The influence of reference knowledge on the digital service quality and incentive mechanism

Hao, Jingjing; Zou, Xin; Chen, Yufeng; Liu, Yuan Article The influence of reference knowledge on the digital service quality and incentive mechanism Journal of Innovation & Knowledge (JIK) Provided in Cooperation with: Elsevier Suggested Citation: Hao, Jingjing; Zou, Xin; Chen, Yufeng; Liu, Yuan (2025) : The influence of reference knowledge on the digital service quality and incentive mechanism, Journal of Innovation & Knowledge (JIK), ISSN 2444-569X, Elsevier, Amsterdam, Vol. 10, Iss. 4, pp. 1-27, https://doi.org/10.1016/j.jik.2025.100745 This Version is available at: https://hdl.handle.net/10419/327640 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ The influence of reference knowledge on the digital service quality and incentive mechanism Jingjing Hao , Xin Zou , Yufeng Chen * , Yuan Liu * College of Economics and Management, Zhejiang Normal University, 688 Yingbing Road, Wucheng District, Jinhua City, Zhejiang Province, PR China ARTICLE INFO JEL codes: M11 C73 M31 O33 M15 O31 Keywords: Benchmark knowledge Varying weight Cost-sharing incentive Prospect theory Principal-agent model ABSTRACT In the digital service supply chain, digital service providers undertake the marketing platform development programs with satisfying digital service quality (DSQ) to help traditional retail enterprises (TREs) achieve digital technologies and merchandizing innovation. To illustrate the influence of external reference knowledge on principals’ feeling on DSQ and improvements, this study develops a novel framework to assess TREs’ perceived DSQ and design incentive strategies concerning differential cooperation scenarios. The study integrates the prospect theory and the principal-agent model to reveal the DSQ incentive strategies influenced by external references. Its contributions include (1) proposing DSQ appraisal indicator system and standardized computation process, (2) revealing the influence of external referencing knowledge on psychological utility in DSQ cooperation, and (3) exploring the incentive framework and equilibrium of DSQ utility in the differential degrees of information asymmetry. The managerial implications can assist the TREs in selecting digital marketing KPIs, determining proper benchmarks, confirming the dynamical dominance of external references, reducing the degree of information asymmetry, and implementing effective incentives. Introduction In the digital economy era, the customers’ shopping habits and activities are dramatically changing to global e-commerce sales via mobile devices (Dolega et al., 2021). As an effective business-driven hand (Azemi et al., 2022), digital marketing platform can provide the professional functions (e.g., precise promotion, real-time interaction, and data security) (Kashyap et al., 2025), enhancing customers’ shopping experience and retailing brand reputation. In the trend of digital transformation, traditional retail enterprises (TREs) have an urgent demand for building the digital marketing platform to achieve marketing innovation, such as data mining (Royle & Laing, 2014), business operation (Reim et al., 2022), and sale prediction (De Caigny et al., 2020). Digital marketing technologies have become the driving force in realizing effective precision marketing (Chou et al., 2022), exact market positioning (Palmi´ e et al., 2022), potential customer recognition (Yang et al., 2021), and clear customer segmentation (Kalia et al., 2022). Regarding platform competitiveness, digital service quality (DSQ) presents the customers’ comprehensive satisfaction with the digital marketing technologies and is required to determine the assessment criteria and standardization measurement. In the development process of digital marketing platform, TREs always cooperate with digital service providers (DSPs) to conduct joint development. As the agent, DSPs guarantee the digital platform with a certain DSQ (Anand & Goyal, 2019). The DSQ can describe the effect of joint development. More importantly, the TRE’s perspective on DSQ is significantly influenced by external reference points, such as the main competitor’s DSQ and industrial DSQ. If the TRE’s received DSQ is better than an external reference level, it will gain additional positive psychological benefits caused by the leading position. If the TRE’s received DSQ is lower than an external reference level, it will experience additional negative psychological effects because of the lagging DSQ. The influence of external reference knowledge on the TRE’s perceived DSQ should be explored to show its psychological utility. Particularly in the situation of many references, the varying weights of different benchmarks should be appropriately determined to describe the aggression effect. In the digital supply-chain cooperation, the degree of information asymmetry determines the participant’s dominant position, which affects the DSQ incentive strategy selection. In digital cooperation, the TRE is the principle and asks the DSP to develop the digital marketing platform with competitive advantages. As the agent, the DSP, first, * Corresponding authors. E-mail addresses: [email protected] (J. Hao), [email protected] (X. Zou), [email protected] (Y. Chen), [email protected] (Y. Liu). Contents lists available at ScienceDirect Journal of Innovation & Knowledge journal homepage: www.elsevier.com/locate/jik https://doi.org/10.1016/j.jik.2025.100745 Received 9 November 2024; Accepted 27 May 2025 Journal of Innovation & Knowledge 10 (2025) 100745 Available online 18 June 2025 2444-569X/© 2025 The Author(s). Published by Elsevier España, S.L.U. on behalf of Journal of Innovation & Knowledge. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ). always devises the initial decision-making on development investment, which is often influenced by self-interest toward its own optimal strategy (Greenstone et al., 2022). Later, the TRE has to accept the DSP’s investment result and final digital platform with DSQ, which leads to an adverse selection consequence (Pavlov et al., 2022). Because of information asymmetry, moral hazard is generated and may be detrimental to the TRE’s interests (Zhang et al., 2023). Consequently, establishing an effective incentive mechanism is a crucial management solution for the above ethical dilemma (Liu et al., 2022). Although previous studies contributed to the direct transaction effect, the incentive focused on the independent improvement. According to the prospect theory, the TRE’s perspective on DSQ is highly reliant on external references. The incentive objective can be expanded to psychological utility. To prevent the DSP’s moral hazard in the development cooperation, this study merges the prospect theory into a principal-agent model considering the TRE’s psychological utility regarding competition position and information asymmetry. The proposed cost-sharing incentive method can assist the TRE in achieving satisfied perceived DSQ in the digital service supply chain. As indicated in Figure 1, the steps of the study are indicated to highlight its general perspective. The contributions of the research include the following (1) The definition and a set of indicators of innovation-driven DSQ have been established, providing a foundational analytical framework for measuring digital marketing performance. (2) How external reference points affect the TRE’s psychological utility is examined with a focus on optimistic preferences. (3) The incentive solution under symmetric and asymmetric information situation is explored. The contents of the study are organized as follows. Section 2 summarizes existing research and research gaps. Section 3 presents the theoretical framework of the research. In Section 4, the definition of DSQ and the perceived utility considering dual reference points are presented, and the perceived DSQ under a single reference point is given. In Section 5, the incentive mechanism is conducted through the “principal-agent” theory. In Section 6, the incentive solution is provided under symmetric and asymmetric information situations. In Section 7, a numerical study is conducted to prove the effectiveness of the above method. Section 8 provides the research conclusions and future research topics. Literature review The study considers the overlapping digital marketing domains, reference points, and incentive methods. Consequently, this section provides a brief overview of the following three aspects. The subsection describes the research gap for precisely assessing the TRE’s overall psychological utility and designing related incentive solutions. The impact of digital technology on digital marketing In the new retail era, emerging digital technologies are rapidly changing the marketing environment in the areas as consumer behavior (Ratchford et al., 2022), social media with user-generated content (Babi´ c et al., 2020; ˇ Sola et al., 2022), digital marketing platforms (Veile et al., 2022) and online searching strategy (Lin et al., 2020; Agnihotri, 2020)). Ratchford et al. (2022) examined how digital technology affected consumers’ search costs and search behavior through online shopping, which revealed that the Internet shortened the customers’ consideration time. Babi´ c et al. (2020) explored the generation process of consumers’ electronic word-of-mouth in social media related to associate monetary value. Veile et al. (2022) conducted an exploratory numerical study to analyze how digital platforms changed industrial firms’ business models and marketing strategies. Lin et al. (2020) revealed that paid search engines could promote users’ purchasing frequency and increase customers’ lifetime value by effectively identifying high-value customers. The above related research contributes to understanding the various digital marketing processes affected by technology and provides the support for identifying the relevant DSQ indicators that reflect the current digital marketing landscape. The role of psychological utility and weighting methods in the supply chain Prior research in this domain provides a solid foundation for better understanding how reference knowledge impacts supply chain activities, providing a basis for incorporating psychological factors into the TRE’s economic benefit. Figure 1. Study steps. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 2 Psychological utility in supply-chain cooperation under reference points In supply-chain cooperation, reference points significantly influence the participants’ psychological competitive utility, which is widely used in ordering decisions (Wei et al., 2019; Uppari & Hasija, 2019)), pricing strategies (Das et al., 2021), supply-chain coordinate tactics (Qiu et al., 2022; Vipin & Amit, 2021), risk control (Liu & Chen, 2019), supplier selection (Chai et al., 2023), and supply-chain performance evaluation (Liang et al., 2022). Wei et al. (2019) studied the impact of external industry level and minimum profit expectations on the newsboy decision problem. Das et al. (2021) proposed a manufacturer’s loss aversion model under the reference level to design a pricing strategy in a green supply chain. Qiu et al. (2022) addressed the coordination problem concerning dynamic reference points in online-offline channels with different structures. Liu and Chen (2019) introduced a profit reference point into the decision-makers’ psychological perception of risk. Chai et al. (2023) established a sustainable supplier selection decision framework in which positive and negative ideal reference points were considered to describe decision-makers’ risk preferences. Liang et al. (2022) considered decision-makers’ bounded rationality under random subjective reference points and constructed a supplier performance evaluation model in five dimensions. The weighting method of psychological competitive utilities under multiple reference points To consider the contributions of multiple reference points, the weights of different reference points should be suitably designed to aggregate the participants’ psychological competitive utilities. Existing weighting methods include subjective designation (Zhong et al., 2022; Liang et al., 2020), additive method (Wei et al., 2019; Wang et al., 2020), and attitude evaluation (Zhu et al., 2017). Zhong et al. (2022) employed subjective equal weights to integrate psychological utility with monetary and time reference points. Wei et al. (2019) simply added the influence of the bottom line and the status quo reference point when measuring the psychological utility of newsboys. Zhu et al. (2017) treated decision-makers’ attitudes toward the reference points as the coefficient for determining the weights. The incentive solutions in supply chain cooperation In supply-chain cooperation, the research on incentive mainly focuses on the impact of incentives on supply-chain performance (Gao et al., 2023), incentive mechanism design (Chakraborty et al., 2019; Liu et al., 2022), and information management in incentive system (Li & Zhang, 2021; Fu & Xing, 2021). Gao et al. (2023) analyzed the response decisions of the supply chain under the incentive strategies, which revealed that incentives could enhance inventory carryover capability in decentralized supply chains. Chakraborty et al. (2019) addressed the cost-sharing mechanism between the retailer and the manufacturer, which intensified the value of a cost-sharing contract on improving supply-chain performance. Li and Zhang (2021) explored the influence of real-time information and the participants’ forecasting ability on the design of incentive mechanism in the supply chain, in which information acquisition could promote supply-chain members to distort optimal decisions. These studies on incentive solutions in supply-chain cooperation can provide a basic framework for us to design more effective incentive mechanisms that consider comprehensive psychological utility and external DSQ reference points in our research. In summary, existing research has revealed various incentive methods for improving the participants’ economic benefits and mitigating the agents’ moral hazard. However, in the digital economy era, the principal’s psychological feeling on DSQ is significantly influenced by the external reference knowledge and future potential. The incentive focus should be extended from single economic benefit to comprehensive psychological utilities, considering the effect of external DSQ reference points and varying weights. First, the definition, criteria, and computation process of DSQ should be updated according to the feature of digital economy. Second, the TRE’s psychological utility regarding the DSQ needs to be reasonably measured to illustrate the influence of external benchmarks. More importantly, the exploration of psychological utility was not employed in the principal-agent framework. In digital service cooperation, the DSP prioritizes its own benefits because of information asymmetry, which may be detrimental to the TRE’s interests. The degree of information asymmetry can affect the equilibrium of the principal-agent analysis. Consequently, an incentive method, which reasonably evaluates the TRE’s psychological utility and Figure 2. Theoretical framework. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 3 considers the degree of information asymmetry, should be explored to directly support the service supplier’s management activities. Theoretical framework This paper selects the digital service supply chain to explore the incentive solution for improving DSQ with regard to dual external references and varying weights. Combining digital marketing (Ratchford et al., 2022), the prospect theory (Wei et al., 2019), and weighting (Zhong et al., 2022) and incentive methods (Liu et al., 2022), the theoretical framework is proposed in Figure 2. The logic of the study is developed as “Actual DSQ and perceived DSQ” → “Aggression for comprehensive DSQ with varying weight” → “principal-agent framework” → “Incentive solutions in specific scenarios” → “Managerial implications.” In particular, the novel requirements of digital marketing provide the guidance on designing the definition and potential indicators of DSQ, which is the answer to the first research question. Next, the prospect theory is used to transfer the DSQ to the TRE’s perceived DSQ, which considers external reference points and varying weights to demonstrate future potentials, as the exploration of the second research question. Furthermore, to fulfill the third research gap, the principal-agent model is established to describe the improvement requirement of the TRE’s perceived DSQ, and the incentive theory explains the cost-sharing incentive solutions to prevent the DSPs’ moral hazard caused by information asymmetry. The TRE can use the incentive solutions to design suitable supply-chain contract to solve the adverse selection problem. Stage 1: Actual DSQ. Referring to the digital marketing requirements, first, DSQ is defined, and multiple indicators in the dimensions of digital tangibles, digital trust, digital interaction, customer centricity, and reliability are proposed as the KPIs (Büyük¨ ozkan et al., 2020). Second, the raw performance data, qi, as well as the expectations and tolerant intervals of KPIs, can be obtained. Next, the KPIs can be divided into the smaller-the-better, the larger-the-better, and the nominal-the-better, which provides a framework for standardizing and aggregating the DSQ (Taguchi, 1986). At the technology level, Artificial Intelligence (AI) can be utilized to determine appropriate DSQ indicators deconstructed from the TRE’s vision and mission. AI can handle a large amount of data and identify the key factors related to DSQ, which is in line with the insights into market and customer needs in the marketing theory. To avoid human operating error, Machine Learning (ML) could be employed in the data standardized process and ensure automated computation. A detailed calculation process is conducted in Section 4.1. Stage 2: Comprehensive DSQ under dual reference knowledge. Guided by the prospect theory (Barberis, 2013), the TRE’s value function under a single reference knowledge is developed. Additionally, optimistic preference, ki, is proposed to reflect the TRE’s attitude on the future improvement potential of DSQ. Considering the fierce market competition (Llopis-Albert et al., 2021), the main competitor’s DSQ, rc, and industrial DSQ, rh,are selected as dual references points. Moreover, to calculate the TRE’s comprehensive perceived DSQ, the influence of optimistic preference and varying DSQ distances are integrated, which induces dynamic weight in the aggregation process. The prospect theory focuses on an individual’s reliance on reference points when making decisions and their different perceptions of gains and losses. In this stage, data mining can be applied to obtain unstructured knowledge (e. g., industry survey and competitor’s operation report) online, identifying “industrial-level” and “competitor-level” DSQ benchmarks. Through data mining, specific and quantifiable reference points are found, making the application of the prospect theory in DSQ evaluation more specific and operable, and achieving a deep integration of theory and cutting-edge technologies in a quantitative perception of DSQ. Section 4.2 presents the above specific operations. Stage 3: Principal-agent framework and incentive mechanism. First, based on the comprehensive calculation of the TRE’s perceived DSQ, its psychological utility can be obtained, which concerns the influence of external reference points with economic benefits. Second, a principal-agent model containing incentive compatibility constraints and individual rationality constraint is proposed. Next, the incentive process of cost-sharing is designed to explore the optimal solution of the cooperation. In this stage, reinforcement learning can be applied to dynamically optimize incentive parameters (e.g., cost-sharing ratios) in the “principal-agent” model by analyzing real-time data on market conditions and psychological utility preferences. The trial-feedbackadjustment cycle can refine the related incentive strategies through iterative improvement and maintain robustness across differential scenarios containing risk preference shift or competitive intensification. This enables the “principal-agent” theory to adapt to the dynamically changing market environment in practical applications and transform the abstract incentive mechanism into specific strategies that can be adjusted and optimized in real time. The detailed operations are illustrated in Section 5. Stage 4: Incentive solutions in specific scenarios. According to the degree of the DSP’s private information, the optimal solutions in different supply-chain dominant conditions are discussed. First, under the condition of complete symmetric information, the TRE has a dominant position in the supply-chain cooperation, which prioritizes Table 1 Variables and their meanings. Variable Meaning Variable Meaning Y DSQ characteristic ylThe minimum boundaries of the tolerance interval of characteristic μ The optimal target value of characteristic yuThe maximum boundaries the tolerance interval of characteristic r Actual DSQ level qLThe standardized quality level of the large-the-better qSThe standardized quality level of the small-thebetter qNThe standardized quality level of the nominal-thebetter ω iThe weight of indicator in DSQ k The optimistic preference d The distance between actual DSQ and reference DSQ P(r)TRE’s perceived DSQ rhThe average DSQ level in the industry rmin The smaller of the two reference points rcThe main competitor’s DSQ level rmax The greater of the two reference points k1The optimistic preference of rmin P1The perceived DSQ under rmin k2The optimistic preference of rmax P2The perceived DSQ under rmax λThe weight of the reference point in TRE’s Perceived DSQ α The risk preference coefficient βThe risk aversion coefficient θThe loss aversion coefficient λ1The weight of rmin d1The distance between actual DSQ and rmin λ2The weight of rmax d2The distance between actual DSQ and rmax PI iThe comprehensive perceived DSQ when r ≥ rmax >rmin λI iThe weight of the ithreference point when r≥rmax >rmin PII iThe comprehensive perceived DSQ when r < rmin <rmax λII iThe weight of the ithreference point when r<rmin <rmax PIII iThe comprehensive perceived DSQ when rmin ≤r<rmax λIII iThe weight of the ithreference point when rmin ≤r<rmax φ(r)Value-added benefits of TRE φ[P(r)] Perceived value-added benefits of TRE ∅(r)Incentive fee B Fixed fee CS(r)Development cost of DSP V[ π T(r)] TRE’s benefit function of perceived DSQ V[ π S(r)] DSP’s benefit function of perceived DSQ J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 4 achieving its expected psychological utility. Second, the cost-sharing incentive solution of the “principal-agent” model in the case of complete asymmetric information is analyzed. Next, under partly asymmetric information, the equilibrium of the transaction is explored where the participants are fighting for the dominance. The incentive theory is centered on devising efficient incentive mechanisms to drive agents toward fulfilling principals’ objectives. In this stage, the blockchain technology is harnessed to ensure the transparency of information flow by recording unalterable transaction data, which serve as a dependable basis for evaluating the level of information symmetry. Blockchain can be leveraged to ensure transparent information flow by recording immutable transaction data. Assessing the degree of information symmetry (e.g., symmetric, partially asymmetric) could enable tamperproof validation on DSP performance and reduce moral hazard in incentive strategy design. The calculation process can be found in Section 6. Stage 5: Managerial implications. After the empirical study, some policy implications, such as, the selection of DSQ KPIs, determination of competitive benchmarks, adoption of varying weights and designation of incentive solutions, are provided, which can directly help the TRE to enhance the DSQ and improve the operation performance. In the following sections, the main terminologies and notations used in this paper are summarized in Table 1. Digital service quality and perceived utility As shown in Figure 3, this section illustrates the definition of DSQ and its computation method in Section 4.1, which contains the indicators, standardization and aggregation. The perceived DSQ concerning a reference point and the optimistic preference are put forward in Section 4.2. The TRE’s comprehensive perceived DSQ under dual reference points is calculated with regard to the dynamic dominance of external reference points in Section 4.3. Digital service quality and its computation method Digital service quality and its indicators Traditional Service Quality (SQ) primarily describes the customers’ satisfaction with the service (Chen et al., 2022). In the SERVQUAL framework, SQ reflects the customers’ expectations and needs regarding the service trust in offline channels (Barakabitze et al., 2019), which can be measured with the following five dimensions: tangibles, reliability, responsiveness, assurance, and empathy (Parasuraman et al., 2002). Because of the rapid development of mobile Internet, electronic SQ (e-SQ) focuses on the customers’ interactive assessments on online SQ, primarily evaluating independent online service processes (e.g., web browsing and online transactions) through Internet technologies with metrics such as response time and usability (Chao et al., 2024). E-SQ can be measured in four dimensions as follows: efficiency, system availability, fulfillment, and privacy (Chao et al., 2024). In the new retailing era, the integration of online service is emerging, and digital marketing platform can provide systematic digital solutions covering the overall marketing life cycle, which not only focuses on technological implementation (such as platform stability) but also emphasizes the deep integration of technology and business. For example, AI-driven precision marketing push directly improves the marketing return on investment Figure 3. Perceived DSQ calculation process. Figure 4. The evolutionary roadmap. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 5 (ROI) in retail enterprises, rather than merely optimizing online interactive experiences. DSQ represents a holistic evaluation of end-to-end digital solutions in the new retail era, extending to the entire marketing life cycle from real-time data collection and AI-driven personalization to customer engagement in innovation. The evolution of SQ, e-SQ, and DSQ is illustrated in Figure 4. To realize digital transformation from separated offline business to smart e-commerce, TREs always outsource the developing tasks of digital marketing platforms to digital technology companies (Anand & Goyal, 2019). In this digital cooperation, the traditional SQ should be expanded to smart system level, thus, the novel comprehensive concept of DSQ was born (Büyük¨ ozkan et al., 2020), emphasizing emerging digital marketing technologies, such as real-time data integration, AI-driven personalization, and value co-creation (Buyukozkan et al., 2020). Different from the SERVQUAL focusing on offline reliability and responsiveness (Collier & Bienstock, 2006), DSQ exhibits a series of digital capabilities, such as dynamic customer insights, tailored experiences, and customer engagement in innovation. Definition 1. DSQ refers to users’ subjective satisfaction in how digital services meet their digital needs. It is a dynamic construct that not only reflects the integration effectiveness in digital marketing life cycle but also concerns the outcomes of the digital service. The DSQ of digital marketing platform represents the TRE’s satisfaction with the digital service functions of a systematic solution, such as real-time data collection, smart preference recognition, accurate customer portrait, precise marketing push, and AI. Emerging information technologies have made the most important developments in the field of interactivity through the shifting from general mass marketing to individual precise marketing (Demirel, 2022). According to user expectations on digital platform, DSQ highly relies on extracting information from big data to enhance marketing performance. For example, during Alibaba’s Double Eleven campaign, DSQ manifested as the seamless alignment of technical performance and customer experience on its digital marketing platform. Real-time data collection ensures system reliability and sub-3-second latency. Smart preference recognition uses ML models to effectively predict purchase intention and significantly reduce customers’ acquisition costs. Precise marketing push servers’ dynamic advertisements to high-value segments identified via the Recency-Frequency-Monetary Value analysis. These DSQ-driven capabilities not only align with customer expectations but also demonstrate how big data extraction and AI integration contribute to measurable business outcomes (Kamble & Gunasekaran, 2020; Elia et al, 2022). According to Büyük¨ ozkan (2020), the indicators of DSQ comprise five dimensions as follows: digital tangibles, digital trust, digital interaction, customer centricity, and reliability. Some indicators reflect the application of digital technologies in the supply chain, such as traffic, time spent on page visit, customer information assets, and packet loss rate. Other indicators present the improvement of marketing performance because of the application of digital technology, such as average transaction value, ROI, and customer acquisition cost. The indicators in the digital tangibles dimension represent digitized equipment, facilities, and their digital properties (Büyük¨ ozkan et al., 2019). In particular, functionality reflects the availability of digital channel and service characteristics (Chan et al., 2020; Melovi´ c et al., 2021). Efficiency reflects the capability of providing suitable products and information with minimum effort (Liu et al., 2022; Varadarajan, 2020). The indicators in the digital trust dimension represent the performance and the stability of the digital platform, which can be measured by network performance indicators such as packet loss rate, transmission delay, and throughput (Skaka-ˇ Ceki´ c et al., 2023; Huang et al., 2018; Alnawas & Al Khateeb, 2022). The indicators in the digital interaction dimension consider the digital communication networks between companies and the supply chain members through digital platforms (Büyük¨ ozkan et al., 2019). Collaboration and mobile communication have been selected in this study to reflect the capability of digital interaction, which will be enhanced using digital technology in the marketing activities. The indicators in the customer centricity dimension represent an “outside-in” approach through innovative service delivery experience to fulfill the customer’s emotional needs by putting them at the heart of an organization (Büyük¨ ozkan et al., 2019). In particular, customer segmentation measures the ability to understand precisely the customers’ preferences and shopping behavior, such as frequency, recency, and monetary (Si et al., 2015). Customer insights are used to measure the transforming ability from customer analysis into marketing performance. The indicators in the reliability dimension consider the role of digital technology in achieving marketing objectives and reducing input costs (Büyük¨ ozkan et al., 2019). Some financial indicators, such as marketing ROI, marketing cost, and customer acquisition cost, are selected as the second-grade indicators. Some market performance indicators, such as international market share, trade competitiveness index, and revealed comparative advantage index, are included to reflect the improved performance after the trial operation on the digital platform. This indicator system is designed to provide an evaluation framework for the core operational dimensions of digital platforms. However, as different enterprises may have varying strategic priorities and operational environments, organizations can adapt or supplement relevant indicators according to their development goals and business needs in practical applications, ensuring that the indicator system aligns closely with strategic objectives. Note: Ns: Number of customers at the start of the period; Ne: Number of customers at the end of the period; Na: Number of customers acquired during the period; Nc: Number of chained customers in the given period; Nt: Total number of customers at the start of the period; Sc: overall marketing campaign costs spent on acquisition; St: marketing team salary; Ss: the cost of marketing software; So: overhead related to marketing (e.g. designers, consultants); CE: Company’s Export; TCE: Total Company’s Export; GE: Global Export; TGE: Total Global Export Standardization and aggregation of DSQ To ensure additivity and consistency across diverse DSQ indicators (with varying units, ranges, and definitions), data standardization is required. Additionally, there are three kinds of quality characteristics: the large-the-better (L type), the small-the-better (S type), and the nominal-the-better (N type). Suppose that the tolerance interval of characteristic Y is [yl,yu], in which yl and yu refer to the minimum and maximum boundaries, μ is the optimal target value. Let ε be an infinitesimal positive number extremely close to 0. The standardized quality level of the large-the-better, small-the-better and nominal-the-better quality characteristics, qL,qS and qN, can be designed as qL= ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ y−yl μ −yl ,y∈ (yl,yu) ε ,y=yl 0,y<yl ,qS= ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ yu−y yu− μ ,y∈ (yl,yu) ε ,y=yu 0,y>yu , qN= ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ y−yl μ −yl y∈ [yl, μ ] yu−y yu− μ y∈ ( μ ,yu) ε y=yloryu 0 y ∕∈ [yl,yu] (1) For aggregation, let n DSQ indicators have weights ω i( ω i≥0, ∑n i=1 ω i=1). The DSQ can be comprehensively described as the J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 6 weighted sum of qL, qS and qN. r=⎧ ⎨ ⎩∑ n i=1 ω iqi,∀qi∕= 0 0,∀qi=0 (2) Here, r ∈ [0,1]. If any quality performance of an indicator is not located in the quality interval, r =0. Only if the performances of all the quality characteristics meet the quality requirement r >0. Especially, if any metric is located at the boundary, r = ε →0+. TRE’s perceived DSQ and optimistic preference concerning dual DSQ reference knowledge TRE’s perceived DSQ based on prospect theory According to the prospect theory, the participant’s gain-loss state significantly impacts psychological utility, especially when it faces reference level (Barberis, 2013). The essence of a user’s perceived utility is the outcome of the psychological accounting process determining the gain/loss interval through reference points and an asymmetric value function (Tian et al., 2022). Different from the “absolute utility maximization” assumption, perceived utility in the prospect theory reflects the differential psychological feelings regarding benefits and losses (Jin et al., 2024). In this study, TREs’ perceived DSQ represent principals’ subjective utilities—gain and loss—because of the dynamic comparison between DSQ and the external reference points. In the digital service supply chain, the prospect theory can reveal how external reference knowledge influence TREs’ perceived DSQ. TREs may have reference knowledge based on past experiences, industry norms, or anticipated future scenarios. Consequently, the prospect theory can help TREs gain deeper insights into the psychological dynamics driving the preferences and choices. The prospect theory is essentially applied to model TREs’ preferences for adopting digital technologies in precision marketing in the digital retailing era. Consequently, perceived DSQ is conceptualized as the TREs’ subjective evaluation of the digital performance derived from digital marketing platforms, caused by the cognitive comparisons between actual DSQ outcomes and external reference points. Guided by the prospect theory (Tversky & Kahneman, 1981), the formation of perceived DSQ involves two interdependent psychological elements as follows: reference dependence and loss aversion. Reference dependence means that the TRE evaluates the DSQ not only in absolute digital performance but also relative to external knowledge as benchmarks. Loss aversion shows that negative deviations from reference knowledge can generate stronger psychological impacts than equivalent gains. In particular, if the TRE’s DSQ is larger than an external reference, it will obtain the additional positive psychological benefit caused by leading position, and vice versa. Additionally, the distances between actual DSQ and external reference points can show the future development space and influence the TRE’s perceived DSQ as well. If the actual DSQ is lower than a referencing level, the TRE’s pessimistic perspective damages its perceived DSQ. As the gap is continuously changing, the TRE’s optimistic attitudes regarding external reference points are dynamically switching, which creates the varying dominance of external reference points. If the TRE’s received DSQ level is r, let us assume that the DSQ reference point, such as industrial DSQ or competitor’s DSQ, is r0. The TRE’s perceived DSQ under the influence of DSQ reference point r0 is as follows: P(r) = {(r−r0) α ,r0≤r≤1 −θ(r−r0)β,0≤r<r0(3) According to empirical data, α =β=0.88, and θ=2.25 (Barberis, 2013). The relationship between TRE’s perceived DSQ, P(r), and DSQ level, r, can be represented as shown in Figure 5, let P(r=r0) = 0. If there is no DSQ reference point, assume that TRE’s psychological utility is a linear function L(r), ∂ L ∂ r>0, L(r0) = 0. As illustrated by Figure 5, the DSQ reference point enhances the TRE’s perceived DSQ brought by the gap between actual quality r and referenced level r0. In particular, when r =r1<r0, the risk aversion coefficient, β, will let TRE feel more depressed due to the backward situation, P(r1)<L(r1). Once r=r2>r0, the risk preference coefficient, α , will let TRE be more proud because of quality leading, P(r2)>L(r2). TRE’s optimistic preference-driven dynamic aggregation of perceived DSQ In addition to its reference points, the TRE exhibits an optimistic preference—a behavioral propensity to prioritize future development potential over current performance gaps, which can be formalized through the second derivative of the value function Definition 2: Optimistic preference is the decision-makers’ positive perception for future development, which is induced by the gaps between actual performance and reference levels. The TRE’s optimistic preference can be designed as follows: k= ∂ 2P(r) ∂ r2(4) Figure 5. TRE’s psychological utility curve. Figure 6. The TRE’s value function under double reference points. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 7 Suppose that industrial DSQ reference is rh and the competitive DSQ reference is rc, rmax =max{rh,rc},rmin =min{rh,rc}. As shown in Figure 6, TRE’s perceived DSQ caused by rmin and rmax are P1(r)and P2(r), which behaves the weight as λ1 and λ2. The second derivative of the value functions k1, k2 are k1= ∂ 2P1(r) ∂ r2,k2= ∂ 2P2(r) ∂ r2(5) The weights of DSQ reference point are related to the optimistic preference coefficients, which reflect the TRE’s attitude on the future development potential of various DSQ reference points. If the TRE is in the lagging position, i.e. the perceived DSQ is positive but has a more promising future potential, it is more inclined to endure current unpleasant events and alleviate its sense of apprehension, which leads to a lower weight to this reference knowledge. If the TRE is in the dominance competition position, it experiences a more declining trend, the restricted opportunity for quality development will result in reduced prospects and less positive attitude on perceived DSQ. The changing dominant position of reference points creates varying weights of industrial and competitive psychological utilities, which can be designed as λ1=|k2| |k1| + |k2|,λ2=|k1| |k1| + |k2|(6) The comprehensive utility function is P(r) = ∑ i=1,2 λiPi=λ1P1+λ2P2 = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ −θk2 k1+k2 (r−rmin)β−θk1 k1+k2 (r−rmax)β,r<rmin <rmax k2 −k1+k2 (r−rmin) α +θk1 −k1+k2 (r−rmax)β,rmin ≤r<rmax k2 k1+k2 (r−rmin) α +k1 k1+k2 (r−rmax) α ,r≥rmax >rmin (7) When r <rmin <rmax, the TRE’s DSQ is weaker than all reference levels, which generates dual negative utilities, P1= − θ(r−rmin)β <0, P2= − θ(r−rmax)β<0. According to the dual references rmin and rmax, the corresponding reference weighs are λ1=k2 k1+k2 and λ2 =k1 k1+k2. Because the comparative smaller improving space of P2 creates more panic feeling, P2 occupies more dominant position than P1, λ2 >λ1. When rmin ≤r<rmax, the TRE’s DSQ is located between the external references. The leading on rmin generates a positive utility, P1 = (r−rmin) α ≥0 and the lag on rmax causes a negative utility, P2 = − θ(r−rmax)β<0. Additionally, the related reference weighs are λ1 = k2 −k1+k2 and λ2=−k1 −k1+k2. When r increases from rmin, because P2 creates more panic feeling, P2 occupies more dominant position than P1, λ2 >λ1. If r is far from rmin, the development space of P2 is higher than the deterioration space of P1, which induces TRE’s comprehensive focus on the positive utility P1, λ2<λ1. When r ≥rmax >rmin, the TRE’s DSQ is higher than all reference levels, which generates dual positive utilities, P1= (r−rmin) α >0,P2= (r−rmax) α ≥0. According to the dual references rmin and rmax, the corresponding reference weighs are λ1=k2 k1+k2 and λ2=k1 k1+k2. Because the comparative larger P2 creates more satisfying feeling, P2 occupies more dominant position than P1, λ2>λ1. Further discussion on geographic location and firm size Let us suppose that a targeted TRE, i, in a certain city, has determined its industrial DSQ, rh, and competitor’s DSQ, rc; its annual sale revenue is sri, and the city’s annual GDP is gdpi. To expand the reference knowledge to another firm in another city, the prosperity efficient and the scale efficient can be used to describe the influence of the TRE’s geographic location and firm size on external reference levels. Prosperity efficient, θj, shows the influence of geographic locations, such as city j, on industrial DSQ, rh, comparing to that of the targeted city i. Let us assume that the annual GDP of city j is gdpj. The prosperity efficient equals the ratio of annual GDPs: θj=gdpj gdpi. If another TRE in city j wants to determine its industrial DSQ, rj h, it will be directly based on city’s industrial DSQ, rh, rj h=θjrh=gdpj gdpirh. Scale efficient, ϑk, denotes the influence of firm size, such as sale revenue srk, on the competitor’s DSQ rh, compared to the targeted TRE i. Let us assume that TRE k’s annual sale revenue is srk. The size efficient can be set as the ratio of annual sale revenue, ϑk=srk sri. If another TRE k determines its competitor’s DSQ, rk c, it will be directly based on city’s industrial DSQ, rc, rk c=ϑjrc=srk srirc. Incentive mechanism for improving TRE’s DSQ After achieving the TRE’s perceived DSQ, a “principal-agent” model describing the outsourcing cooperation between it and the DSP is established to explore the incentive mechanism, and the analysis process is demonstrated in Figure 7. Section 5.1 illustrates the benefits and costs of TREs and DSPs. In Section 5.2, the “principal-agent” model containing the cost-sharing incentive solution, individual rationality constraint (IR), and incentive compatibility constraint (IC) is designed to explore the cooperative relationship. In Section 5.3, the incentive solution design process is explored. The incentive mechanism plays a crucial role in motivating the DSPs to improve the DSQ of the digital marketing platform and providing stronger marketing support for the TREs. Concerning the influence of the incentive mechanism, the DSPs actively strive to improve the DSQ from multiple dimensions. Specially, in the digital tangible dimension, DSPs can innovatively optimize the infrastructure and functional modules to increase the online review time and page visiting length. According to the digital trust dimension, they could optimize algorithms to enhance data security and service stability. In the digital interaction dimension, Figure 7. Steps of incentive mechanism. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 8 in which the TRE’s and the DSP’s psychological utility are V[ π T(r)] = 0.178, V[ π S(r)] = 0.982, respectively. The comparison is presented in Table 4. As shown in Table 4, through cost sharing incentive, the second-best will be obtained at r∗ 2=0.5. The DSP will actively improve the DSQ level from r∗ 2(0.26)to r∗ 2(0.5), achieving an increase of 92.31%. The TRE’s psychologically utility is increased from 0.178 to 1.81, reaching a promotion of 916.85%. And the DSP’s psychologically utility is improved from 0.982 to 1.25, obtaining an elevation of 27.29%. Optimal solution of the outsourcing cooperation under partly asymmetric information condition In this situation, let V[ π S(r)] = π S(r) = 1−r3+g∗r, V1(r) = (1− ω )V[ π S(r)] + ω V[ π T(r)] and ω =0.4. The TRE’s perceived DSQ increases as the enhancement of the received DSQ level. In this situation, V1(r) = 0.6∗(1−r3+g∗r)+0.4{ln[P(r) + 1] + 2−g∗r} The information advantage of the DSP is weaker than that of completely incomplete information but stronger than that of complete information, resulting in r∗ 3 meets ∂ V[ π S(r∗ 3)] ∂ r∗ 3=0. When r ∈[0,r∗ 3), ∂ V[ π S(r∗ 3)] ∂ r∗ 3 >0; When r ∈[r∗ 3,1), ∂ V[ π S(r∗ 3)] ∂ r∗ 3<0. At the same time, the TRE’s psychological utility should not be lower than that in the completely asymmetric information condition, i.e. V[ π T(r)] >1.81. Referencing to Equation (8) the “principal-agent” model under partly asymmetric information can be designed as maximize 0.6∗(1−r3+g∗r)+0.4{ln[P(r) + 1] + 2−g∗r},(obj −I) s.t.⎧ ⎨ ⎩ r∈ [0,1],(C1) ln[P(r) + 1] + 2−g∗r>1.81,(C2) 1−r3+g∗r>0.657,(C3) The equilibrium solution of this model is obtained through Lingo. The cost-sharing ratio, g3, is 0.554, r∗ 3=0.643, and V[ π T(r∗ 3)]=2.015. In summary, the comparison of incentive effects in different situations is shown in Table 5. According to Table 5, high DSQ level, r∗ 1=0.7, is achieved without additional incentive fees in the completely symmetric information situation, i.e. g1=0. In the asymmetric information, if no incentive fees, g− 2=0, are given to the DSP, the delivered DSQ was at a low level as r∗ 2 =0.26. However, the DSQ level was significantly improved as r∗ 3(0.643)>r∗ 2(0.5)>r∗ 2(0.26)after the implement of incentives. Especially, the DSQ levels in the asymmetric information are lower than that in the completely symmetric information, r∗ 1, which is mainly caused by the TRE’s dominance position. Comparison analysis To aggregate the specific psychological utilities in different reference points, the subjective weighting method is commonly used by attaching fixed weights to different reference points (Wei et al., 2019; Uppari & Hasija, 2019; Zhong et al., 2022; Wang et al., 2020; Weingarten et al., 2019; Tu et al., 2022). However, the fixed weights failed to describe the principal’s psychological fluctuation in the dominance of reference points. Especially when r =ri, i =c,h, Vi=0, the principal will pay complete notice on another reference point by giving absolute dominant weight. Comparison of the perceived DSQ For example, Zhong introduced equal weights to dual reference points (Zhong et al., 2022), Pʹ(r) = 0.5P1+0.5P2, which is described as a red line in the absolute middle of P1 and P2. The result comparison between Zhong’s equal and dynamic weights proposed in this study provides the curve displays in Figure 12. In the part of 0 ≤r<0.24, the comprehensive psychological utility PII(r)is flatter than Pʹ(r). Due to PII 2<PII 1<0, P2 creates more panic feeling, λII 1<0.5<λII 2. Because the DSQ gap d1 is reducing, negative PII 1 is increasing up to 0, and the dominance position of PII 2 is continuously enhanced. In the part of 0.24 ≤r<0.62, the positive PIII 1 is increasing from 0, which starts to play a role in comprehensive utility. Driven by the increase in positive PIII 1 and its weight λIII 1, PIII(r)is rapidly rising. Additionally, when r is closer to rh, DSQ gap d2 is eliminating and negative PIII 2 is increasing up to 0, which causes the absolute dominance of PIII 1. In the part of 0.62 ≤r≤1, both PI 1 and PI 2 are positive, PI 1>PI 2>0, which contributes to the increase of comprehensive utility. The principal determines the different weights on dual reference points according to future development prospects. Due to k2<k1<0, the deteriorating space feeling on PI 2 is larger than that on PI 1, which leads to λI 2<0.5<λI 1, PI(r)>Pʹ(r). With the gap between PI 2 and PI 1 is reducing, λI 1 and λI 2 are tending to equal condition. Comparison of the optimal solution In the symmetric information situation. Under dual reference points, considering varying weights, r∗ 1=0.7, g1=0, V[ π T(r1)] = 2.37. Similarly, for the fixed weights, λ1=λ2=0.5, the DSP’s IR is a hard constraint, and it will cooperate only if its actual benefit is not less than its opportunity benefits, π S. Therefore, the optimal solution is located at r∗ 1 ʹ=0.7, gʹ 1=0, Vʹ[ π T(r1)] = 2.27. Because of the consideration of prospect, the TRE’s comprehensive utility increases. In the completely asymmetric information situation. In a completely asymmetric information situation, considering the varying weight, the optimal solution can be obtained at r∗ 2=0.47, g2=0.66, and V[ π T(r∗ 2)]=1.61. Similarly, when the fixed weights, λ1=λ2=0.5, the “principal-agent” model under incomplete information can be designed as follows: maximize ln[Pʹ(r) + 1] + 2−g∗r,(obj −I) s.t.⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 3∗r2=g,(C1) r∈ [0,1],(C2) ln[P’(r) + 1] + 2−g∗r>0.178,(C3) 1+r3−g∗r>0.657,(C4) The equilibrium solution of this model is obtained through Lingo. Using the fixed weights, the optimal solution is obtained at r∗ 2 ʹ=0.47, Figure 12. Comparison of different psychological utility measurement method. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 15 gʹ 2=0.66, and Vʹ[ π T(r∗ 2)]=1.61. In the partly asymmetric information situation. In a partly asymmetric information situation, considering the varying weight, the optimal solution can be obtained at r∗ 3=0.643, g3=0.554, and V[ π T(r∗ 3)]= 2.015. Similarly, when the fixed weights, λ1=λ2=0.5, the “principalagent” model under incomplete information can be designed as maximize 0.6(1−r3+g∗r)+0.4{ln[Pʹ(r) + 1] + 2−g∗r},(obj −I) s.t.⎧ ⎨ ⎩ r∈ [0,1],(C1) ln[P’(r) + 1] + 2−g∗r>1.61,(C2) 1+r3−g∗r>0.657,(C3) The equilibrium solution of this model is obtained through Lingo. Under fixed weights, the optimal solution is located at r∗ 3 ʹ =0.62, gʹ 3 = 0.94, and Vʹ[ π T(r∗ 3)]=1.62. According to the result in Table 6, in the symmetric information situation, the optimal solution is obtained at the same DSQ level under the dual weighting method, which is mainly caused by the same hard constraint. However, although the DSQ level and cost-sharing ratio is equal, the TRE’s psychological utility is different, V[ π T(r1)] >Vʹ[ π T(r1)], due to the consideration on the development potential. In the completely asymmetric information situation, the incentive ratio is lower than the situation under varying weights. However, the TRE’s psychological utility, V[ π T(r∗ 2)], is higher than that in fixed weight method, Vʹ[ π T(r∗ 2)], which is consistent with the conclusion of the perceived DSQ comparison above. In the partly asymmetric information situation, the DSQ level in the fixed weighting method is lower than that under varying weights, i.e., r∗ 3 >r∗ 3 ʹ, which is is mainly caused by the impact of future development potential on the TRE’s psychological utility. In general, considering the varying weights, higher DSQ levels and psychological utility can be obtained with a lower incentive cost. Sensitivity analysis on incentive effect Sensitivity analysis of reference knowledge Let us suppose that the industry-average reference level is fixed, rh = 0.24 and rc>rh. The sensitivity analysis of the cost-sharing incentive ratio on the changing reference level can be conducted. In particular, when the reference level gradually changes 10% from 0.62, the set of rc values is obtained by increasing and decreasing it by 10%,20%, 30%, and 40%, respectively (rc=0.372, 0.434, 0.496, 0.558, 0.62, 0.744, 0.806, and 0.868). Repeating the incentive design process above, the optimal solution under different information situation can be obtained. Symmetric information situation. In a completely symmetric information situation, referring to Theorem 1, the optimal solution is located where r∗ 1=0.7, g1=0. If so, the TRE’s competitive utilization is V[ π T(r1)] = 2.37. Similarly, repeating the steps, one can obtain the optimal solution under different information situations, shown in Table 7. In completely symmetric information, the optimal DSQ is not related to the competitor’s reference level, which depends only on the DSP’s opportunity benefit π S. As the TRE handles the information advantage, it can directly observe the DSP’s DSQ investment and force the latter to choose its most expected level. In this situation, the TRE does not need to pay additional incentive fee. Completely asymmetric information situation. When rc=0.558, rh= 0.24, referring to Equation (8), the “principal-agent” model can be designed as maximize ln[P(r) + 1] + 2−g∗r,(obj −I) s.t.⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 3∗r2=g,(C1) r∈ [0,1],(C2) ln[P(r) + 1] + 2−g∗r>0.178,(C3) 1−r3+g∗r>0.657,(C4) The equilibrium solution of this model is obtained through Lingo. In the optimal condition, the cost-sharing ratio, g2=0.288, r∗ 2=0.31, and V[ π T(r∗ 2)]=1.874. Similarly, repeating the above steps, one can obtain the optimal solution under different information situations when rc=0.372, 0.434, 0.496, 0.558, 0.62, 0.744, 0.806, and 0.868, respectively, which are shown in Table 8. In completely asymmetric information situation, the DSQ equilibrium is positively correlated to the main competitor’s reference level. Because the DSP absolutely handle the the information advantage, it can hide its DSQ investment. In this situation, the TRE needs to pay additional incentive fee to improve the DSQ level. The TRE’s comprehensive utility is negatively correlated to the main competitor’s reference level, which is mainly due to the increasing incentive fee as the improvement of DSQ level. As shown in Figure 13, influenced by the completely asymmetric information, the graphical trends illustrate the dynamic interplay among the competitive reference knowledge, rc, cooperative equilibrium, r∗ 2, cost incentive coefficient, g, and the TRE’s comprehensive utility, V. As the reference knowledge, rc, increases, the blue curve exhibits a gradual upward trajectory with decelerating growth, indicating diminishing marginal improvement of DSQ regarding incentives on cooperation. Concurrently, the yellow curve rises sharply (from 0.415 to 0.961) reflecting the additional costs required to sustain cooperation. The interaction between these trends drives the green curve into a persistent decline (from 1.999 to 1.493), suggesting accelerated erosion of the TRE’s comprehensive utility by incentive costs. Therefore, the TRE needs to identify a reasonable competitive reference level to prevent the blind improvement in DSQ and pay more incentive costs, which may lead to a reduction in overall utility. In partly asymmetric information situation. In partly asymmetric information situation, when rc=0.558, rh=0.24, referring to Equation (8), the “principal-agent” model can be designed as follows: maximize 0.6∗(1−r3+g∗r)+0.4{ln[P(r) + 1] + 2−g∗r},(obj −I) s.t.⎧ ⎨ ⎩ r∈ [0,1],(C1) ln[P(r) + 1] + 2−g∗r>1.874,(C2) 1−r3+g∗r>0.657,(C3) The equilibrium solution of this model is obtained through Lingo. The cost-sharing ratio, g3, is 0.278, r∗ 3=0.513, and V[ π T(r∗ 3)]=2.114. Similarly, repeating the above operations, we can obtain the optimal solutions under different information situations when rc=0.372, 0.434, Figure 13. Sensitivity analysis of rc in completely asymmetric information situation. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 16 0.496, 0.558, 0.62, 0.744, 0.806, and 0.868, respectively, shown in Table 9. In partly asymmetric information situation, the DSQ equilibrium and the TRE’s comprehensive utility are lower than that at the completely symmetric information situation but higher than that at the completely asymmetric information. The incentive equilibrium solution, r∗ 3, and the TRE’s comprehensive utility, V[ π T(r∗ 3)], is primarily related to the bargaining power between the DSP and the TRE, where neither can prioritize their own utility. In this case, the DSP’s relative information advantage prioritizes its comprehensive utility in the incentive goal, resulting in an overall decline in the TRE’s comprehensive utility. Particularly, at a certain reference level (rc=0.62), the TRE’s incentive fee decreased because of participation constraints, resulting in a temporary rebound in its comprehensive utility. As shown in Figure 14, the increase in competitive reference knowledge, rc, drives complex interactions among the cooperative equilibrium, r∗ 3, cost incentive coefficient, g, and the TRE’s comprehensive utility, V. The adjustment of incentive cost, g, keeps nonlinear correlation to the competitive reference knowledge, rc, which is primarily caused by the TRE’s partly information advantage. The sensitivity of r∗ 3 on the reference knowledge, rc, is characterized by non–monotonic fluctuations with an overall upward trend. In the initial stage (rc=0.372→0.496), the cooperative equilibrium, r∗ 3 drops from 0.495 to 0.434 and then rebounds to 0.496, reflecting short-term suppression of cooperation by competitive pressure. In the mid-phase (rc=0.558→0.744), the cooperative equilibrium, r∗ 3, rises steadily to 0.836, indicating significant efficiency gains from incentives under moderate competition. In the late phase (rc>0.744), the growth of rc slows (0.836→0.925) as the surge in incentive fee offsetting the positive effects of competition. Overall, rc exhibits phase-specific optimization, but incentive efficiency diminishes under high competition intensity. The sensitivity of V to the reference knowledge, rc, follows a “decline-brief rebound-accelerated decline” pattern. In the initial stage (rc=0.372→0.558), the TRE’s comprehensive utility, V, drops from 2.100 to 1.895 because of the rising incentive fee, which erodes its utility. In the mid-stage (rc=0.620), V briefly rebounds to 2.015, consistent with the dip in the incentive fee, g, suggesting transient efficiency gains from partly asymmetric information. In the late stage (rc >0.620), the incentive fee, g, rebounds sharply (up to 0.974), driving the TRE’s comprehensive utility down from 1.892 to 1.675. Overall, the TRE’s comprehensive utility, V, is dominated by the nonlinear fluctuations of incentive fee, where high competition intensity leading to the utility decreases because of prohibitive incentive costs. Sensitivity analysis of the degree of information symmetry To explore the influence of the degree of information symmetry on incentive effect, let ω increase from 0.1 to 0.9. Repeating the calculation process as ω =0.4, the corresponding excitation equilibrium solution can be obtained. For example, when ω =0.1, the TRE’s perceived DSQ increases as the enhancement of the received DSQ level. V1(r) = 0.9∗(1−r3+ g∗r)+0.1{ln[P(r) + 1] + 2−g∗r}. Referencing to Equation (8) the “principal-agent” model under partly asymmetric information can be designed as follows: maximize 0.9∗(1−r3+g∗r)+0.1{ln[P(r) + 1] + 2−g∗r},(obj −I) s.t.⎧ ⎨ ⎩ r∈ [0,1],(C1) ln[P(r) + 1] + 2−g∗r>1.81,(C2) 1−r3+g∗r>0.657,(C3) The equilibrium solution of this model is obtained through Lingo. The cost-sharing ratio, g3, is 0.721, r∗ 3=0.708, and V[ π T(r∗ 3)]=1.871. In summary, the comparison of incentive effects in different situations is shown in Table 10. According to Table 10, when ω is in the range of 0.1–0.3, r∗ 3 remains stable at 0.708, and the incentive fee keeps at 0.721 because both parties have limited information. The DSP occupies the dominance because of its larger weight. As ω increases, r∗ 3 decreases and, then, remains stable within a certain range and finally shows a small-scale changing trend. The reason is the TRE constantly adjusts its incentive strategy because of the change in its dominant power. The incentive fee decreases significantly when ω increases. When the degree of information symmetry is low, high incentives are needed to mobilize enthusiasm. However, when the degree of information symmetry increases, the TRE can guide the cooperation through a reasonable mechanism by virtue of its dominant power, and no high-level incentives are required. Regarding on the TRE’s utility, when ω is lower than 0.3, due to the stability of the cooperation model and the incentive cost, the utility remains unchanged at 1.871. As ω increases, the TRE’s utility is positively related to the degree of information symmetry. The adjustment of the equilibrium solution and the decrease in the incentive cost enable the enterprise to better integrate resources, reduce costs and risks, and create more value. That is the reason of continuous promotion and increasing cooperation utility. In the completely symmetric information situation, the TRE’s psychological utility V[ π T(r∗ 1)]=2.37, is higher than that in other situations, which is caused by its dominance position in the supply-chain cooperation. In completely asymmetric information situation, with the implementation of incentives, the TRE’s psychological utility, V[ π T(r∗ 2)], is gradually improved from 0.178 to 1.81.In particular, the TRE’s psychological utility, V[ π T(r∗ 3)], is higher than V[ π T(r∗ 2)], but lower than V[ π T(r∗ 1)], which is consistent with the TRE’s information advantage. Sensitivity Analysis of geographic location When the GDP of the targeted city is fluctuating compared to Hangzhou GDP, the prosperity coefficient, θj=gdpj gdpHangzhou, gradually changes from 1. Let the set of θjvalues increase and decrease by 10%, 20%, 30%,and 40%, respectively (rj h=0.144, 0.168, 0.192, 0.216, 0.24, 0.264, 0.288, 0.312, and 0.336). Repeating the above incentive process, the optimal solution under different information situation can be obtained in the following situations. Symmetric information situation. In the completely symmetric information situation, referring to Theorem 1, the optimal solution is determined by the DSP’s opportunity benefit π S, where r∗ 1=0.7, g1=0. TRE’s competitive utilization is V[ π T(r1)] = 2.37. Similarly, one can obtain the optimal solution when rj h=0.144, 0.168,0.192,0.216,0.24,0.264,0.288,0.312,and 0.336, respectively (Table 11). In completely symmetric information, the optimal DSQ is not related to the prosperity coefficient, θj, which shows the validation of Theorem 1. Figure 14. Sensitivity analysis of rc in partly asymmetric information situation. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 17 Completely asymmetric information situation. In this situation, when rh = 0.24, rj h=90%rh=0.216, referring to Equation (8), the “principalagent” model can be designed as follows: maximize ln[P(r) + 1] + 2−g∗r,(obj −I) s.t.⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 3∗r2=g,(C1) r∈ [0,1],(C2) ln[P(r) + 1] + 2−g∗r>0.178,(C3) 1−r3+g∗r>0.657,(C4) The equilibrium solution of this model is obtained through Lingo. In the optimal condition, the cost-sharing ratio, g2=0.288, r∗ 2 =0.484, and V[ π T(r∗ 2)]=1.836. Similarly, one can obtain the optimal solution under different information situations when rj h=0.372, 0.434, 0.496, 0.558, 0.62, 0.744, 0.806, and 0.868, respectively, which are shown in Table 12. The trends of equilibrium, incentive cost and the TRE’s utility are shown in Figure 15. As shown in Figure 15, influenced by the completely asymmetric information, the graphical trends illustrate the dynamic interplay of the prosperity coefficient, θj, cooperative equilibrium, r∗ 2, incentive coefficient, g, and the TRE’s comprehensive utility, V. As the GDP of geographic location, θj, increases, the blue curve (equilibrium trend) exhibits a gradual upward trajectory with decelerating growth, indicating diminishing marginal improvement on the DSQ of incentives on cooperation. In addition to that, the yellow curve (incentive intensity) rises sharply (from 0.654 to 0.872), reflecting the additional costs required to maintain the cooperation. The interaction between these trends drives the green curve, the TRE’s utility trend, into a persistent decline (from 1.91 to 1.694), presenting the accelerated erosion of the TRE’s comprehensive utility influenced by the additional incentive cost. To sum up, in a completely asymmetric information situation, the DSQ equilibrium is positively correlated to the prosperity coefficient, θj, because of the increasing industrial level in the prosperity area. In this situation, the TRE needs to pay an additional incentive fee to improve the DSQ level. The TRE’s comprehensive utility is negatively correlated to the prosperity coefficient, θj, because of the increasing incentive fee for improving the DSQ level. In partly asymmetric information situation. In the partly asymmetric information situation, when rc=0.62, rj h=90%rh=0.216, referring to Equation (8), the “principal-agent” model can be designed as maximize 0.6∗(1−r3+g∗r)+0.4{ln[P(r) + 1] + 2−g∗r},(obj −I) s.t.⎧ ⎨ ⎩ r∈ [0,1],(C1) ln[P(r) + 1] + 2−g∗r>1.836,(C2) 1−r3+g∗r>0.657,(C3) The equilibrium solution of this model is obtained through Lingo. The cost-sharing ratio, g3, is 0.848, r∗ 3=0.62, and V[ π T(r∗ 3)]=1.845. Similarly, repeating the above operations, the optimal solutions under different situations can be gained when rj h=0.372,0.434,0.496, 0.558,0.62,0.744,0.806,and 0.868, respectively, shown in Table 13. The trends of changing equilibrium, incentive cost and TRE’s utility are shown in Figure 16. As shown in Figure 16, the cooperative equilibrium solutionr∗ 3remains at 0.62 when θj ranges from 0.6 to 0.9, consistent with the competitive reference knowledge (rc=0.62). That indicates that r∗ 3 is absolutely influenced by the competitive reference point during this range, and there is no obvious effect caused by varying θj∈ [0.6,0.9]. When θj≥1, the increasing θj leads to the raise of industrial knowledge, and r∗ 3 jumps to 0.643and remains stable. In addition to that, the incentive fee, g, increases when θj∈ [0.6,0.9]but drops sharply to 0.554when θj≥1 and remains constant. Additionally, the TRE’s comprehensive utility, V, decreases from 1.921 to 1.845 according to the increase in incentive ratio when θj∈ [0.6,0.9]. When θj=1, because of the jump of r∗ 3 and the sharp drop in incentive fee, g, the TRE’s comprehensive utility, V, rises to 2.015. When θj>1, the TRE’s comprehensive utility decreases from 2.015 to 1.934, responding to the increase of θj, which is primarily caused by the DSQ lag. To sum up, in partly asymmetric information, the prosperity coefficient, θj, does not directly affect the outcomes, including the incentive equilibrium solution, r∗ 3, incentive ratio, g, and the TRE’s comprehensive utility, V. However, there is a turning point on trends. When the prosperity coefficient is lower than 1 (i.e., θj<1), the incentive equilibrium solution equals to the main competitor’s DSQ level. Moreover, when the prosperity coefficient is higher than 1 (i.e., θj>1), the TRE’s psychological utility is improved because of the improving DSQ and lower incentive fee. Sensitivity analysis of firm size When the scale of the targeted enterprise is fluctuating compared to that of the Jiebai group, the scale coefficient, ϑk=srk srJiebai, gradually changes from 1 . Let the set of values increase and decrease by 10%, 20%, 30% and 40%, respectively. The competitor’s reference level, rk c= 0.372,0.434,0.496,0.558,0.62,0.682,0.744,0.806 and 0.868, as shown in Table 14. The detailed analysis of equilibrium, incentive parameter, and the TRE’s utility are the same as shown in Section 7.5.1. Sensitivity analysis of incentive budget To consider the incentive budget’s impact on the TRE’s incentive solution, the incentive fee under the optimal solution, φ(r∗ i), can be used to set the constraint of incentive budget, ρ =φ(r∗ i), which can be treated as the incentive threshold. When the incentive budget, ρ , gradually changes from the original optimal level, φ(r∗ i). Let the set of ρ values increase and decrease by Figure 15. The sensitivity influence of geographic location (completely asymmetric information). Figure 16. The sensitivity influence of geographic location (partly asymmetric information). J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 18 10%, 20%, 30% and 40%, respectively. Repeating the above incentive process, the optimal solution under different information situation can be obtained in the following situations. Symmetric information situation. In the completely symmetric information situation, referring to Theorem 1, the optimal solution is located at where r∗ 1=0.7, g1=0. The TRE’s comprehensive utilization is V[ π T(r1)] = 2.37. Similarly, repeat the steps, we can obtain the optimal solution under different information situations can be shown in Table 15. In the completely symmetric information situation, the optimal DSQ is not related to the incentive budget, in which the TRE need not to pay additional incentive fee because of the information advantage. Completely asymmetric information situation. In this situation, when ρ = 0.9∗φ(r∗ 2)=0.9∗0.375 =0.338, referring to Equation (8), the “principal-agent” model can be designed as follows: maximize ln[P(r) + 1] + 2−g∗r,(obj −I) s.t. ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ 3∗r2=g,(C1) r∈ [0,1],(C2) ln[P(r) + 1] + 2−g∗r>0.178,(C3) 1−r3+g∗r>0.657,(C4) g∗r<0.338,(C5) The equilibrium solution of this model is obtained through Lingo. In the optimal condition, the cost-sharing ratio, g2=0.696, r∗ 2 =0.482, and V[ π T(r∗ 2)]=1.808. Similarly, repeat the steps, we can obtain the optimal solution under different incentive budgets can be shown in Table 16. The trends of equilibrium, incentive cost and the TRE’s utility are shown in Figure 17. As shown in Figure 17, influenced by the completely asymmetric information, the graphical trends illustrate the dynamic interplay of the incentive budget, ρ , cooperative equilibrium, r∗ 2, incentive coefficient, g, and the TRE’s comprehensive utility, V. When the incentive budget, ρ , is lower than the original level (i.e., ρ ≤0.375), both the cooperative equilibrium solution, r∗ 2, and the incentive ratio, g, will increase. The increasing incentive budget boosts the increase of the TRE’s comprehensive utility, V, from 1.761 to 1.81. Once the incentive budget, ρ , is higher than the original level (i.e., ρ >0.375), the cooperative equilibrium solution r∗ 2=0.5, incentive ratio g =0.75, and the TRE’s comprehensive utility V =1.81, remain stable, indicating that the incentive budget’s impact on incentives becomes ineffective under such conditions. To sum up, in a completely asymmetric information situation, when the incentive budget is changing lower than the optimal condition, the DSQ equilibrium will be positively correlated to the incentive budget. Once the incentive budget is enhanced more than the optimal condition, the DSQ equilibrium, incentive ratio, and the TRE’s comprehensive utility will keep stable, which equal to that at the original optimal level. Therefore, there is an optimal budget threshold for incentive when ρ = 0.375, where the DSQ equilibrium, r∗ 2, and the TRE’s optimal psychological utility, V, can be achieved at the lowest budget. In partly asymmetric information situation. In partly asymmetric information, when ρ =0.9∗φ(r∗ 3)=0.9∗0.356 =0.322, referring to Equation (8), the “principal-agent” model can be designed as follows: maximize 0.6∗(1−r3+g∗r)+0.4{ln[P(r) + 1] + 2−g∗r},(obj −I) s.t.⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ r∈ [0,1],(C1) ln[P(r) + 1] + 2−g∗r>1.808,(C2) 1−r3+g∗r>0.657,(C3) g∗r<0.322 The equilibrium solution can be achieved through smart algorithms. In the optimization condition, the cost-sharing ratio g3=0.518, the equilibrium DSQ r∗ 3=0.62, and the TRE’s utility is V[ π T(r∗ 3)]=2.034. Similarly, repeating the above operations, we can obtain the optimal solutions, shown in Table 17. The trends of changing equilibrium, incentive cost and utility are shown in Figure 18. As shown in Figure 18, when the incentive budget, ρ , increases from 0.214 to 0.498, the incentive ratio, g, is enhanced from 0.345 to 0.804. However, the incentive equilibrium solution, r∗ 3, remains stable at 0.62, only when ρ =0.356, r∗ 3 has a small increase to the equilibrium point 0.643. In this situation, the TRE’s comprehensive utility, V, keeps decreasing from 2.142 to 1.855, inducing by the increasing incentive ratio, g, and stable DSQ level, r∗ 3. In summary, in a partly asymmetric information situation, the incentive ratio, g, is positively related to the incentive budget, ρ . However, the cooperative equilibrium solution, r∗ 3, is almost unaffected by incentive budgets, primarily because the TRE and the DSP implement a bargaining game in partial asymmetric information. The TRE’s comprehensive utility, V, is negatively related to the incentive budget, ρ , which is primarily caused by the increasing incentive ratio as the raise of total cost. Further discussions on the applications across regions To extend the application across regions, 20 Chinese TREs are selected and their detailed information is shown in Table 18. The TREs’ sale revenue data are from the enterprises’ annual financial reports in 2023, and their location city GDP data are collected from National Bureau of Statistics in 2023. Comparing to benchmark TRE data and Hangzhou GDP, the prosperity coefficients and the scale coefficients can be calculated to the crossregional applications of the incentive method. The influence of geographic location on incentive effect To extend the application from the current city Hangzhou to more Figure 17. The sensitivity influence of incentive budgets (completely asymmetric information). Figure 18. The sensitivity influence of incentive budget (partly asymmetric information). J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 19 targeted cities, prosperity coefficient, θj=gdpj gdpHangzhou, can be used to normalize the industrial reference knowledge in the city j. The external industrial reference in city j can be rj h=gdpj gdpHangzhourh. Symmetric information situation. Based on the GDP of each region and Hangzhou, the prosperity coefficients, θj, of each region and the revised industrial reference knowledge are presented in Table 11. In a completely symmetric information situation, the optimal solution is determined by the DSP’s opportunity benefit π S, where r∗ 1 =0.7, g1 =0, and V[ π T(r1)] = 2.37. Similarly, referring to Theorem 1, one can obtain the optimal solution when rj h at different levels, which are shown in Table 19. According to the equilibrium DSQ, r∗ 1, and incentive parameter, g, because the TRE absolutely exploits the information advantage, it can force the DSPs to take the basic opportunity benefit. The forcing contract can ensure that the optimal DSQ is not related to regional GDP and no additional incentive is needed. Completely asymmetric information situation. Let us consider the Ningbo Zhongbai company in Ningbo city as an example. The GDP of Ningbo city is 15704.30 and the prosperity coefficients is 0.837. In this situation, when the adjusted industrial reference rj h=0.837 ∗0.24 =0.201 and competitor reference rc=0.62, referring to Equation (8), the “principal-agent” model can be designed as follows: maximize ln[P(r) + 1] + 2−g∗r,(obj −I) s.t.⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 3∗r2=g,(C1) r∈ [0,1],(C2) ln[P(r) + 1] + 2−g∗r>0.178,(C3) 1−r3+g∗r>0.657,(C4) The equilibrium solution of this model is obtained through Lingo. In the optimal condition, the cost-sharing ratio, g2=0.668, r∗ 2=0.472, and V[ π T(r∗ 2)]=1.856. Similarly, one can obtain the optimal solutions in other cities. The equilibrium conditions are provided in Table 20. Because of the increasing regional GDPs, the industrial reference levels,rj h, will be raised as well, creating more serious marketing competition and reducing the TREs’ feelings on their DSQ levels. The trends of the equilibrium DSQ, r∗ 2, incentive parameter, g, the TRE’s comprehensive utility, V, are shown in Figure 19, which have a clear relationship with the prosperity coefficient, θj. 1) The equilibrium DSQ, r∗ 2, and the incentive parameter, g, are positively related to regional GDP level. Because of the TRE’s participant constraint, V[ π T(r)] ≥ V[ π T], the increasing industrial reference improves its opportunity profit π T, which leads to the increasing equilibrium DSQ, r∗ 2. To induce the DSP to provide higher DSQ, there should be more incentive intensity, and the incentive parameter, g, should be increased to maintain cooperation in more prosperous regions. 2) The TRE’s comprehensive utility, V, is negatively related to regional GDP level. The increasing regional GDP improves the industrial reference level and reduces the TRE’s feeling on perceived DSQ. Higher regional GDP signifies a more developed industrial base and stronger market potential. However, the positive association is accompanied by the diminishing marginal effect. The incremental gains in cooperation stability slow down when θj reaches an advanced level. The increasing equilibrium DSQ, r∗ 2, and the incentive parameter, g, greatly improve the TRE’s outsourcing payment, which imposes heavier cost burden and harms its cooperative utility. The TRE’s comprehensive utility, V, declines persistently from 2.011 to 1.368, which is caused by the growth rate of additional incentive costs exceeding the growth rate of cooperative equilibrium, r∗ 2. The influence of firm size on incentive effort To extend the application from the current enterprise to more targeted enterprises, the scale coefficient, ϑk, is used to adjust the competitor’s reference knowledge between the target enterprise, k, and the Jiebai group, where ϑk=srk srJiebai. The scale level considering the influence of company size as rk c=ϑkrc=srk srJiebairc. Symmetric information situation. Through the transformation of TREs’ sale revenue, the scale coefficients, ϑk, and the revised competitor reference levels are presented in Table 21. In a completely symmetric information situation, the optimal solution is determined by the DSP’s opportunity benefit π S, where r∗ 1=0.7, g1=0, V[ π T(r1)] = 2.37. Similarly, referring to Theorem 1, one can obtain the optimal solution when rk c is in different levels. In completely symmetric information, the optimal DSQ is not related to the prosperity coefficient, ϑk. Completely asymmetric information situation Let us consider Ningbo Zhongbai as an example. In this situation, when the sale revenue of 119030.84 is and its scale coefficient is 0.587. Its adjusted competitor reference rk c=0.587 ∗0.62 =0.364 and the industrial reference rh=0.24. Referring to Equation (8), the “principalagent” model can be designed as follows: maximize ln[P(r) + 1] + 2−g∗r,(obj −I) s.t.⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 3∗r2=g,(C1) r∈ [0,1],(C2) ln[P(r) + 1] + 2−g∗r>0.178,(C3) 1−r3+g∗r>0.657,(C4) The equilibrium solution of this model is obtained through Lingo. In the optimal condition, the cost-sharing ratio, g2=0.389, r∗ 2=0.360, and V[ π T(r∗ 2)]=2.000. Figure 19. The influence of the prosperity coefficient in completely asymmetric information. Figure 20. The influence of the scale coefficient in completely asymmetric information. J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 20 Repeating the above operation to the other TREs, one can obtain the optimal solutions with varying competitor references, rk c, shown in Table 22. Because of increasing firm sizes, the TREs’ competitor references, rk c will be improved and reduce TREs’ subjective feeling on their DSQ values. As shown in Figure 20, the trends of the equilibrium DSQ, r∗ 2, incentive parameter, g, TRE’s comprehensive utility, V, have clear relationships with the scale coefficient, ϑk. Table 2 Some Indicators of DSQ. Dimension First-grade indicators Second-grade indicators Equation Quality Characteristics Sources Digital Tangibles Functionality Traffic Number of registered members L type (Chan et al., 2020; Melovi´ c et al., 2021)   Time Spent on Page Visit The time that users spend browsing the web N type (Chan et al., 2020; Si et al., 2015)   Customer Information Assets The amount of customer information L type (Chan et al., 2020; Varadarajan, 2020) Efficiency Member Increase Ne−NsL type (Liu et al., 2022; Varadarajan, 2020   Conversion Rate Conversion frequency Total visitors L type (Melovi´ c et al., 2021; Morgan et al., 2022; Mintz et al., 2021) Digital Trust Data Integrity Packet Loss Rate Loss pockets Total pockets S type (Skaka-ˇ Ceki´ c & Barakovi´ c Husi´ c, 2023; Huang et al., 2018; Alnawas and Al Khateeb, 2022) Service Availability Transmission Delay Channel length Transmission rate S type (Skaka-ˇ Ceki´ c & Barakovi´ c Husi´ c, 2023; Huang et al., 2018; Alnawas & Al Khateeb, 2022))   Throughput Input/Output Total seconds L type (Chan et al., 2020; Liu et al., 2022; Mintz et al., 2021) Digital Interaction Collaboration Social Media Interaction Number of cooperation social media L type (Chan et al., 2020; Morgan et al., 2022; Saura, 2021)   Brand Mentions Number of brand mentions L type (Chan et al., 2020; Melovi´ c et al., 2021) Mobile Communication User-generated Content Number of user-generated content L type (Babi´ c et al., 2020) Customer Centricity Customer Insights Average Transaction Value Total sales Total order volume L type (Huang et al., 2018)   Customer Retention Rate (Ne −Na)/Ns L type (Melovi´ c et al., 2021)   Customer Churn Rate Nc/Nt S type (J¨ arvinen & Karjaluoto, 2015) Customer Segmentation Frequency Number of purchases a customer makes in a period L type (Si et al., 2015)   Recency Last purchase interval S type (Si et al., 2015)   Monetary Total amount spent by a customer in a period L type (Melovi´ c et al., 2021; Mintz et al., 2021) Reliability Operational Efficiency Return on Marketing Investment Marketing revenue Marketing Investment S type (J¨ arvinen & Karjaluoto, 2015)   Marketing Cost Total cost of the marketing activities N type (Melovi´ c et al., 2021; Mintz et al., 2021)   Customer Acquisition Cost SC+St+Ss+SoS type (Si et al., 2015) Market Performance International Market Share Company’s sales/Global market sales L type (French, 2017)   Trade Competitiveness Export value-Import value/Export value+Import value L type (French, 2017)   Revealed Comparative Advantage (CE/TCE) ∗ (TGE /GE)L type (French, 2017) Table 3 Service quality requirement and performance information. KPI ①Type ②Weight ③Tolerance interval ④Optimal target value ⑤Competitor’s DSQ Industry average DSQ Actual DSQ ⑥Standard DSQ ⑦Actual value ⑧Standard DSQ ⑨ CRR L 0.4 [10,30] 30 25 0.75 15 0.25 CAC S 0.4 [0.01,0.05] 0.01 0.03 0.5 0.04 0.25 MC N 0.2 [25,35] 30 32 0.6 34 0.2 Table 4 Incentive effect analysis in the completely asymmetric information situation. Completely asymmetric information Fixed fee Cost-sharing incentive Increase rate rr∗ 2=0.26 r∗ 2=0.592.31% V[ π T(r)] V[ π T(r∗ 2)]= 0.178 V[ π T(r∗ 2)]=1.81 916.85% V[ π S(r)] V[ π S(r∗ 2)]= 0.982 V[ π S(r∗ 2)]=1.25 27.29% Table 5 Incentive effect and cost sharing ratio under different scenarios. Scenario Completely symmetric information Completely asymmetric information without incentive Completely asymmetric information under incentive Partly asymmetric information under incentive r r∗ 1=0.7r∗ 2=0.26 r∗ 2=0.5r∗ 3=0.643 V[ π T(r)] V[ π T(r∗ 1)]= 2.37 V[ π T(r∗ 2)]= 0.178 V[ π T(r∗ 2)]= 1.81 V[ π T(r∗ 3)]= 2.015 g g1=0g− 2=0 g2=0.75 g3=0.554 J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 21 The equilibrium DSQ, r∗ 2, and the incentive parameter, g, exhibit positive correlation with the scale coefficient, ϑk. As the enlarged firm size leads to the increased competitor reference level, the TRE should change its focus on its competitor to reach better DSQ. Larger scale signifies a stronger market influence, more complex supply chain, and higher resource integration capability. To compete with a stronger rival, the TRE needs to improve the incentive intensity and induce the DSP to guarantee larger DSQ of the digital marketing platform. The TRE’s comprehensive utility, V, has a negative relationship with scale coefficient, ϑk. The increasing firm size makes the TRE focus on a more powerful competitor, and the larger competitor reference directly reduces the TRE’s feeling on perceived DSQ. To keep comparative advantage, the TRE has to improve its requirements on DSQ level and incentive investment, which reduce its economic utility. The TRE’s Table 6 Incentive effect comparison of different weighting methods. Scenario Completely symmetric information Completely asymmetric information under incentive Partly asymmetric information under incentive Fixed weight Varying weight Fixed weight Varying weight Fixed weight Varying weight rr∗ 1 ʹ=0.7r∗ 1=0.7r∗ 2 ʹ=0.47 r∗ 2=0.5r∗ 3 ʹ=0.62 r∗ 3=0.643 V[ π T(r)] Vʹ[ π T(r1)] = 2.37 V[ π T(r1)] = 2.37 Vʹ[ π T(r∗ 2)]=1.61 V[ π T(r∗ 2)]=1.81 Vʹ[ π T(r∗ 3)]=1.62 V[ π T(r∗ 3)]=2.015 ggʹ 1=0g1=0gʹ 2=0.66 g2=0.75 gʹ 3=0.94 g3=0.554 Table 7 Optimal solutions caused by changing rc in symmetric information situation. rc40% decrease 30% decrease 20% decrease 10% decrease 0.62 10% increase 20% increase 30% increase 40% increase r∗ 10.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 g 0 0 0 0 0 0 0 0 0 V 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 Table 8 Optimal solution by changing rc in completely asymmetric information situation. rc0.372 0.434 0.496 0.558 0.62 0.682 0.744 0.806 0.868 r∗ 20.372 0.413 0.441 0.467 0.5 0.524 0.537 0.554 0.566 g 0.415 0.565 0.583 0.654 0.75 0.824 0.865 0.921 0.961 V 1.999 1.973 1.929 1.874 1.810 1.738 1.661 1.581 1.493 Table 9 Optimal solutions caused by changing rc in partly asymmetric information. rc0.372 0.434 0.496 0.558 0.620 0.682 0.744 0.806 0.868 r∗ 30.495 0.434 0.496 0.558 0.643 0.708 0.836 0.843 0.925 g 0.464 0.551 0.674 0.783 0.554 0.721 0.733 0.974 0.910 V 2.100 1.984 1.932 1.895 2.015 1.892 1.844 1.688 1.675 Table 10 Incentive effect and cost sharing ratio under different ω . ω 0.1 0.2 0.3 0.4 0.5 >0.6 0.7 0.8 0.9 r∗ 30.708 0.708 0.708 0.643 0.62 0.62 0.62 0.621 0.679 V[ π T(r)] 1.871 1.871 1.871 2.015 2.170 2.355 2.355 2.359 2.368 g 0.721 0.721 0.721 0.554 0.3 0 0 0 0 Table 11 Optimal solutions caused by changing θj under symmetric information situation. θj0.6 0.7 0.8 0.9 11.1 1.2 1.3 1.4 rj h0.144 0.168 0.192 0.216 0.24 0.264 0.288 0.312 0.336 r∗ 10.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 g 0 0 0 0 0 0 0 0 0 V 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 Table 12 Optimal solutions caused by changing θj in completely asymmetric information. θj0.6 0.7 0.8 0.9 11.1 1.2 1.3 1.4 rj h0.144 0.168 0.192 0.216 0.24 0.264 0.288 0.312 0.336 r∗ 20.467 0.475 0.483 0.484 0.5 0.506 0.525 0.532 0.539 g 0.654 0.677 0.699 0.703 0.75 0.768 0.827 0.849 0.872 V 1.91 1.886 1.861 1.836 1.810 1.783 1.751 1.723 1.694 J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 22 comprehensive utility, V, declines persistently from 2.002 to 1.339, which is caused by the growth rate of additional incentive cost. Conclusions, implications, and future work Research conclusions In the digital service supply chain, the DSP designs and develops the digital marketing platform for the TRE, trying to satisfy the latter’s digital requirements, such as data mining, business operations, and sales prediction. Regarding the trend of digital marketing transformation, the TRE’s perceived DSQ is greatly influenced by external reference knowledge, such as the main competitor’s DSQ and industrial DSQ. Regarding the service supply chain containing asymmetric information, the TRE lacks the information advantage and has to face the DSP’s adverse selection. Consequently, DSQ incentive solutions concerning external reference knowledge should be suitably exploded to regulate the DSP’s DSQ-assurance investment and eliminate the negative influence of information asymmetry. This study contributes to the incentive mechanism in digital service supply chain influenced by external reference knowledge. In theoretical level, two Nobel Prize theories—the prospect theory and the principalagent theory—are effectively integrated to explore the role of external reference knowledge on the utility equilibrium and incentive strategy. The introduction of the TRE’s psychological utility caused by external reference knowledge is the core driving force to evaluate the DSQ effect and future potential. The objective of the principal-agent model is updated to psychological utility, and the outcome of incentive strategy concerns external reference constraints. Regarding methodology, the study explores a dynamic varying weighting method to describe the optimistic preference and dynamic dominance of external references. The novel varying weighing method can overcome the rigidity of traditional fixed weighting approach. On a practical level, this study provides the incentive tools for TREs to appraise the DSQ level and design differential DSQ incentive strategies. The incentive effect can improve TREs’ psychological DSQ utility by mitigating the DSPs’ moral hazard under asymmetric information. The above theoretical, methodological, and practical explorations concerning the external reference knowledge not only fill gaps in revealing the psychological DSQ utility but also offer novel incentive method and practical tool to enhance the managerial ability in digital service supply chain. Managerial implications In the digital service supply chain, TREs outsource the digital marketing platform development missions to DSPs. A competitive digital Table 13 Optimal solutions caused by changing θj in partly asymmetric information situation. θj0.6 0.7 0.8 0.9 11.1 1.2 1.3 1.4 rj h0.144 0.168 0.192 0.216 0.24 0.264 0.288 0.312 0.336 r∗ 30.62 0.62 0.62 0.62 0.643 0.643 0.643 0.643 0.643 g 0.804 0.819 0.834 0.848 0.554 0.554 0.554 0.554 0.554 V 1.921 1.897 1.872 1.845 2.015 1.987 1.971 1.953 1.934 Table 14 Optimal solutions caused by changing ϑk in symmetric information situation. ϑj0.6 0.7 0.8 0.9 11.1 1.2 1.3 1.4 rk c0.372 0.434 0.496 0.558 0.62 0.682 0.744 0.806 0.868 Table 15 Optimal solutions caused by ρ in symmetric information situation. ρ 40% decrease 30% decrease 20% decrease 10% decrease ρ =φ(r∗ i)10% increase 20% increase 30% increase 40% increase r∗ 10.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 g 0 0 0 0 0 0 0 0 0 V 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 φʹ(r)0 0 0 0 0 0 0 0 0 Table 16 Optimal solutions caused by ρ in symmetric information situation. ρ 40% decrease 30% decrease 20% decrease 10% decrease ρ =0.375 10% increase 20% increase 30% increase 40% increase 0.225 0.263 0.3 0.338 0.413 0.45 0.488 0.525 g 0.534 0.591 0.646 0.696 0.75 0.75 0.75 0.75 0.75 r∗ 20.422 0.444 0.464 0.482 0.5 0.5 0.5 0.5 0.5 V 1.761 1.783 1.804 1.808 1.81 1.81 1.81 1.81 1.81 Table 17 Optimal solutions caused by caused by ρ in partly asymmetric information. ρ 40% decrease 30% decrease 20% decrease 10% decrease ρ =0.375 10% increase 20% increase 30% increase 40% increase 0.214 0.245 0.285 0.322 0.392 0.427 0.463 0.498 g 0.345 0.395 0.46 0.518 0.554 0.632 0.689 0.747 0.804 r∗ 30.62 0.62 0.62 0.62 0.643 0.62 0.62 0.62 0.62 V 2.142 2.110 2.070 2.034 2.015 1.964 1.928 1.893 1.855 J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 23 marketing platform can precisely recognize potential customers, effectively develop online customer adherence, highly enhance social media influence, and consistently improve customers’ loyalty, which directly represents the enterprise’s core competitiveness. In a competitive Table 18 The TREs’ sale revenue data and urban GDP in 2023. NO Enterprise City City GDP (Billion RMB) Sale revenue (Ten thousand RMB) 1 Ningbo Zhongbai Ningbo 15704.30 119030.84 2 Lifu Group Xianggang 3808.10 134897.50 3 Zhongshang Group Nanjing 17421.00 249697.27 4 Hanshang Group Wuhan 20012.00 138960.13 5 Dongbai Group Fuzhou 12928.00 188607.16 6 Marketing Dajiang Group Hainan 7551.18 140000.95 7 Huijia Times Urumqi 4168.46 249420.53 8 Maoye Commercial Chengdu 22075.00 241194.33 9 Huaguang Commercial Jian 2735.07 606542.7 10 Gofun Group Lanzhou 3487.00 96962.74 11 Tongcheng Holdings Changsha 12332.00 213286.99 12 Shenzhen Seg Shenzhen 34606.00 194906.55 13 Renrenle Shenzhen 34606.00 285267.95 14 Hualian Holdings Beijing 43760.70 109946.23 15 You-A Department Store Changsha 14332.00 134245.19 16 Better Life Commerce Group Xiangtan 2741.84 310114.33 17 Wenfeng Great World Chain Nantong 11813.30 216565.63 18 New Huadu Retail Group Quanzhou 12172.33 282392.16 19 Zhongxing Commercial Group Shenyang 8122.00 80994.67 20 Jiebai Group Hangzhou 18753.07 202731.78 Average value 15156.47 195288.17   Standard deviation 11470.14 115188.81   Table 19 Optimal solutions under symmetric information situation. θjrj hr∗ 1g V 1 0.240 0.7 0 2.37 0.837 0.201 0.7 0 2.37 0.203 0.049 0.7 0 2.37 0.929 0.223 0.7 0 2.37 1.067 0.256 0.7 0 2.37 0.689 0.165 0.7 0 2.37 0.403 0.097 0.7 0 2.37 0.222 0.053 0.7 0 2.37 1.177 0.283 0.7 0 2.37 0.146 0.035 0.7 0 2.37 0.186 0.045 0.7 0 2.37 0.658 0.158 0.7 0 2.37 1.845 0.443 0.7 0 2.37 1.845 0.443 0.7 0 2.37 2.334 0.560 0.7 0 2.37 0.764 0.183 0.7 0 2.37 0.146 0.035 0.7 0 2.37 0.630 0.151 0.7 0 2.37 0.649 0.156 0.7 0 2.37 0.433 0.104 0.7 0 2.37 Table 20 Optimal solutions under completely asymmetric information situation. θjrj hr∗ 2g V 1 0.240 0.500 0.750 1.810 0.837 0.201 0.472 0.668 1.852 0.203 0.049 0.457 0.627 1.998 0.929 0.223 0.492 0.726 1.832 1.067 0.256 0.503 0.759 1.792 0.689 0.165 0.474 0.674 1.889 0.403 0.097 0.471 0.666 1.954 0.222 0.053 0.458 0.629 1.995 1.177 0.283 0.488 0.714 1.759 0.146 0.035 0.453 0.616 2.011 0.186 0.045 0.456 0.624 2.002 0.658 0.158 0.472 0.668 1.896 1.845 0.443 0.557 0.931 1.562 1.845 0.443 0.557 0.931 1.562 2.334 0.560 0.592 1.051 1.368 0.764 0.183 0.480 0.691 1.871 0.146 0.035 0.453 0.616 2.011 0.630 0.151 0.470 0.663 1.903 0.649 0.156 0.471 0.666 1.898 0.433 0.104 0.454 0.618 1.949 Table 21 Optimal solutions under symmetric information situation. ϑkrk cr∗ 1g V 1 0.24 0.7 0 2.37 0.587 0.364 0.7 0 2.37 0.665 0.413 0.7 0 2.37 1.232 0.764 0.7 0 2.37 0.685 0.425 0.7 0 2.37 0.930 0.577 0.7 0 2.37 0.691 0.428 0.7 0 2.37 1.230 0.763 0.7 0 2.37 1.561 0.968 0.7 0 2.37 1.190 0.738 0.7 0 2.37 0.478 0.297 0.7 0 2.37 1.052 0.652 0.7 0 2.37 0.961 0.596 0.7 0 2.37 1.407 0.872 0.7 0 2.37 0.542 0.336 0.7 0 2.37 0.662 0.411 0.7 0 2.37 1.530 0.948 0.7 0 2.37 1.068 0.662 0.7 0 2.37 1.393 0.864 0.7 0 2.37 0.400 0.248 0.7 0 2.37 0.587 0.364 0.7 0 2.37 Table 22 Optimal solutions under completely asymmetric information situation. ϑkrk cr∗ 2g V 1 0.620 0.5 0.750 1.810 0.587 0.364 0.360 0.389 2.000 0.665 0.413 0.398 0.475 1.984 1.232 0.764 0.539 0.872 1.638 0.685 0.425 0.409 0.502 1.978 0.930 0.577 0.481 0.694 1.855 0.691 0.428 0.418 0.524 1.975 1.230 0.763 0.538 0.868 1.639 1.561 0.968 0.604 1.094 1.339 1.190 0.738 0.525 0.827 1.671 0.478 0.297 0.302 0.274 1.996 1.052 0.652 0.505 0.765 1.775 0.961 0.596 0.494 0.732 1.834 1.407 0.872 0.581 1.013 1.486 0.542 0.336 0.326 0.319 2.001 0.662 0.411 0.396 0.470 1.985 1.530 0.948 0.594 1.059 1.371 1.068 0.662 0.511 0.783 1.763 1.393 0.864 0.576 0.995 1.498 J. Hao et al. Journal of Innovation & Knowledge 10 (2025) 100745 24