels and shape physicians’ effort exertion decisions?

Against this dual-channel healthcare backdrop, this study systematically investigates the design of incentive mechanisms for physicians concurrently performing multiple tasks across offline and online medical services. Our core theoretical contributions are twofold: First, we integrated economic incentives and non-economic incentives (especially online reputation) into a unified analytical framework for dual-channel healthcare, revealing their substitution relationship in this environment. Second, by incorporating cross-channel spillover effects, we analyze how these effects moderate the influence of online reputation and elucidate the underlying mechanism through which online reputation affects offline channel outcomes via spillover pathways. In addition to theoretical contributions, this study also provides actionable insights for designing effective incentive mechanisms for online platforms and hospitals, while laying the foundation for optimizing the cross-channel allocation of high-quality medical resources. These contributions have significant practical significance for promoting the coordinated development of the online and offline medical service system under the “Healthy China” initiative.

The paper is structured as follows: Section 1 introduces the challenges and underlying causes associated with the dual-channel healthcare delivery model. Section 2 reviews the extant literature on China’s healthcare service system, principal–agent theory, incentive factors, and spillover effects. Section 3 develops a principal–agent model under the dual-channel setting and conducts a comparative analysis of equilibrium outcomes across different scenarios. Section 4 discusses the simulation results, while Section 5 summarizes the key findings and limitations.

2. Literature

This section reviews the relevant literature related to this study, including the research results on healthcare service system in China, principal–agent theory, incentive factors, and spillover effects.

2.1. Healthcare Service System in China

Under the strategic guidance of “Healthy China 2030” and the “Internet + Healthcare” policy, China’s healthcare system is transitioning from a predominantly offline model to an integrated online–offline dual-channel approach [19]. The development of this dual-channel system is heavily policy-driven. In 2018, the General Office of the State Council issued the “Guidelines on Promoting Internet + Healthcare Development,” formally establishing the legal framework for integrated online–offline services and marking the official creation of China’s dual-channel healthcare system that combines physical medical institutions with online healthcare platforms for complementary advantages.

Offline healthcare maintains its position as the fundamental form of medical services owing to its direct nature, comprehensive scope, and reliability. It principally delivers medical services that necessitate in-person interaction, including diagnosis of new conditions, management of multiple complex health issues [20], and specialized nursing care, while performing essential medical functions such as initial patient evaluations, physical examinations, and diagnostic imaging procedures. Consequently, offline healthcare demonstrates superior efficacy for first-time patients and those presenting with complicated, difficult-to-diagnose, or acute critical medical conditions. Within China’s healthcare framework, public hospitals serve as the principal providers of offline medical services, assuming a leadership role in both inpatient hospital care and outpatient clinical services [21]. The public hospital system is organized into three distinct levels: primary hospitals (delivering basic medical services), secondary hospitals (providing comprehensive medical treatment), and tertiary hospitals (offering specialized care for critical and terminal illnesses, while also conducting advanced medical education and research initiatives) [22]. However, primary healthcare institutions demonstrate relatively weaker service capabilities, characterized by insufficient medical equipment and shortages of specialized medical personnel, resulting in diminished public confidence. When granted the freedom to select between primary-level healthcare facilities and tertiary comprehensive hospitals for treatment, patients exhibit a marked preference for tertiary institutions. This preference pattern leads to inefficient allocation of high-quality medical resources for common ailments within tertiary hospitals, while healthcare resources at primary institutions remain substantially underutilized. In China’s current healthcare landscape, tertiary hospitals constitute merely 0.34% of all medical institutions yet account for 26.48% of patient consultations [23], exacerbating a series of systemic challenges including the following: congestion within tertiary hospital systems, prolonged patient waiting times, and escalating healthcare costs. Furthermore, the compensation structure for physicians within China’s public hospital system comprises both fixed salary components and performance-based incentive remuneration. Given that many general practitioners and mid-level physicians earn relatively modest incomes, they frequently elect to participate in external part-time medical services to enhance their financial compensation and expand their professional influence.

Online healthcare represents an innovative medical service model that integrates traditional healthcare with internet information technology. Online medical care is suitable for diseases with stable conditions, clear diagnoses, and no need for physical examinations or emergency interventions. It mainly focuses on the management of mild and chronic conditions and health consultations, mainly for follow-up visits of previous patients, and does not involve initial diagnosis and treatment. The absence of physical interaction inherently limits physicians’ ability to conduct comprehensive diagnoses through physical examinations (e.g., palpation and auscultation) or immediate instrumental testing, making its applicability contingent upon multiple factors including disease type, patient characteristics, and technology acceptance levels. Empirical evidence demonstrates strong adoption among patients with minor and common ailments [24], as well as chronic disease patients requiring frequent follow-ups and continuous communication [6]. The ease of technology use constitutes a critical factor in the adoption of online healthcare services, with younger generations demonstrating greater acceptance and utilization of online medical consultations while elderly populations exhibit limited technological proficiency and consequently rely heavily on assistance from younger family members [25]. Patients residing in remote or rural areas gain improved access to high-quality medical resources through online healthcare platforms, yet significant disparities persist in service utilization among educationally disadvantaged vulnerable groups, revealing ongoing inequities in the accessibility of digital medical services [26]. China’s online healthcare services are primarily delivered through two types of platforms: public online medical platforms and third-party online medical platforms [27]. Public online medical platforms are internet hospitals established and operated by physical public hospitals, particularly tertiary hospitals, with representative examples including Peking Union Medical College Internet Hospital and West China Internet Hospital. These platforms exhibit the following characteristics: First, the service providers are primarily practicing physicians from the host hospital who typically offer online diagnosis and treatment services on a part-time basis during their off-hours. Second, a small number of departments may arrange dedicated physicians to provide online services during fixed time slots, though such cases are limited in number. Third-party online medical platforms are represented by platforms such as Haodf.com, Ping An Good Doctor, and Chunyu Doctor. Their operational models demonstrate distinct features: First, over 90% of healthcare providers on these platforms are part-time physicians from public hospitals across the country [27,28]. Second, the relationship between the platform and physicians is not traditional employment but rather resembles a cooperative partnership. Both types of online medical platforms share two common characteristics: On one hand, the platforms do not provide fixed salaries to physicians, only offering revenue sharing based on service volume. On the other hand, platforms cannot impose mandatory service requirements on physicians, who retain complete autonomy in determining their service hours and level of engagement. While this flexible cooperative model grants physicians a high degree of autonomy, it also presents significant challenges for platform operations: how to design effective incentive mechanisms to encourage part-time physicians to provide online medical services consistently and reliably has become a core issue that platforms must address [29].

Traditional health management models were mainly limited to single service scenarios such as households, communities, or hospitals. The emergence and development of online medical services have brought significant changes to traditional medical service models, gradually transforming the original, single, offline, decentralized health service model into an integrated online–offline digital health service management model. Both third-party online medical platforms and public hospitals have recognized the importance of channel integration and are expanding towards dual-channel medical service integration models. On one hand, third-party online medical platforms integrate with offline public hospitals either indirectly or by establishing their own offline medical institutions. These platforms not only provide online medical consultation services for patients, but also offer offline clinic appointment services, which indirectly promotes the integration of offline and online dual-channel medical services [14]. If online medical consultation solves patients’ health problems, they will rate and evaluate doctors online, reducing unnecessary face-to-face visits, alleviating pressure on offline medical resources, and enhancing professional reputation [13]. When online consultation cannot resolve health issues due to disease complexity, but patients express trust and satisfaction with the online service, they will visit offline hospitals in person for further diagnosis and treatment [12]. For well-established third-party medical platforms, building their own offline clinics has become a way to achieve channel integration. Chinese, third-party, online medical platforms like WeDoctor and Chunyu Doctor have established offline clinics or hospitals to provide continuous health management for patients who need further diagnosis after online consultation [30]. On the other hand, public hospitals have accelerated the construction of internet hospitals after COVID-19, promoting closer integration of online and offline dual-channel medical services. Large tertiary hospitals have integrated online and offline services through establishing internet hospitals, significantly improving medical service supply, service efficiency, and patient experience [31]. The introduction of online channels by Chinese public hospitals has increased offline medical demand, with particularly noticeable integration effects for junior physicians [32]. Online–offline dual-channel integration represents the current and future development model for medical services. However, channel integration may bring additional workload to healthcare providers, and the mutual influence between channels requires further exploration [24].

2.2. Principal–Agent Theory

The principal–agent theory is one of the contract theories, focusing on how a principal can design an optimal contract to incentivize an agent under conditions of information asymmetry and conflicting interests [33]. With the development of the economy and social division of labor, it has become increasingly common for an agent to undertake multiple tasks. In scenarios involving multiple principals or multiple delegated tasks, an agent must allocate effort across these tasks. Bernheim, B. D. and Whinston, M. D. [34] proposed the foundational model of common agency, examining how multiple principals jointly design incentive mechanisms. In common agency, optimal contract design must account for the relationship between multiple tasks. Some studies assume competitive relationships among different principals. Holmstrom, B. and Milgrom, P [35] explored how task design can address free-riding behavior in common agency. Other studies assume complementary or substitutable relationships between tasks. Dixit, A. et al. [36] assumed cooperation among multiple principals and discussed production efficiency and surplus distribution under such cooperation. Additionally, some research assumes independence between tasks. Siqueira, K. et al. [37] studied incentive issues in Chinese state-owned enterprises as agents under the assumption of independent delegated tasks.

In the healthcare sector, principal–agent theory has also been widely applied. The doctor–patient relationship is the most fundamental dynamic in healthcare, encompassing key features of traditional principal–agent theory. Information asymmetry clearly plays a central role in medical care, as doctors possess significantly more specialized knowledge than patients [38]. Jiang, H. et al. [39] established a performance-based principal–agent framework with patients as principals and doctors as agents, analyzing fee-for-service (FFS) and performance-based contracting (PBC) methods under conditions of adverse selection (information asymmetry) and moral hazard (hidden actions). Additionally, a principal–agent relationship exists between healthcare providers and higher-level healthcare regulatory bodies. Jacob, J. et al. [40] developed a principal–agent model between hospitals and doctors, examining how effort costs influence service platform models with multiple care delivery options. Alex, B. and González-Chordá, V. M. [41], within a principal–agent framework, assumed a principal (head nurse) assigning a task to an agent (nurse) for a specific patient and analyzed nurse–manager interactions in the context of error reporting. Although the principal–agent relationship between healthcare providers and regulatory institutions has been examined, the multi-task common agency scenario where doctors undertake both offline and online healthcare services simultaneously remains unexplored.

2.3. Motivating Factors for Doctors in Online Healthcare

In the standard principal–agent model, agents are assumed to be rational economic actors who aim to maximize their economic benefits. Financial incentives serve as a key driver motivating doctors to participate in online healthcare. These monetary rewards provide tangible compensation for doctors seeking to improve their financial situation. Doctors can earn financial incentives by offering online consultation services. Following consultations, patients may purchase digital gifts for doctors, which translate into monetary compensation. Such economic rewards help offset the time, effort, and costs incurred by doctors.

However, agents care not only about economic gains but also non-economic benefits, such as social exchange and social reputation. The observation that social exchange provides non-economic incentives within organizations has long been recognized in the management literature and organizational sociology [42]. Dur, R. and Roelfsema, H. [43] incorporated social interactions between managers and workers to develop an economic model of social exchange within firms, examining how social interactions and employee reciprocity influence optimal organizational design. Fama, E.F. [44] proposed that reputation is an incomplete alternative to explicit incentives. Even without explicit incentives, agents will obtain a good reputation through hard work to enhance their market competitiveness. Kreps, D. et al. [45] further formalized this idea by developing the KMRW reputation model, which resolved the paradox of finite repeated games. Reputation is a personal motivating factor that can enhance an individual’s professional image. In online medical care, doctors mainly obtain reputation rewards through patients’ feedback, such as ratings and reviews. Positive evaluations and feedback provide valuable information, helping other patients assess the quality of a doctor’s service while allowing doctors to build their online reputation [7]. This kind of feedback meets doctors’ demand for professional recognition, which is crucial for career development and influence. Therefore, online reputation is the most important non-economic factor that motivates doctors to participate in online medical services.

2.4. Spillover Effects in Supply Chain Channels

With the development of e-commerce, an increasing number of businesses have established online sales or service channels. The spillover effects between online and offline channels have been extensively studied in the e-commerce field. Abhishek, V. et al. [46] examined the impact of online channels on various sales formats of traditional offline channels by considering both positive and negative demand spillover effects. Zhen, X. et al. [47] discussed the interaction between offline and online channels, establishing a game-theoretic model of demand spillovers under a multi-channel structure. Yang, W. et al. [48] considered two channels—manufacturer direct sales and e-retailer resales—and investigated whether and which party (manufacturer or retailer) should collaborate with key opinion leaders, assuming that introducing live streaming in one channel could generate positive or negative spillover effects on the other channel. However, most of these studies focus on manufacturers’ and retailers’ online and offline channels, and their findings are not directly applicable to the healthcare sector. While e-commerce primarily involves the distribution and transaction of different goods through online or offline channels, medical consultations typically require repeated interactions and continuous communication between doctors and patients, with doctors needing to exert effort across different channels.

In China, there are numerous online healthcare platforms such as Haodf.com and Ping An Good Doctor, which allow doctors from public hospitals to provide part-time services. This creates a dual-channel healthcare service model where doctors deliver offline healthcare services in public hospitals while also offering online medical services during their spare time. The interaction between online and offline healthcare channels has become an important research topic in dual-channel healthcare services. On one hand, patients whose conditions cannot be fully addressed online may be referred by doctors from online platforms to offline channels, thereby increasing offline patient volume. Chang, Y. et al. [12] found that doctors can attract patients to physical hospitals by providing quality online services, demonstrating that online participation has a patient diversion effect on offline practice. Using difference-in-differences and fixed-effects models, Wu, H. et al. [49] analyzed doctors’ online behaviors and offline performance, revealing that online medical services enhance doctors’ offline clinical performance. Similarly, Wang, L. et al. [8] employed a structural vector autoregression model to examine the relationship between online and offline medical services, finding that doctors’ online participation increases service volume at their affiliated public hospitals. On the other hand, patients with improved health conditions requiring follow-up consultations may be guided from offline to online channels, reducing the burden on offline resources. Huang, N. et al. [13] noted that, after integrating online and offline services, overall online demand increases while offline demand may decrease. This indicates that, in dual-channel healthcare systems, online channels can generate both positive and negative spillover effects on offline channels. As online healthcare in China has only begun to gain popularity in recent years, especially after the COVID-19 pandemic, the influence between channels has mainly been tested in empirical studies but is often overlooked in the doctor incentive model.

This study constructs common agency models involving doctors, public hospitals, and online healthcare platforms under the dual-channel healthcare service context, distinguishing between scenarios where online medical services do or do not generate spillover effects on offline services. We derive optimal equilibrium solutions for principals and agents, analyze factors influencing incentive intensity and effort levels, and investigate how online reputation and spillover effects impact these variables.

3. Modeling and Comparative Analysis

3.1. Problem Description and Model Assumptions

In this study, doctors, as agents, mainly undertake the offline healthcare tasks of public hospitals, while taking into account the online healthcare tasks of online medical platforms. Public hospitals and online medical platforms are clients who entrust doctors to complete tasks independently of each other, and there is no collusion between different clients. When doctors perform the tasks of online healthcare, they may have positive or negative spillover effects on offline healthcare, or they may not have spillover effects. The principal and agent’s decision goal is to maximize their own utility. The agent determines the level of effort based on the contract given by the principal.

To study the related issues, this paper makes the following assumptions about the incentive model:

Assumption 1.

As an agent, doctors undertake both offline and online healthcare tasks, and the clients of these two tasks are public hospitals and online medical platforms, respectively. Because the two tasks have different meanings for the doctor, the different tasks have different weights for the doctor. We used ${\theta }_1$ to indicate doctors’ attention to offline healthcare and ${\theta }_2$ to indicate doctors’ attention to online healthcare.

Assumption 2.

All principals (public hospitals and online healthcare platforms) are risk neutral, and agents (doctors) are risk averse. The absolute risk aversion coefficient is $\rho$ , that is, $U\left(w\right) = -e^{-\rho w}$ , where $w$ is the total wealth level of the agent.

Assumption 3.

The doctor’s effort levels in offline and online healthcare are denoted as $e_1(e_1>0)$ and $e_2(e_2>0)$ , respectively. The corresponding outputs for offline and online healthcare are $G_1 = {\beta }_1{e}_1+{\epsilon }_1$ and $G_2 = {\beta }_2{e}_2 + {\epsilon }_2$ , where ${\beta }_1$ represents the output coefficient for effort level $e_1$ and ${\beta }_2$ represents the output coefficient for effort level $e_2$. Due to external environmental factors and other uncertainties, both outputs $G_1$ and $G_2$ are stochastic. Here, ${\epsilon }_1$ and ${\epsilon }_2$ denote the random variables accounting for the uncertainty in offline and online healthcare outputs, respectively. Without loss of generality, we assume ${\epsilon }_1~N(0,{\sigma }_1^2)$ ; ${\epsilon }_2~N(0,{\sigma }_2^2)$; and $COV\left({\epsilon }_1,{\epsilon }_2\right) = 0$.

Assumption 4.

The public hospital and the online healthcare platform each sign a principal–agent contract with the doctor, who decides whether to accept and determines the effort levels based on the principle of utility maximization. Both the public hospital and the online healthcare platform propose linear payment contracts, denoted as $W_1 = Q + {\gamma }_1{G}_1$ and $W_2 = {\gamma }_2{G}_2$ , respectively. Here, $W_1$ and $W_2$ represent the doctor’s economic compensation from the public hospital and the online healthcare platform. ${\gamma }_1$ and ${\gamma }_2$ are the incentive reward shares offered by the public hospital and the online healthcare platform, with $0\le {\gamma }_1\le 1$ and $0\le {\gamma }_2\le 1$. $Q$ is the fixed payment provided by the public hospital to the doctor. Since the doctor’s service on the online healthcare platform is considered part-time, the platform does not offer a fixed payment. Although the online healthcare platform does not provide fixed compensation, due to features such as online reviews and ratings, the doctor can obtain additional non-economic value—online reputation expressed as $W_k = k{G}_2$. Here, $W_k$ represents the online reputation gained by the doctor from online medical services, and $k$ is the online reputation coefficient ($k>0$ and $k<{\gamma }_2$).

Assumption 5.

Regardless of whether the doctor provides medical services through online or offline channels, effort costs are inevitably incurred. Following the generalized expression of the principal–agent model, the effort costs for offline and online medical services are denoted as $C_1 = {\displaystyle \frac{1}{2}}c{e}_1^2$ and $C_2 = {\displaystyle \frac{1}{2}}c{e}_2^2$, respectively. Here, $c$ represents the doctor’s effort cost coefficient. For simplicity, we ignore potential differences in the effort cost coefficients across different medical channels.

Assumption 6.

In traditional offline healthcare employment relationships, physicians’ decision-making is constrained by reservation utility, the minimum expected benefit (fixed compensation + performance incentives) required for physicians to accept employment; otherwise they would exit the relationship. Thus, the physician’s reservation utility level is denoted as $\tilde{\omega }$. An agent will only accept employment from the principal when their utility level is no less than $\tilde{\omega }$. However, when physicians provide online medical services through healthcare platforms as part-time work, the platform does not offer fixed compensation. This part-time model in online healthcare is characterized by the absence of fixed salaries and zero exit costs. While fixed compensation serves as the baseline for physicians “not exiting” in traditional employment, this constraint is not considered in the online part-time service model.

Based on the above assumptions, this paper will establish common agency models for two scenarios—without spillover effects and with spillover effects—according to practical conditions, followed by solution derivation and a comparative analysis of both models.

3.2. Dual-Channel Healthcare Service Common Agency Model Without Spillover Effects

When online patients and the doctor’s physical hospital are not in the same region—meaning they are geographically distant—it is difficult for online patients to convert into offline patients. Patients who choose online consultations typically have non-severe medical conditions, and even if they require further treatment later, they tend to opt for other nearby physical hospitals rather than the doctor’s affiliated hospital. Therefore, in this model we consider that online patients and the doctor’s physical hospital are located in different regions, meaning the online healthcare channel has no spillover effects on the offline healthcare channel.

As illustrated in Figure 1, this study constructs a dual-channel healthcare service system comprising physicians, patients (differentiated by disease severity), public hospitals, and online healthcare platforms. Within this system, inter-entity interactions are represented through two distinct connectors: dashed arrows depict patient flows and healthcare-seeking behavior choices, while solid arrows represent physicians’ service provision behaviors. Physicians, as core service providers, concurrently deliver diagnostic and treatment services through both physical public hospital institutions and online healthcare platforms, establishing a parallel online–offline dual-channel service model. Patients make channel selections based on their health condition complexity: those with less severe follow-up cases tend to prefer online healthcare channels for convenient follow-up services, while patients with complex conditions typically opt for offline channels to obtain more comprehensive care. Importantly, when online consultations prove ineffective in resolving health issues, physicians recommend transitioning to offline channels for further treatment. However, constrained by factors like geographical distance, some patients may choose not to visit the referring physician’s affiliated physical hospital, instead seeking care at alternative medical institutions—a phenomenon resulting in the absence of online-to-offline spillover effects.

The total earnings of doctors consist of revenue from two channels: offline medical services and online medical services. Among these, the revenue from offline medical services is composed of fixed compensation and incentive compensation, while the revenue from online medical services includes incentive compensation and online reputation.

$$W=W_1+W_2+W_k=Q+{\gamma }_1\left({\beta }_1{e}_1+{\epsilon }_1\right)+\left({\gamma }_2+k\right)\left({\beta }_2{e}_2+{\epsilon }_2\right)$$

(1)

Based on the Arrow–Pratt measure, the risk cost for doctors providing offline healthcare is $RC\left(W_1\right)={\displaystyle \frac{1}{2}}\rho {\gamma }_1^2{\sigma }_1^2$, where $\rho$ represents the degree of risk aversion. Therefore, the utility function for the doctor engaging in offline healthcare is as follows:

$$E\left[U\left(W_1\right)\right] = E\left(W_1\right) - RC\left(W_1\right) -{ C}_1 = Q + {\gamma }_1{\beta }_1{e}_1- {\displaystyle \frac{1}{2}}\rho {\gamma }_1^2{\sigma }_1^2 - {\displaystyle \frac{1}{2}}c{e}_1^2$$

(2)

Similarly, the risk cost for the doctor engaging in online healthcare is $RC\left(W_2+W_k\right) = {\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2 + k\right)}^2{\sigma }_2^2$. Therefore, the utility function for the doctor engaging in online healthcare is as follows:

$$E\left[U\left(W_2+W_k\right)\right] = E\left(W_2 + W_k\right) - RC\left(W_2 + W_k\right) - C_2 = \left({\gamma }_2 + k\right){\beta }_2{e}_2 - {\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2 + k\right)}^2{\sigma }_2^2 - {\displaystyle \frac{1}{2}}c{e}_2^2$$

(3)

Since medical tasks from different channels carry different weights for doctors, the doctor’s total utility function is expressed as the weighted sum of utilities across all tasks, namely the following:

$$\begin{gathered} E\left[U\left(W\right)\right] = {\theta }_{1}E\left[U\left(W_1\right)\right] + {\theta }_{2}E\left[U\left(W_2 + W_k\right)\right] ={ \theta }_1\left(Q + {\gamma }_1{\beta }_1{e}_1 - {\displaystyle \frac{1}{2}}\rho {\gamma }_1^2{\sigma }_1^2 - {\displaystyle \frac{1}{2}}c{e}_1^2\right) + \\ {\theta }_2\left[\left({\gamma }_2 + k\right){\beta }_2{e}_2 - {\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2 + k\right)}^2{\sigma }_2^2 - {\displaystyle \frac{1}{2}}c{e}_2^2\right] \end{gathered}$$

(4)

Doctors are subject to participation constraints when engaging in offline medical tasks. Public hospitals must ensure that the utility derived from doctors’ offline healthcare is no less than their reservation utility level ω, i.e., ${\theta }_1\left(Q + {\gamma }_1{\beta }_1{e}_1 - {\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2 - {\displaystyle \frac{1}{2}}c{e}_1^2\right)\ge \tilde{\omega }$.

Public hospitals and online medical platforms, acting as risk-neutral principals, have a utility function defined as total output minus payments to agents, as specified below:

$$E\left[U\left(R_1\right)\right] = E\left(G_1-W_1\right) = {\beta }_1{e}_1 - \left(Q + {\gamma }_1{\beta }_1{e}_1\right)$$

(5)

$$E\left[U\left(R_2\right)\right]=E\left(G_2-W_2\right)={\beta }_2{e}_2-{\gamma }_2{\beta }_2{e}_2$$

(6)

Based on the above analysis, we establish a common agency model consisting of one public hospital, one online medical platform, and one doctor, as specified below:

$$\underset{{\gamma }_1}{\mathit{max}}E\left[U\left(R_1\right)\right] = -Q + \left(1 - {\gamma }_1\right){\beta }_1{e}_1$$

(7)

$$\underset{{\gamma }_2}{\mathit{max}}E\left[U\left(R_2\right)\right]=\left(1-{\gamma }_2\right){\beta }_2{e}_2$$

(8)

s. t.

$${\theta }_1\left(Q+{\gamma }_1{\beta }_1{e}_1-{\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2-{\displaystyle \frac{1}{2}}c{e}_1^2\right)\ge \tilde{\omega }$$

(9)

$$e_1\in \mathit{arg}max:{\theta }_1\left(Q+{\gamma }_1{\beta }_1{e}_1-{\displaystyle \frac{1}{2}}\rho {\gamma }_1^2{\sigma }_1^2-{\displaystyle \frac{1}{2}}c{e}_1^2\right)+{\theta }_2\left[\left({\gamma }_2+k\right){\beta }_2{e}_2-{\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2+k\right)}^2{\sigma }_2^2-{\displaystyle \frac{1}{2}}c{e}_2^2\right]$$

(10)

$$e_2\in \mathit{arg}max:{\theta }_1\left(Q+{\gamma }_1{\beta }_1{e}_1-{\displaystyle \frac{1}{2}}\rho {\gamma }_1^2{\sigma }_1^2-{\displaystyle \frac{1}{2}}c{e}_1^2\right)+{\theta }_2\left[\left({\gamma }_2+k\right){\beta }_2{e}_2-{\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2+k\right)}^2{\sigma }_2^2-{\displaystyle \frac{1}{2}}c{e}_2^2\right]$$

(11)

In the aforementioned model, Equation (7) represents the public hospital’s objective function. Equation (8) corresponds to the online healthcare platform’s objective function. Equation (9) establishes the doctor’s participation constraint for offline healthcare. Equation (10) characterizes the incentive compatibility constraint for offline healthcare. Equation (11) specifies the incentive compatibility constraint for online healthcare.

Proposition 1.

The optimal equilibrium solutions for the principals and agent without spillover effects are derived as follows:

$$\left\{\begin{array}{c}{\gamma }_1^{*}={\displaystyle \frac{{\beta }_1^2}{c\rho {\sigma }_1^2+{ \beta }_1^2}}\\ {\gamma }_2^{*}={\displaystyle \frac{1-k}{2}}\\ e_1^{*}={\displaystyle \frac{{\beta }_1^3}{c\left(c\rho {\sigma }_1^2+{\beta }_1^2\right)}}\\ e_2^{*}={\displaystyle \frac{ {\left(1+k\right)\beta }_2}{2c}}\end{array}\right.$$

(12)

The proof of Proposition 1 is provided in Appendix A.1.

3.3. Common Agency Model of Dual-Channel Healthcare Service with Spillover Effects

Due to the individuality of patients and the heterogeneity of diseases, some patients cannot be cured through online healthcare and require further in-person consultations offline. When online patients and doctors are in the same region—meaning the offline distance between them is relatively short—patients can more easily transition from the online channel to the offline channel. Therefore, in this model, we assume that online patients and the doctors’ physical public hospitals are located in the same region, resulting in a spillover effect from the online healthcare channel to the offline healthcare channel.

As depicted in Figure 2, the constituent elements of this dual-channel healthcare service system remain consistent with those in Figure 1. The system incorporates a critical service linkage mechanism: when online consultations cannot fully resolve patients’ health issues, doctors proactively recommend transitioning to offline channels for further treatment. Distinct from the scenario in Figure 1, in this case the geographical proximity between online patients and the doctors’ affiliated, physical public hospitals leads patients to follow the referral advice and subsequently visit the same doctors at their offline public hospital facilities for continued care.

Considering the spillover effect from the online healthcare channel to the offline healthcare channel, the offline healthcare output function is given by $G_1 = {\beta }_1{e}_1 + {\epsilon }_1 + \alpha {\beta }_2{e}_2$. Correspondingly, the doctor’s offline healthcare revenue becomes $W_1 = Q + {\gamma }_1({\beta }_1{e}_1 + {\epsilon }_1 + \alpha {\beta }_2{e}_2)$. According to the actual situation, it can be known that $0<\alpha <1$.

The form of the online healthcare output function remains unchanged. Based on the Arrow–Pratt measure, the doctor’s risk costs for both offline and online healthcare remain unaffected by the spillover effect and are still expressed as ${\displaystyle \frac{1}{2}}\rho {\gamma }_1^2{\sigma }_1^2$ and ${\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2+ k\right)}^2{\sigma }_2^2$.

The doctor’s utility function for offline healthcare is given by the following:

$$E\left[U\left(W_1\right)\right] = Q + {\gamma }_1\left({\beta }_1{e}_1 + \alpha {\beta }_2{e}_2\right) - {\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2 - {\displaystyle \frac{1}{2}}c{e}_1^2$$

(13)

The doctor’s utility function for online healthcare is given by the following:

$$E\left[U\left(W_2\right)\right] = \left({\gamma }_2 + k\right){\beta }_2{e}_2 - {\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2 + k\right)}^2{\sigma }_2^2 - {\displaystyle \frac{1}{2}}c{e}_2^2$$

(14)

Since the doctor assigns different weights ${\theta }_1$ and ${\theta }_2$ to offline and online healthcare, respectively, the total utility function when engaging in both tasks can be rewritten as follows:

$$E\left[U\left(W\right)\right] = {\theta }_1\left[Q + {\gamma }_1\left({\beta }_1{e}_1 + \alpha {\beta }_2{e}_2\right) - {\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2 - {\displaystyle \frac{1}{2}}c{e}_1^2\right] + {\theta }_2\left[\left({\gamma }_2+ k\right){\beta }_2{e}_2 - {\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2 + k\right)}^2{\sigma }_2^2 - {\displaystyle \frac{1}{2}}c{e}_2^2\right]$$

(15)

The doctor’s participation constraint for offline healthcare can be rewritten as ${\theta }_1\left[Q +{\gamma }_1\left({\beta }_1{e}_1+\alpha {\beta }_2{e}_2\right)-{\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2-{\displaystyle \frac{1}{2}}c{e}_1^2\right]\ge \tilde{\omega }$.

The utility functions of the public hospital and the online healthcare platform remain unchanged, and the following common agency model is established:

$$\underset{{\gamma }_1}{\mathit{max}}E\left[U\left(R_1\right)\right] = -Q + \left(1 - {\gamma }_1\right){\beta }_1{e}_1$$

(16)

$$\underset{{\gamma }_2}{\mathit{max}}E\left[U\left(R_2\right)\right]=\left(1-{\gamma }_2\right){\beta }_2{e}_2$$

(17)

s. t.

$${\theta }_1\left[Q+{\gamma }_1\left({\beta }_1{e}_1+\alpha {\beta }_2{e}_2\right)-{\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2-{\displaystyle \frac{1}{2}}c{e}_1^2\right]\ge \tilde{\omega }$$

(18)

$$e_1\in \mathit{arg}max:{\theta }_1\left[Q+{\gamma }_1\left({\beta }_1{e}_1+\alpha {\beta }_2{e}_2\right)-{\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2-{\displaystyle \frac{1}{2}}c{e}_1^2\right]+{\theta }_2\left[\left({\gamma }_2+k\right){\beta }_2{e}_2-{\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2+k\right)}^2{\sigma }_2^{2 }-{\displaystyle \frac{1}{2}}c{e}_2^2\right]$$

(19)

$$e_2\in \mathit{arg}max:{\theta }_1\left[Q+{\gamma }_1\left({\beta }_1{e}_1+\alpha {\beta }_2{e}_2\right)-{\displaystyle \frac{1}{2}}\rho {{\gamma }_1}^2{\sigma }_1^2-{\displaystyle \frac{1}{2}}c{e}_1^2\right]+{\theta }_2\left[\left({\gamma }_2+k\right){\beta }_2{e}_2-{\displaystyle \frac{1}{2}}\rho {\left({\gamma }_2+k\right)}^2{\sigma }_2^2-{\displaystyle \frac{1}{2}}c{e}_2^2\right]$$

(20)

In the aforementioned model, Equation (16) represents the public hospital’s objective function. Equation (17) corresponds to the online healthcare platform’s objective function. Equation (18) establishes the doctor’s participation constraint for offline healthcare. Equation (19) characterizes the incentive compatibility constraint for offline healthcare. Equation (20) specifies the incentive compatibility constraint for online healthcare.

Proposition 2.

The optimal equilibrium solutions for the principals and agent with spillover effects are derived as follows:

$$\left\{\begin{array}{c}{\gamma }_1^{**}={\displaystyle \frac{2{\theta }_2{\beta }_1^2+\alpha {\theta }_2{\beta }_2^2\left(1+k\right)}{2{\theta }_2{\beta }_1^2+2{\theta }_{2}c\rho {\sigma }_1^2-3{\theta }_1{\alpha }^2{\beta }_2^2}}\\ {\gamma }_2^{**}={\displaystyle \frac{1-k}{2}}-\alpha {\displaystyle \frac{{\theta }_1}{2}}{\displaystyle \frac{2{\beta }_1^2+\alpha {\beta }_2^2\left(1+k\right)}{2{\theta }_2{\beta }_1^2+2{\theta }_{2}c\rho {\sigma }_1^2-3{\theta }_1{\alpha }^2{\beta }_2^2}}\\ e_1^{**}={\displaystyle \frac{2{\theta }_2{\beta }_1^3+\alpha {\beta }_1{\beta }_2^2{\theta }_2\left(1+k\right)}{c\left(2{\theta }_2{\beta }_1^2+2{\theta }_{2}c\rho {\sigma }_1^2-3{\theta }_1{\alpha }^2{\beta }_2^2\right)}}\\ e_2^{**}={\displaystyle \frac{2\alpha {\beta }_1^2{\beta }_2{\theta }_1+2{\beta }_2\left({\beta }_1^2{\theta }_2+{\theta }_{2}c\rho {\sigma }_1^2-{\alpha }^2{\beta }_2^2{\theta }_1\right)\left(1+k\right)}{2c\left(2{\beta }_1^2{\theta }_2+2{\theta }_{2}c\rho {\sigma }_1^2-3{\alpha }^2{\beta }_2^2{\theta }_1\right)}}\end{array}\right.$$

(21)

where ${\theta }_{2}c\rho {\sigma }_1^2+{\theta }_2{\beta }_1^2>2{\theta }_1{\alpha }^2{\beta }_2^2$ and $2\alpha {\theta }_1{\beta }_1^2+{\alpha }^2{\theta }_1{\beta }_2^2\left(1+k\right)<\left(1-k\right)<2\alpha {\theta }_1{\beta }_1^2+{\alpha }^2{\theta }_1{\beta }_2^2\left(1+k\right)+2\left(2{\theta }_2{\beta }_1^2+2{\theta }_{2}c\rho {\sigma }_1^2-3{\theta }_1{\alpha }^2{\beta }_2^2\right)$.

The proof of Proposition 2 is provided in Appendix A.2.

3.4. Comparison of Equilibrium Results

To examine the impact of spillover effects on the decisions of both the principals and the agent, this section compares the equilibrium outcomes under different scenarios. Through this comparison, the following meaningful conclusions can be drawn.

Lemma 1.

When there is a spillover effect, the incentive intensity of offline healthcare is higher than that without considering the spillover effect, i.e., ${\gamma }_1^{**}>{\gamma }_1^{*}$.

The proof of Lemma 1 is provided in Appendix B.1.

The economic rationale of Lemma 1 is evident. When spillover effects exist, it implies that some patients shift from online to offline channels. Since offline patient volume increases, public hospitals have an incentive to enhance doctors’ effort incentives for offline medical care. To address the rising offline demand driven by online services, public hospitals must strengthen incentive mechanisms to ensure adequate doctor supply.

Lemma 2.

When there is a spillover effect, the incentive intensity of online healthcare is less than that without considering the spillover effect, i.e., ${\gamma }_2^{**}<{\gamma }_2^{*}$.

The proof of Lemma 2 is provided in Appendix B.2.

When spillover effects exist, it means that some patients shift from the online healthcare channel to the offline healthcare channel. Lemma 1 shows that, when spillover effects are present, the incentive intensity for offline healthcare increases. Given a fixed level of effort, if doctors allocate more effort to the offline healthcare channel, their effort allocated to the online healthcare channel must decrease. Consequently, the incentive intensity provided by the online healthcare platform will decline. Moreover, when spillover effects exist, doctors may increase their voluntary effort in the online healthcare channel to boost patient flow in the offline channel. By reducing the incentive intensity, the online healthcare platform can control costs while minimizing the impact on doctors’ online behavior.

Lemma 3.

When there is a spillover effect, the doctor’s level of effort in offline healthcare is higher than that without considering the spillover effect, i.e., $e_1^{**}>e_1^{*}$.

The proof of Lemma 3 is provided in Appendix B.3.

When Lemma 3 indicates that doctors’ engagement in online healthcare services does not necessarily have a negative impact on their effort investment in offline healthcare—it may instead have a positive effect. First, as shown in Lemma 1, when spillover effects exist, the incentive intensity for offline healthcare increases. Since doctors’ effort levels in offline healthcare are directly influenced by these incentives, their effort investment rises accordingly. Second, by providing online healthcare services, doctors accumulate online reputation, which indirectly boosts their offline patient demand.

Lemma 4.

When there is a spillover effect, the doctor’s level of effort in online healthcare is higher than that without considering the spillover effect, i.e., $e_2^{**}>e_2^{*}$.

The proof of Lemma 4 is provided in Appendix B.4.

When spillover effects exist, it means that some online patients shift to offline channels, leading to an increase in the volume of offline healthcare. In this scenario, even if the incentive intensity for online healthcare decreases, doctors will not readily reduce their effort level in online healthcare. On one hand, online healthcare exerts a spillover effect on offline healthcare. To maintain the overall service quality across both channels, doctors need to sustain their effort in online healthcare. On the other hand, online healthcare enables faster reputation dissemination, and maintaining effort in this channel helps expand a doctor’s online reputation. Therefore, even if the incentive intensity for online healthcare may decrease (as shown in Lemma 2), doctors will not easily lower their effort level in online healthcare.

4. Numerical Analysis

The previous section modeled and solved the dual-channel healthcare incentive problem for doctors in different scenarios, deriving the equilibrium outcomes of the principal’s and agent’s decisions, and compared the equilibrium results across these scenarios. This section further explores the influence of several key parameters (spillover effect and online reputation) on the intensity of motivation and effort through numerical research. Referring to the relevant papers on principal–agents to set the dimensional relationships of each parameter, we assume that ${\beta }_1 = 4$;${ \beta }_2 = 3$;${\theta }_2 = 8$;${\theta }_1 = 2$;$c = 5$;${\sigma }_{1 }^2 = 0.25$; and $\rho = 2$.

4.1. The Influence of Online Reputation on Equilibrium Outcomes Without Spillover Effects

As shown in Figure 3, without considering the spillover effect, there is a positive correlation between doctors’ efforts on online medical channels and their online reputation. This discovery indicates that online reputation, as a non-economic incentive method, can effectively enhance doctors’ online service efforts. Especially for reputation-sensitive occupations like doctors, non-economic incentive methods can also achieve considerable incentive effects to a certain extent. In practice, online healthcare platforms frequently organize voluntary medical consultation activities that provide free healthcare advisory services to patients, as exemplified by Alibaba Health’s “Free Clinic for Traffic” initiative where physicians completing a designated volume of pro bono services receive prominent homepage exposure as compensation. While physician participation in either online or offline charitable medical services yields limited direct financial returns, it significantly enhances their digital reputation, subsequently generating increased patient trust, greater platform visibility, and enhanced professional fulfillment—representing a strategic exchange of service for reputation capital that aligns with platform-mediated professional development mechanisms in digital healthcare ecosystems.

As shown in Figure 4, in the scenario without considering the spillover effect, there is a negative correlation between the incentive intensity of online healthcare and the online reputation of doctors. This discovery indicates that online reputation, as a form of non-economic incentive, has a substitution effect on economic incentives. When the online reputation reaches a sufficiently high level, non-economic incentives can completely replace economic incentives. Under certain circumstances, such as when a platform organizes free online healthcare activities, doctors may be willing to provide online healthcare services with zero economic compensation merely to gain reputation.

4.2. The Influence of Online Reputation on Several Equilibrium Outcomes with Spillover Effects

As shown in Figure 5, in the scenario considering the spillover effect, there is a positive correlation between the incentive intensity of offline medical care and the online reputation of doctors. This indicates that, under the influence of spillover effects, online reputation not only affects the incentive intensity of online medical channels, but also has an impact on the incentive intensity of offline medical channels. This finding is significantly different from the situation without spillover effects. In the scenario without spillover effects, online reputation only affects the incentive intensity of the online medical channel but has no impact on the offline medical channel. From this, it can be concluded that, when there is a spillover effect, online reputation simultaneously influences the incentive decisions of the two channel entities. Real-world cases frequently demonstrate how online reputation influences offline channel incentives, as illustrated by a cardiologist at a tertiary hospital in Beijing who maintained consistently high ratings (above 4.9/5) on the “Haodf.com” platform. The physician’s substantial positive evaluations attracted numerous out-of-town patients who, after initial online consultations, specifically traveled for in-person visits at the offline clinic—extending the specialist appointment waiting period from one week to three months. This cross-channel spillover effect prompted hospital administration to both increase the physician’s offline consultation frequency and raise the corresponding registration fees, empirically validating that, when spillover effects exist, online reputation directly impacts offline channel incentive structures.

As shown in Figure 6, in the scenario of considering the spillover effect, there is a negative correlation between the intensity of online healthcare incentives and the online reputation of doctors. The same conclusion holds true in the absence of spillover effects. This indicates that, regardless of whether there is a spillover effect or not, online reputation has a certain substitution effect on the economic incentives of online healthcare. As doctors’ online reputation improves, online healthcare platforms may accordingly reduce economic incentives. In practice, platforms often implement differentiated incentive structures where higher-reputation physicians receive proportionally lower economic incentives, as exemplified by WeDoctor’s compensation model that provides substantial subsidies for novice physicians with lower reputation scores while applying reduced subsidy rates for established “gold-medal” physicians with superior reputations. Although this results in decreased per-consultation income for top-rated physicians, their stable patient flow derived from accumulated reputation capital maintains high service volumes, rendering the marginal reduction in financial incentives insufficient to significantly affect their service provision willingness—demonstrating how reputation effects create inelasticity in physician responsiveness to monetary incentives at higher reputation tiers.

As shown in Figure 7, in the scenario of considering the spillover effect, the online reputation of doctors is positively correlated with their efforts in offline healthcare. This indicates that online reputation not only affects online medical channels, but also influences offline healthcare channel through spillover effects. There are two explanations that can account for this cross-channel influence. Firstly, as doctors’ online reputation keeps rising, the economic incentives for online consultations may decrease (as shown in Figure 6), prompting those with greater economic motivation to turn their attention to offline healthcare channel. Secondly, online reputation overflows from online healthcare channels to offline healthcare channels, affecting patients’ decisions to seek offline healthcare based on doctors’ online reputation. With the improvement of their online reputation, doctors have gained greater recognition among patients. The spillover effect has led some online patients to turn to offline healthcare channels, thereby increasing the workload of doctors in offline healthcare. The dermatologists at Peking Union Medical College Hospital achieved a 99.2% satisfaction rate through online medical services on the Haodf.com platform, which subsequently led to their offline daily outpatient volume exceeding 100 visits—significantly higher than the industry average of 30–40 visits. This empirical evidence demonstrates that the enhancement of physicians’ online reputation strengthens patients’ willingness to seek offline care. To accommodate the growing patient influx, physicians correspondingly increase their service effort levels. While this spillover effect generates beneficial outcomes by boosting offline demand, it simultaneously creates adverse impacts through increased workload pressure. This necessitates physicians to exercise prudent workload management within reasonable boundaries to prevent excessive work stress and prolonged patient waiting times caused by overcrowding.

As shown in Figure 8, in the scenario of spillover effect, the online reputation of doctors is positively correlated with their efforts in online healthcare. This is consistent with the scenario where the spillover effect is not considered. This trend indicates that, regardless of whether there are spillover effects or not, enhancing doctors’ online reputation can promote their online healthcare efforts. Doctors represent a highly specialized profession, and reputation holds substantial significance for them. On one hand, online reputation serves as a critical metric to demonstrate both professional competence and service capabilities, which in turn attracts a larger patient base. On the other hand, online reputation constitutes comprehensive feedback from patients regarding doctors’ services. It facilitates the realization of doctors’ social value and enhances their personal sense of accomplishment.

5. Managerial Implications

This study examines the incentives for physicians in a dual-channel healthcare service environment, employing modeling, analytical solutions, and simulation analysis to derive valuable insights. Based on these findings, we discuss incentive strategies and reputation system design from the perspectives of offline medical institutions and online healthcare platforms. Our research not only provides a theoretical foundation for offline public hospitals to establish cross-channel collaborative incentive mechanisms but also offers critical guidance for online platforms to implement tiered reputation-based incentives and integrate economic with non-economic incentives.

First, regarding establishing a cross-channel collaborative incentive mechanism, offline medical institutions should fully recognize the trans-channel value of online reputation and develop a linkage mechanism between online service performance and offline incentives. For public hospitals, physicians’ online evaluation metrics (such as patient satisfaction rates and consultation volume) can be incorporated into the performance assessment system and linked to incentive measures including professional promotion and allocation of specialist appointments. For instance, physicians with higher online reputation may be appropriately assigned increased offline consultation frequency or granted higher revenue-sharing ratios for registration fees, commensurate with the patient flow they generate.

Second, regarding implementing differentiated reputation-based incentive strategies, when it comes to tailored incentives for physician groups, online healthcare platforms should design tiered incentive schemes for different physician segments. For high-reputation physicians (e.g., “gold-tier doctors”), platforms can offer non-economic incentives such as exclusive traffic portals and brand exposure, supplemented by premium service pricing authority to meet their professional development needs. For early career physicians, basic incentives (e.g., guaranteed compensation) combined with reputation-based growth rewards (e.g., bonuses for each rating upgrade) can help them quickly establish an online presence. When it comes to patient-group-specific reputation incentives, younger patients, who rely more on internet-based healthcare, can be engaged through transparent reputation-building systems, such as “reputation badges” or “public service tags,” enhancing their interaction with physicians and incentivizing online participation. Older patients, who tend to trust offline physicians more, may benefit from displays of physicians’ online reputations (e.g., “10,000+ positive consultations”) to alleviate skepticism toward new channels. Additionally, under China’s traditional filial piety culture, adult children often play a pivotal role in elderly patients’ healthcare decisions. Platforms can introduce features like “family account linkage” and “proxy payment for medical expenses” to strengthen family involvement. Recognizing frequent caregivers with “Filial Caregiver” e-badges and enabling social sharing can further satisfy emotional and social recognition needs.

Third, regarding integrating economic and non-economic incentives, medical institutions and online platforms should flexibly combine economic and non-economic incentives based on physicians’ needs. For junior physicians, economic incentives (e.g., performance bonuses and consultation revenue-sharing) should dominate, supplemented by non-economic support like online training and patient feedback. For senior specialists, career development incentives (e.g., academic exchange opportunities and brand-building support) and social recognition (e.g., honorary titles and media exposure) are more effective. Platforms can also design hybrid incentive models, such as linking economic rewards with public service attributes (e.g., “volunteer consultation points redeemable for training opportunities”), addressing multi-tiered needs. This approach not only enhances physician engagement but also fosters long-term professional commitment.

6. Conclusions and Future Research Directions

6.1. Conclusions

This study constructs a common agency model under information asymmetry to systematically examine the impact of spillover effects on incentive mechanisms in dual-channel healthcare services, revealing the complex interplay between online reputation and cross-channel incentives. The main findings are summarized as follows:

(1)

In the absence of spillover effects, physicians’ online effort level exhibits a positive correlation with their online reputation, while the economic incentive intensity for online medical services shows a negative correlation with physicians’ online reputation. The positive relationship between online effort and reputation demonstrates a “effort-reputation” positive feedback mechanism in online healthcare services. High-quality services directly enhance patient satisfaction and platform visibility, while accumulated online reputation further motivates physicians to maintain or increase their service engagement. The negative correlation between incentive intensity and online reputation verifies the substitutive role of non-economic factors for traditional economic incentives. Unlike conventional service industries, healthcare is characterized by distinct humanitarian attributes and professional value orientations, where physicians’ decision-making is driven not only by financial rewards but also moderated by non-economic factors such as online reputation and professional fulfillment.

(2)

Under spillover effects, as online reputation increases, offline hospitals enhance their incentive intensity for physicians, while online healthcare platforms reduce economic incentives. When significant spillover effects exist, the incentive structure displays clear channel differentiation. Physicians with high online reputation experience “spillover” of their digital influence to offline settings, attracting more patients to seek in-person consultations. Offline hospitals respond by adjusting incentives to balance supply-demand dynamics or recognize physician value. This triggers an “online reputation-offline demand” conversion pathway: high online reputation → conversion of online consultations to offline demand → offline service shortage → adjustment of offline incentives. In the online channel, spillover effects enable high-reputation physicians to attract patients organically, diminishing the marginal utility of economic incentives and prompting platforms to reallocate incentives toward newer physicians. Thus, in dual-channel healthcare environments, spillover effects elevate online reputation from a single-channel incentive factor to a dual-channel determinant.

(3)

Compared to scenarios without spillover effects, both offline and online effort levels increase under spillover effects, demonstrating synergistic growth across channels. Typically, heightened offline incentives would prompt physicians to allocate more effort to offline services, while reduced online incentives would discourage online engagement. However, the asymmetric time cost between online lightweight consultations (e.g., 5 min responses) and offline visits (e.g., 30 min appointments) allows physicians to sustain online effort through “fragmented time utilization” even while increasing offline commitments. Consequently, despite the opposing incentive trends described in (2), physicians achieve coordinated effort growth in both channels due to reputation spillovers.

The study’s discovery of the “dual-channel effort synergy” phenomenon challenges the conventional assumption that online services may encroach on offline capacity, demonstrating that spillover effects can foster simultaneous effort enhancement across channels. Furthermore, this research proposes the “online reputation-offline demand” conversion pathway, elucidating the cross-channel influence mechanism of online reputation from a spillover perspective.

6.2. Limitations and Future Directions

While this study has produced several important findings, it is necessary to acknowledge certain limitations that simultaneously point to valuable directions for future research. First, regarding research perspective, this study primarily examines spillover effects between online and offline healthcare services but does not thoroughly investigate potential competitive relationships that may exist between these two channels. Second, in terms of research subject selection, the study is based on an assumption of physician homogeneity and fails to adequately consider the heterogeneous characteristics of physician groups. Third, concerning the selection of variables affecting spillover effects, the research mainly focuses on geographic distance as a key factor, while other potentially important non-geographic variables are not examined, including but not limited to patient satisfaction levels, establishment of doctor–patient trust relationships, and professional referrals from peer physicians.

Based on these research limitations and current development trends in dual-channel healthcare services, we propose the following research directions with significant theoretical and practical value: First, studies on incentive mechanisms in dual-channel healthcare services from a competition perspective could focus on examining how competitive relationships among physicians at different professional levels within the same platform influence physicians’ service provision decisions and incentive effects. Alternatively, they could explore how market competition between different online healthcare platforms affects physicians’ channel selection behavior and service incentive structures. Second, research on behavioral mechanisms from the perspective of physician or patient heterogeneity could investigate how factors such as physician titles and specialty types differentially influence the transmission pathway of “online reputation to offline incentives” or conduct an in-depth analysis of how individual patient factors including disease types and healthcare-seeking habits moderate their willingness and behavior regarding cross-channel service migration. These directions would not only address the current gaps but also contribute to a more nuanced understanding of the evolving dynamics in dual-channel healthcare ecosystems.