Revenue allocation for shared manufacturing collaboration considering participants’ contributions based on a differential game and an improved Shapley algorithm

The profound integration of advanced information technology with manufacturing has positioned shared manufacturing. As a key driver of the sharing economy, shared manufacturing provides critical momentum for industrial transformation and upgrading. By integrating dispersed and idle resources, shared manufacturing alleviates the constraints of traditional manufacturing resources and enhances resource allocation efficiency. Furthermore, through collaborative innovation, it accelerates technology diffusion and value creation, promoting high-quality development of the manufacturing industry. Shared manufacturing is utilized in production through platforms such as “Floow2” (Link to the website), “MFG” (Link to the website), and “Haizol” (Link to the website) (Duran et al., 2025).

However, significant disparities persist in the implementation of shared manufacturing. A reasonable profit allocation mechanism can incentivize manufacturing enterprises to collaborate and share resources (Xing et al., 2024). In practice, some capacity suppliers leverage their technological or scale advantages to establish a monopolistic position, thereby dominating the profit distribution (Gao et al., 2026). This imbalance not only discourages the participation of capacity demanders and third-party platforms but may also exacerbate imbalances within the industrial ecosystem. Therefore, establishing a fair and unified profit allocation model is crucial for the stable and sustainable development of shared manufacturing systems (Wang et al., 2024).

This paper proposes a collaborative manufacturing cooperation comprising a capacity supplier, a third-party shared manufacturing platform, and a capacity demander. Using differential games, it develops non-cooperative, partially cooperative, and fully cooperative game models to derive equilibrium solutions for revenue maximization under different scenarios. The historical reputation, effort, and revenue contribution indices of the participating entities are considered. Based on these indices, an improved Shapley algorithm is used to design a revenue allocation mechanism. Numerical simulations validate the feasibility of the proposed strategy.

The contributions of this study are primarily reflected in the following two core dimensions. First, in constructing the profit distribution system, the differential game method is employed to characterize and analyze the dynamic process of profit formation. Second, this study establishes a revenue allocation mechanism for tripartite collaboration. It incorporates historical credibility, level of effort, and profit contribution as core parameters of the improved Shapley value, with an emphasis on the actual gains of demanders and the third-party shared manufacturing platform (who possess limited bargaining power). This approach aims to improve the equity of the allocation.

The following structure guides the subsequent sections of the paper. Section 2 examines the relevant literature. Section 3 delineates the problem description and fundamental assumptions. Section 4 establishes and addresses the differential games. Section 5 formulates the correction factors and proposes a revenue allocation strategy utilizing the improved Shapley algorithm. Section 6 conducts numerical simulations. Section 7 encapsulates the primary contributions and managerial suggestions.

The shared manufacturing service model differentiates itself from conventional cloud manufacturing by focusing on single-point resource sharing and on-demand elastic matching. Jiang et al. (2022) proposed the attributes and theoretical framework of shared manufacturing services (SMS) as a new model of social manufacturing. Yu et al. (2020) delineated three types of shared factories—order-sharing, resource-sharing, and capability-sharing—and examined their technological support and associated obstacles. Peng et al. (2024) posited that the shared manufacturing model possesses significant potential to enhance the efficacy of production and distribution networks. Zhang et al. (2023) introduced a perception-driven hybrid methodology for the monitoring and maintenance of shared manufacturing resources. Wang et al. (2021) developed a digital twin-driven service model to manage and coordinate shared manufacturing resources. Li and Jiang (2021) investigated equipment suppliers' decision-making in the context of shared manufacturing by comprehensively considering multiple cost factors. Cao et al. (2025) developed a capacity-splitting matching model or divisible orders on a third-party shared manufacturing platform. Cheng et al. (2025a) combined multi-attribute bargaining with dual auctions to design a more complex market transaction mechanism. Yu et al. (2024) proposes a sequential auction-based paradigm for the trading of manufacturing resources. Li et al. (2024a) proposed the sales and sharing decisions of the equipment supplier under shared manufacturing environment. Yang et al. (2025) studied the problem of matching limited resources with sequential orders on Shared manufacturing platforms under incomplete information. Tong et al. (2024) utilized digital twin technology to optimize data collection frequency and scheduling under resource constraints. Wei et al. (2024) enhanced the operational efficiency of the solution by performing a collaborative optimization of supply-demand matching in the supply chain and distributed workshop scheduling. Cheng et al. (2025b) investigated the energy-aware parallel machine scheduling problem and devised an efficient tailored heuristic (ETH). Lei et al. (2025) proposed a mixed-integer programming model for dual objectives and improved the search process of the meta-heuristic algorithm. Zhang et al. (2022) designed various incentive models and developed the corresponding smart contracts to encourage enterprise participation. Lupi et al. (2023) presented a blockchain-based shared additive manufacturing structure to facilitate the development of smart contracts. Krämer et al. (2025) utilized network latency simulations to guide and optimize the design and implementation of blockchain applications.

The allocation of revenue, an essential issue in multi-party collaboration, has garnered increased attention from the scholarly community. Lv and Ma (2020) established a revenue allocation strategy based on relative risk sharing, directly linking risk to reward. Zhang et al. (2021a) introduced a revenue allocation mechanism utilizing Swing Option to balance the returns and risks between the public and private sectors. Zhou and Wu (2025) examined the multi-period revenue allocation mechanism and the dynamic incentive challenge prompted by long-term payments. An et al. (2022) utilized the frontier rate of change (FCR) and presented two frontier-based incentive mechanisms for the allocation of common revenues or fixed expenses. Li et al. (2024b) constructed a two-layer road data asset revenue allocation model based on a modified Shapley algorithm. Wang et al. (2023) utilized an improved Shapley value method to achieve a fair distribution of revenue generated from private charging pile sharing. Dawande et al. (2023) introduced the “Robin Hood” model, which achieves the integration of individual rationality, coalition stability, and Pareto optimality by partial income redistribution. Liu et al. (2025) employed non-cooperative and cooperative game theory to investigate the selection of cooperative modes and the allocation of revenue. Li et al. (2020) constructed two efficient mechanisms, founded on cooperative game-theoretic principles, the first including a benefit distribution scheme. Tiwari and Singh (2024) developed an improved revenue-sharing scheme based on cooperative theory to guarantee the economic stability of emission-free electricity generation. Ding and Jian (2024) established the revenue-sharing mechanism using a cooperative game and optimized the noncooperative game using a resource allocation strategy. Zhou and Yang (2023) built two discount frameworks and analyzed the effects of different discount schemes on the performance of supply chain members. Fan and Cheng (2021) applied a differential game approach to allocate the revenue generated from data sharing. López-Flores et al. (2022) synthesized multiple welfare and equity criteria to determine the most equitable benefit distribution scheme.

As shown in Table 1, research on shared manufacturing has matured in terms of technical architecture and operational models. But the significant shortcomings remain in the systematic development and practical application of revenue allocation mechanism. Most existing studies rely on static analytical frameworks, which are not well-suited to the dynamic nature of shared manufacturing alliances.

Different from the previous research, this research constructs a two-stage model integrating differential games with an improved Shapley value. First, we employ differential games to characterize the dynamic generation of cooperative benefits among the three key participants: capacity suppliers, third-party shared manufacturing platforms, and capacity demanders. Second, we incorporate historical credibility, effort and revenue contributions from this dynamic process as core parameters for the modified Shapley value. And we established a collaborative revenue-sharing mechanism among the three parties.

In a collaborative manufacturing setup involving a capacity provider, a third-party shared manufacturing platform, and a capacity demander, revenue is generated through complex interactions. Due to technological advantages and capital advantages, the capacity provider establishes a resource monopoly. By manipulating prices and bargaining advantages, it restricts the revenues of both the third-party shared manufacturing platform and the demander. This reduces their willingness to cooperate, ultimately resulting in the dissolution of the shared manufacturing cooperation.

This study examines the intrinsic connection between third-party revenue and the strategy for allocating it. The study formulates enhancement variables and employs the improved Shapley algorithm to optimize the revenue-sharing ratio between the capacity demander and the third-party shared manufacturing platform. It may moderately diminish the surplus revenue acquired by the capacity supplier as a result of its monopolistic advantage.

This study examines a collaborative manufacturing system comprising a capacity supplier, a third-party shared manufacturing platform, and a capacity demander, and proposes the following assumptions.

To clarify the research question, description of the symbols is shown in Table 2.

The following assumptions are formulated.

Where $σ1$⁠, $σ2$ and $σ3$ denote the impact coefficients of the capacity supplier, the third-party shared manufacturing platform and demander on market demand at time t, respectively. The parameter δ (δ > 0) represents the demand attenuation coefficient due to timeliness.

Where $Kp$ and $λp$ represent the coefficients pertaining to the capacity supplier's impact on the sharing cost and opportunity cost, respectively. $Kq$ represents the coefficient of the third-party shared manufacturing platform's contribution to its cost. $Kd$ denotes the coefficient of the capacity demander's contribution to the operational cost.

Where ξ denotes the coefficient representing the capacity supplier's effort for long-term returns. p represents the market price, an external variable. ζ is the coefficient of the capacity demander's effort regarding innovation spillovers.

We formulate the interactions as a Stackelberg game in which the platform acts as leader and the supplier and demander as followers. The platform first chooses its effort level to maximize its payoff, and then the followers, observing this decision, determine their efforts accordingly. The objective functions and constraints are defined as follows:

Proof. See Appendix 1. Proof of Proposition 1 in supplementary material.

When two of the three parties form a binding coalition, they play a Nash game with the outsider. In this setup, all parties choose their effort levels independently to maximize their own revenue, while the coalition's collective effort is determined through internal coordination. This study examines three distinct coalition structures.

• Scenario 1. The third-party shared manufacturing platform waives the commission for the supplier to form a binding coalition aimed at maximizing their joint net revenue. The objective function and constraints are as follows:

Proof. See Appendix 2. Proof of Proposition 2 in supplementary material.

• Scenario 2. The third-party shared manufacturing platform waives its commission for the demander. The two parties form a coalition to maximize their joint net revenue. The objective and constraints are as follows:

Proof. See Appendix 3. Proof of Proposition 3 in supplementary material.

• Scenario 3. The capacity supplier and demander enter into a long-term contract, forming a coalition aimed at maximizing their joint net revenue. The objective and constraints are as follows:

Proof. See Appendix 4. Proof of Proposition 4 in supplementary material.

All three parties abandon independent decision-making and cooperate to mitigate information asymmetry, jointly optimizing their efforts to maximize total net revenue. The objective function and constraints are as follows:

Proof. See Appendix 5. Proof of Proposition 5 in supplementary material.

Comparing Propositions 1-5 across the non-cooperative, incomplete collaboration, and collaborative cooperation scenarios, the following inferences can be drawn:

The above results indicate that, compared to the non-cooperative scenario, the cooperative model achieves higher total revenue, with all participants increasing their effort levels. However, it is worth noting that while the cooperative model yields higher total revenue and enhanced individual efforts, this outcome only provides a necessary condition for a Pareto improvement in individual payoffs. Whether such an improvement ultimately materializes remains contingent upon the specific revenue allocation mechanism.

Cooperation among the three parties maximizes revenue through efficient resource allocation. However, revenue maximization alone is insufficient, as an imbalanced allocation may lead to the dissolution of cooperation. This underscores the need for a well-designed revenue allocation mechanism in shared manufacturing systems. Given that such systems are inherently multi-agent and collaborative, revenue allocation is necessarily asymmetric—participants with stronger credit, greater effort, and higher contributions warrant a larger share of the surplus.

The Shapley value ensures fair allocation based on marginal contributions, avoiding the pitfalls of egalitarian distribution. However, its traditional form considers only outcome-based contributions, overlooking key input factors such as reputation and individual effort in the collaborative process. To address this limitation, we incorporate a corrective factor into the Shapley value framework that accounts for historical reputation, effort contribution, and revenue contribution, thereby enabling a more equitable and rational allocation of cooperative revenue.

Cooperative games commonly employ the Shapley algorithm (Lv and Ma, 2020). The revenue acquired by participant subject i in shared manufacturing using the Shapley algorithm is $Xi$⁠:

Where $Xi$ denotes the revenue allocated to participant i according to the Shapley algorithm. X(S) represents the total revenue generated by the shared manufacturing cooperation S. X(S\i) generated by the shared manufacturing cooperation S without participant i. The probability that the shared manufacturing cooperation S occurs is expressed as (I-|s|)! (|s|-1)!/I!.

Given that reputable participants significantly enhance shared manufacturing revenue, they deserve a larger share. This study defines the contribution of historical reputation as:

Where $Mi′$ denotes the quantity of effective matches for participant i. $Si$ denotes the total number of orders (successful matches or active rejects). $Δt$ denotes the time elapsed since the historical order. U denotes a confidence constant. $n0$ denotes the average order matching success rate. $λ$ denotes the decay rate.

Enterprises making greater effort contributions deserve a larger share of the cooperative revenue, thereby fostering collaboration. This study defines effort contribution as:

Where $μi(S)$ denotes the effort of the shared manufacturing collaboration S. And $μi(S−{i})$ represents the effort of in collaboration S after the exclusion of participant i. $Δμi(S)$ signifies the increase in the total effort of the shared manufacturing collaboration S.

Companies exhibiting higher revenue growth contribute more significantly to shared manufacturing and should therefore receive a larger proportion of the cooperative surplus. This study defines revenue contribution as:

X({i}) represents the revenue of participant i when operating independently of shared manufacturing.

Based on the contribution indices defined above, the correction factor Ri for participant I in shared manufacturing revenue allocation is given by:

Where $ω1$ +$ω2$ +$ω3$ = 1 and $ω1$⁠, $ω2$⁠, and $ω3$ are the weight coefficients of the contribution indexes, allowing dynamic adjustment based on their significance in shared manufacturing.

Based on the revenue allocation correction factor, the improved Shapley value-based revenue allocation model for shared manufacturing is given by:

Let $Xi*$ denotes the final revenue allocated to participant i from the shared manufacturing collaboration under the improved Shapley algorithm, and X(i) denotes the initial Shapley value for participant i.

It is important to emphasize that the proposed method is a heuristic allocation mechanism that integrates multiple indicators. In contrast to classical cooperative game solutions, it does not presuppose axioms such as budget balance or individual rationality. Its value lies in providing an operable and adjustable allocation framework tailored to the complex environment of shared manufacturing.

Under different collaboration and revenue-sharing scenarios, the optimal efforts and revenues of the capacity supplier (CS), third-party shared manufacturing platform (SMP), and capacity demander (CD) are influenced by multiple model parameters. We conduct numerical simulations in MATLAB. According to the literature (Tiwari and Singh, 2024) and (López-Flores et al., 2022), the parameter values are set as follows: $σ1=0.6,σ2=0.6,σ3=0.6,δ=0.1,Kp=0.5,Kq=0.5,Kd=0.5,λp=0.1,ξ=0.5,r=0.2,ζ=0.5,Q=1000,U=30,n0=0.5$⁠. Furthermore, the core parameters are set to $P=100,αs=6.3,αd=10$⁠, and τ = 50 based on the appropriate proportions and the actual transaction revenue.

Due to space limitations, this paper only conducts a sensitivity analysis on the revenue of the shared manufacturing system, though similar analyses extend to other entities and parameters.

As shown in Figure 1, both the supplier-demander coalition and the fully cooperative model are largely insensitive to leasing cost τ, as internal transfer payments fully internalize lease costs. For τ ≥ 40, the demander-platform alliance's net revenue declines curvilinearly with τ, indicating that the demander's leasing costs outpace its marginal revenue. Conversely, for τ < 58, the supplier-platform alliance's net revenue increases curvilinearly with τ, as rising rental costs shift revenue and transfer the burden to the demander.

As shown in Figures 2–3, the fully cooperative model remains largely insensitive to commission variations because these charges are fully internalized through transfer payments. Once $αs>22$⁠, the net revenue of the demander-platform alliance declines, likely because suppliers raise rental prices. When $αd>24$⁠, the net revenue of the supplier-platform alliance decreases, possibly indicating a dampened willingness to pay among demanders and consequently a reduction in the transaction volume.

This study sets t = 20 randomly to facilitate the application of the model developed in this research for the subsequent analysis of the revenue allocation strategy. Table 3 presents the net revenue and surplus revenue for each cooperation combination.

The number of participants in shared manufacturing exhibits a super-linear correlation with the increase in total income, as demonstrated in Table 3. Further study is conducted to validate the economic feasibility of many entities collaborating in shared manufacturing initiatives.

Five revenue allocation strategies are developed to validate the effectiveness of the proposed tactics in this paper:

Strategy 1: Allocate the collaboration's total revenue straight using the Shapley algorithm.

Strategy 2: We set $ω1=1$、 $ω2=ω3=0$ in an improved Shapley algorithm that only takes previous reputation into account.

Strategy 3: We put $ω2=1$、 $ω1=ω3=0$ in the improved Shapley algorithm, which simply takes effort into account.

Strategy 4: We set $ω3=1$、 $ω1=ω2=0$ while taking into account solely the revenue contribution of the improved Shapley algorithm.

Strategy 5: It is an improved Shapley algorithm that incorporates the three elements of improvement. To demonstrate that the core findings are not dependent on a specific parameter set, we examine four distinct weighting scenarios:

1. Historical reputation-dominated: Weight is concentrated on historical reputation (⁠$ω1=$ 0.577), with lower weights on effort (⁠$ω2$ = 0.233) and revenue contribution (⁠$ω3$ = 0.190).

2. Effort-dominated: Weight is primarily allocated to effort (⁠$ω2$ = 0.445), with lesser importance given to historical reputation (⁠$ω1$ = 0.159) and revenue contribution (⁠$ω3$ = 0.396);

3. Revenue contribution-dominated: The revenue contribution indicator is the predominant factor (⁠$ω3$ = 0.400), while historical reputation and effort are assigned lower weights (⁠$ω1$ = 0.230, $ω2$ = 0.370);

4. Balanced weights: All three factors are assigned equal importance (⁠$ω1$ = $ω2$ = $ω3$ = 1/3) to reflect the multifaceted contributions of members and enhance the flexibility of the allocation mechanism.

Furthermore, these weights can be dynamically adjusted based on the collaboration's specific operational requirements or application contexts.

The contribution indicators of the three parties in shared manufacturing exhibit distinct allocation features, as illustrated in Figure 4. The revenue contribution of the third-party shared manufacturing platform is substantial, underscoring its intermediary role. This finding is strongly supported by the quantitative investigation. The adjustment factor results in Table 4 further corroborate this observation.

Table 5 displays the revenue allocation for the participating entities across various strategies. Figure 5 shows the allocation of revenue shares.

In Strategy 1, the third-party shared manufacturing platform's revenue falls below half that of the supplier or demander, as its weak negotiation power leads to a significantly reduced share in the allocation process. Compared to Strategy 1, Strategy 2 allocates larger revenue shares to both the capacity demander and the third-party shared manufacturing platform. This suggests that incorporating historical performance can enhance distributional fairness. In contrast, Strategy 3 grants the capacity supplier a larger share, reflecting its contribution of production equipment. Under Strategy 4, the third-party shared manufacturing platform earns a significantly larger share due to its role in reducing resource mismatch and marginal transaction costs.

Under Strategy 5, the revenue distribution ratios across the four scenarios follow the same pattern for all three participants. Although the supplier's share declines, it remains at a moderate level, while the shares of both the demander and the platform increase. This confirms the robustness of the proposed mechanism across all scenarios and validates its effectiveness in mitigating revenue erosion for capacity demanders and platforms with limited bargaining power.

This study investigates shared manufacturing by developing a differential game model that captures the dynamic evolution of participants' strategies. An improved Shapley value algorithm is subsequently applied to formulate a revenue allocation strategy.

The following are the primary conclusions:

1. The cooperative model allows shared manufacturing participants to fully internalize some sharing costs via internal transfer payments. This form of collaboration leads the system to Pareto optimality.

2. When 40 < τ < 58, revenue is redistributed and the cost burden is transferred to demanders. When $αs>22$⁠, suppliers may raise rental costs, thereby reducing the net revenue of the demander-platform alliance. When $αd>24$⁠, demanders' willingness to pay falls, leading to a reduction in both transaction volume and the net revenue of the supplier-platform alliance.

3. In this study, Strategy 5 raises platform and demander revenue shares by 1.18% and 0.52% relative to Strategy 1, with a corresponding 1.70% decrease for the supplier.

By analyzing the results of the model, we obtained some important managerial implications as follows:

1. Companies engaged in shared manufacturing should either establish a collaborative framework or optimize bilateral cooperation agreements, thereby achieving a Pareto improvement in the overall revenue of the shared manufacturing system.

2. To prevent revenue loss from unilateral dominance (e.g. by a capacity supplier), it is necessary to foster multi-party collaborative governance and build a multi-stakeholder checks-and-balances system through institutional innovation.

3. Optimize shared manufacturing revenue allocation by guiding firms, collaborating with academia on modeling and innovation, and designing incentive-compatible mechanisms aligned with regulations.

This study has several limitations and future research directions: (1) the government's role is not considered in the theoretical model; (2) it does not account for manufacturing resource constraints or endogenous capacity allocation; (3) it uses net revenue as the sole criterion for optimal decisions; (4) the dynamic between short-term collaboration and long-term value creation needs more detailed characterization; and (5) no empirical validation has been conducted. These issues warrant comprehensive follow-up investigation.

The supplementary material for this article can be found online.