Patent Licensing Strategy for Supply Chain Reshaping Under Sudden Disruptive Events

Abstract

Supply chains are increasingly exposed to sudden disruptive events (SDEs) such as natural disasters and trade wars. We develop a multi-stage game-theoretical model to investigate a novel coping mechanism: when a firm is forced to exit the market because of SDEs, the firm can regain profits by licensing its proprietary production tech to a competitor. We find that, compared with the scenario before SDEs, such events can even increase the profit of each manufacturer under certain conditions. Under certain conditions, the cooperative strategy (i.e., supply chain reshaping) yields a higher supply chain system profit than the non-cooperative strategy. After SDEs, the common manufacturer may either accept or reject cooperation, depending on the customer transfer rate and the cooperation cost. Notably, under the cooperation strategy, the high-tech manufacturer extracts part of the common manufacturer’s profit through patent licensing, and the existence of cooperation cost further contributes to a misalignment between the common manufacturer’s optimal decision and the supply chain system optimum. These findings contribute to the literature by identifying a novel supply chain reshaping mechanism driven by patent licensing and offer strategic guidance for firms and policymakers navigating SDE-induced market exits.

1. Introduction

In practice, enterprises are often forced to exit the market due to sudden disruptive events (SDEs) such as wars, pandemics (e.g., COVID-19), geopolitical tensions, and natural disasters [1]. At such moments, patent licensing emerges as a viable strategy for high-tech manufacturers to sustain profit after market exit. For example, U.S. sanctions in 2019 compelled Huawei to withdraw from the 5G smartphone market [2]. In response, Huawei licensed key 5G patents to competitors such as OPPO and Samsung, thereby recouping part of its lost revenue [3]. A similar case occurred in 2012 when Nokia exited the smartphone market following bankruptcy [4] yet continued to generate revenue through patent licensing agreements with firms including Samsung and Xiaomi [5].

The above cases indicate that after SDEs, high-tech manufacturers forced to exit the market tend to license their patents to competitors in order to regain profits. However, the competitor’s strategic choices are more complex. Under the non-cooperative strategy, the high-tech manufacturer’s exit from the product market may lead some of its customers to switch to the competitor. Thereby the competitor’s market share increased. Under the cooperative strategy (i.e., supply chain reshaping), the high-tech manufacturer licenses its patents to the competitor. In this case, most of its customers may switch to the competitor, allowing the competitor to gain a larger market share. Meanwhile, the cooperation cost also affects the competitor’s profit. Therefore, the competitor must balance the customer transfer rate and the cooperation cost when making strategic decisions.

Although many studies have explored supply chain management under SDEs and supply chain decisions related to after-sales services, little attention has been paid to supply chain reshaping via patent licensing in such contexts. To address this research gap, we develop a multi-stage game model. We consider two competing manufacturers: a high-tech manufacturer and a common manufacturer. The former holds the proprietary production tech, while the latter must obtain licenses from the supplier to manufacture the product. Prior to SDEs, both manufacturers supplied products and after-sales services to the market. Following the SDE, the high-tech manufacturer was forced to exit the market but was able to recover part of its profit by cooperating with the common manufacturer through patent licensing. Upon receiving the cooperation request from the high-tech manufacturer, the common one may either accept or reject it. Under the non-cooperative strategy, only a small portion of the former’s customers switch to the latter (i.e., a low customer transfer rate). In contrast, under the cooperative strategy, the common manufacturer incorporates the proprietary production tech into its product, attracting more of the rival’s loyal customers (i.e., a higher customer transfer rate). However, cooperation also entails a fixed cost for both parties.

This model sheds light on the following research questions. First, how does the common manufacturer make strategic choices when receiving a cooperation request from the high-tech manufacturer after the SDE? Second, after SDEs, how does the cooperative strategy (i.e., supply chain reshaping) influence the patent licensing price, the common manufacturer’s output and after-sales service price, as well as the supply chain system profit, in comparison to the non-cooperative strategy? Third, compared with the scenario before the SDE, how does the SDE affect the patent licensing price, the common manufacturer’s output and after-sales service price, as well as the profits of all parties? In response to the first question, we find that the common manufacturer’s decision is jointly determined by the cooperation cost and the customer transfer rate. Specifically, when the cooperation cost is high, the manufacturer rejects cooperation. When the cost is low, the decision depends on the transfer rate: a high transfer rate leads to non-cooperation, while a low transfer rate leads to cooperation. Regarding the second question, we find that, compared to the non-cooperative case, supply chain reshaping not only increases the common manufacturer’s output and the after-sales service price but also raises the patent licensing price. Under certain conditions, it further improves the profit of the supply chain system. As for the third question, compared to the pre-SDE scenario, the SDE not only increases the common manufacturer’s output and after-sales service price but also raises the patent licensing price. Surprisingly, under certain conditions, the SDE may even improve the profit of each manufacturer.

This study makes the following contributions. From an academic perspective, it integrates patent licensing and supply chain reshaping under SDEs within a unified multi-stage game-theoretical framework, providing new insights into cooperation incentives when a market exit occurs. It also bridges the gap between after-sales service decisions and intellectual property strategies in disrupted supply chains, which has been largely overlooked in prior research. From a practical perspective, the findings offer guidance for high-tech firms facing SDEs by showing when patent licensing can serve as an effective recovery mechanism and for policymakers to design collaborative frameworks that enhance supply chain resilience.

The rest of our study is structured as follows. Section 2 reviews the most related literature. Section 3 outlines the model framework. Section 4 provides decision analysis under cooperative and non-cooperative strategies after the SDE. Section 5 contrasts the models before and after the SDE. Section 6 investigates how after-sales service affects the common manufacturer’s strategic behavior. Section 7 extends the model. Section 8 concludes. And Section 9 is discussion and implications.

2. Literature Review

This study relates to two major streams of literature. The first focuses on supply chain management in the context of sudden disruptive events. Paul et al. (2019) developed a mathematical model aimed at maximizing profit under a finite planning horizon with imperfect production and later reconstructed it to formulate recovery strategies after disruptions. Their results confirm that the proposed approach can effectively generate post-disruption recovery plans [6]. Akkermans and Van Wassenhove (2018), using a case from the high-tech electronics sector, introduced the concept of a “supply chain tsunami” and linked it to revitalization strategies and the broader research agenda in supply chain management [7]. Zaefarian et al. (2024) analyzed a dynamic stochastic supply channel game involving a manufacturer and a retailer, demonstrating that government support for green production can help firms survive disruptive shocks [8]. Abolghasemi et al. (2020) proposed a model that quantifies systemic events and integrates them into traditional statistical frameworks, thereby improving demand forecasting accuracy. Empirical validation with Australian firm data showed superior performance compared to expert judgment and machine learning methods [9]. Daghar et al. (2023) conducted a case study on a large multinational firm affected by the COVID-19 pandemic, identifying key drivers of supply chain resilience and providing theoretical insights into phased resilience under demand volatility and geographic dispersion of suppliers [10].

While these studies primarily focus on government interventions and structural factors that influence supply chain resilience, little attention has been paid to the role of patent licensing as a means for distressed firms to regain profitability through cooperation with competitors. Addressing this gap, the present study investigates supply chain reshaping via patent licensing in the aftermath of SDEs.

The second relevant literature stream concerns supply chain decision-making involving after-sales services. Gurnani et al. (2022) studied the motivations of manufacturers and retailers in deciding whether to provide pre-sale and after-sales services. Their findings suggest that when the fixed cost of improving service effectiveness is low, manufacturers prefer to delegate after-sales responsibilities to retailers [11]. Li et al. (2014) examined a manufacturer–retailer supply chain and found that outsourcing after-sales services can lead to lower wholesale prices and increased market demand [12]. In a related work, Li et al. (2019) explored remanufacturing channels and service pricing, concluding that the most efficient configuration is for the retailer to handle both remanufacturing and after-sales services [13]. Kurata and Nam (2013) investigated the impact of demand uncertainty under different information structures, revealing that although uncertainty may temporarily align firm strategy with customer expectations, it does not fundamentally improve supply chain performance [14]. Chen et al. (2022) proposed a multi-channel pricing model that incorporates cross-channel effects, consumer trust, and after-sales service utility, implemented via a revenue-sharing contract. They showed that firms respond differently depending on cross-channel pressure and service effectiveness [15]. Zhang et al. (2019) found that information sharing is more likely when the manufacturer holds a cost advantage in service provision. However, retailers are reluctant to share information unless service costs are low and demand uncertainty is minimal [16].

These studies focus on service provision incentives, uncertainty effects, and the role of information sharing in after-sales settings. However, few have integrated after-sales service with supply chain reshaping. Unlike prior studies, our model considers both after-sales service and cooperation strategies driven by patent-based supply chain reshaping.

In addition to traditional coordination mechanisms and patent licensing, recent research has highlighted the enabling role of emerging technologies such as digital platforms and blockchain, particularly under disruption scenarios. Digital platforms reduce search and transaction costs in patent markets, facilitating more agile licensing agreements. Blockchain ensures transparency and trust in decentralized coordination, enabling secure and verifiable contract execution [17,18,19]. Although our model does not explicitly incorporate these technologies, they represent promising tools for patent-based supply chain collaboration and offer fertile directions for future research.

In summary, prior research has primarily focused on post-disruption recovery planning, resilience metrics, and traditional coordination mechanisms, with little attention paid to patent licensing as a tool for supply chain reshaping under sudden disruptive events. Moreover, studies on after-sales service decisions seldom integrate intellectual property strategies, leaving a gap in understanding how licensing can interact with service provision in disrupted markets. Furthermore, while emerging technologies such as digital platforms and blockchain have been recognized as enablers of supply chain coordination, their role in patent-based collaboration remains underexplored. We address these gaps by developing a multi-stage game-theoretical model that incorporates patent licensing, after-sales service, and supply chain reshaping in the context of sudden disruptive events.

In contrast to previous studies that mainly focused on supply chain resilience metrics or coordination mechanisms after disruptions, we offer a novel perspective by incorporating patent licensing as a strategic reshaping tool under sudden disruptive events. Prior works on patent licensing seldom addressed its role in post-disruption recovery, particularly in conjunction with after-sales service decisions. Furthermore, unlike traditional models, which often treat licensing and service independently, our framework unifies these elements in a multi-stage setting, allowing for a deeper exploration of how licensing affects service incentives and system-wide profit. This integration of intellectual property strategy with service under disruption distinguishes our study from existing literature.

3. Models and Assumptions

3.1. Benchmark Model Before the SDE

Before presenting the benchmark model, we summarize the key notation in

Table 1. Summary of notations.

Notation	Meaning of Notations
$w_k$	Patent licensing price in scenario $k$
$Q_{ki}$	Output of $i$ in scenario $k$
$P_{ki}$	Product price set by $i$ in scenario $k$
$P_{is}$	After-sales service price set by $i$ in the benchmark model
$\theta$	Quantity sensitivity factor
$\delta$	Substitution factor
$\lambda$	Price sensitive factor of after-sales service
$D$	Market potential
${\pi }_k^j$	Profit of $j$ in scenario $k$
$C{S}_k$	Consumer surplus in scenario $k$
$\phi$	Abbreviation: Customer transfer rate
$\tau$	Cooperation cost

for ease of reference. Subscripts $i\in \left\{h,m\right\}$ denote the high-tech and common manufacturer, respectively. Subscripts $k\in \left\{b,n,d,g\right\}$ represent the benchmark case, the non-cooperative scenario, the cooperative scenario, and the scenario without after-sales service, respectively. Superscripts $j\in \left\{h,m,S\right\}$ denote the high-tech manufacturer, common manufacturer, and supplier, respectively.

Consider a high-tech manufacturer and a common manufacturer competing in both the product and after-sales service markets. The former owns the proprietary production tech required for production. The latter must obtain a patent license from the supplier to produce the product.

The inverse demand functions faced by the common and high-tech manufacturers are given by $P_{bm}=D-\theta Q_{bm}-\delta Q_{bh}$ and $P_{bh}=D-\theta Q_{bh}-\delta Q_{bm}$, respectively [20]. In the above two functions, the subscript $b$ denotes the benchmark model; the subscript $m$ and $h$ refer to the common and high-tech manufacturers, respectively. $D$ denotes the market potential. $Q$ is the output of the manufacturers. $\theta$ is the quantity sensitivity factor, and $\delta$ is the substitution factor, where $0<\delta <\theta$. To facilitate computation, we normalize $\theta$ to 1, implying $0<\delta <1$. Accordingly, the inverse demand functions for the common and high-tech manufacturers are given by the following:

$$P_{bm}=D-Q_{bm}-\delta Q_{bh}$$

(1)

$$P_{bh}=D-Q_{bh}-\delta Q_{bm}$$

(2)

We adopt a linear inverse demand function, which is widely used to reflect price-sensitive behavior and enable closed-form solutions [21]. This formulation allows us to derive explicit managerial insights, although more general nonlinear demand structures can be considered in future work.

Both of the two manufacturers offer after-sales services to consumers following product sales. We assume that the quantity of after-sales services equals the product sales volume. This assumption is consistent with common practices in high-tech consumer markets where optional paid after-sales services are closely tied to product sales. For instance, in the smartphone industry, premium services such as extended warranties or professional setup (e.g., AppleCare+, Huawei Premium Service) are typically offered once per device sold. Although consumers can choose whether to purchase such services, studies often model the potential service demand as proportional to product sales on a one-to-one basis for analytical tractability [22]. The demand for after-sales service faced by the common manufacturer is as follows:

$$Q_{ms}=Q_{bm}-\lambda P_{ms}$$

(3)

The high-tech manufacturer faces the following demand for after-sales service:

$$Q_{hs}=Q_{bh}-\lambda P_{hs}$$

(4)

In (3) and (4), $\lambda$ represents the price sensitive factor of after-sales service, satisfying $\lambda >0$. For analytical relevance, we assume $\lambda \ge 1/2(2-\delta )$. For simplicity, let ${\lambda }_0=1/2(2-\delta )$. Figure 1 shows the models.

The sequence of events under the benchmark model is illustrated in Figure 2. First, the supplier sets the patent licensing price $w_b$. Then, the high-tech and common manufacturers determine their output $Q_{bh}$ and $Q_{bm}$, respectively. Finally, the two manufacturers decide their after-sales service prices $P_{hs}$ and $P_{ms}$, respectively.

3.2. Model After Sudden Disruptive Events

In practice, sudden disruptive events (SDEs) often force firms to exit the market. In such cases, patent licensing becomes an effective strategy for high-tech manufacturers to sustain profits. This section explores how supply chains can be reshaped through patent licensing after SDEs.

Our model examines a scenario in which the SDE forces the high-tech manufacturer to exit the market. Subsequently, it may re-enter indirectly by licensing its patent to the common manufacturer, who then decides whether to cooperate. The strategic interaction between manufacturers is modeled as a binary choice—either to cooperate or not. This structure has been employed in the literature [23].

In the case of non-cooperation, the supplier licenses the patent directly to the common manufacturer, who then provides both products and after-sales service to the market. As the high-tech manufacturer exits, part of its original customer base shifts to the common manufacturer. Accordingly, the market potential faced by the latter increases from $D$ to $\left(1+\phi \right)D$ (where $0<\phi <1$), and its product price and after-sales service demand are given by the following:

$$P_{np}=\left(1+\phi \right)D-Q_{np}$$

(5)

$$Q_{ns}=Q_{np}-\lambda P_{ns}$$

(6)

Under the cooperation case, the high-tech manufacturer licenses its patent to the common manufacturer, who then produces the product, sells it, and provides after-sales service. Most customers who previously purchased from the former now switch to the latter, increasing the latter’s market potential from $D$ to $\left(1+\xi \right)D$, where $\xi >\phi$. Without loss of generality, we normalize $\xi =1$. Similar normalizations are common in the literature to reduce model complexity and highlight core strategic interactions [24]. This is a simplifying assumption. To evaluate the generalizability and robustness of our results, Section 7 extends the model by relaxing this constraint and considering a more general case $\phi <\xi \le 1$. The common manufacturer’s product price function is $P_{dp}=2D-Q_{dp}$, and its after-sales service demand is as follows:

$$Q_{ds}=Q_{dp}-\lambda P_{ds}$$

(7)

We assume a fixed cooperation cost $\tau$, which captures the negotiation, adaptation, and coordination costs associated with licensing collaboration. This approach is consistent with existing models that consider fixed cost structures in supply chain relationships [25].

Figure 3 outlines the sequence of events following the SDE. Once the high-tech manufacturer exits the market, the common manufacturer decides whether to accept the cooperation. If cooperation is rejected, the supplier first sets the patent licensing price $w_n$, after which the common manufacturer determines the output $Q_{np}$ and sets the after-sales service price $P_{ns}$. If cooperation is accepted, the high-tech manufacturer first sets the licensing price $w_d$, followed by the common manufacturer’s decisions on output $Q_{dp}$ and service price $P_{ds}$, where subscript $n$ denotes the non-cooperation scenario, and subscript $d$ represents the cooperation scenario.

4. Decision Result

4.1. Benchmark Model Before the SDE

Using backward induction, we first analyze the after-sales service pricing decisions of the common and high-tech manufacturers. Given the supplier’s patent licensing price $w_b$, the common manufacturer’s output is $Q_{bm}$ and high-tech manufacturer’s output is $Q_{bh}$. The common and high-tech manufacturers determine the after-sales service prices $P_{ms}$ and $P_{hs}$ to maximize their own profits ${\pi }_b^m$ and ${\pi }_b^h$, respectively, that is,

$$\underset{P_{ms}}{max} {\pi }_b^m=P_{ms}\left(Q_{bm}-\lambda P_{ms}\right)+Q_{bm}\left(D-Q_{bm}-\delta Q_{bh}-w_b\right)$$

(8)

$$s.t. P_{ms}\ge 0$$

$$\underset{P_{hs}}{max} {\pi }_b^h=P_{hs}\left(Q_{bh}-\lambda P_{hs}\right)+Q_{bh}\left(D-Q_{bh}-\delta Q_{bm}\right)$$

(9)

$$s.t. P_{hs}\ge 0$$

$P_{ms}\left(Q_{bm}-\lambda P_{ms}\right)$ and $Q_{bm}\left(D-Q_{bm}-\delta Q_{bh}-w_b\right)$ denote the after-sales service profit and the product sales profit of the common manufacturer, respectively. $P_{hs}\left(Q_{bh}-\lambda P_{hs}\right)$ and $Q_{bh}\left(D-Q_{bh}-\delta Q_{bm}\right)$ denote the after-sales service profit and the product sales profit of the high-tech manufacturer, respectively. Next, we consider the output decisions of the two manufacturers. Given the supplier’s patent licensing price $w_b$, the common and high-tech manufacturers simultaneously determine their output $Q_{bm}$ and $Q_{bh}$ to maximize their profits ${\pi }_b^m$ and ${\pi }_b^h$, respectively, that is,

$$\underset{Q_{bm}}{max} {\pi }_b^m=P_{ms}\left(Q_{bm}-\lambda P_{ms}\right)+Q_{bm}\left(D-Q_{bm}-\delta Q_{bh}-w_b\right)$$

(10)

$$s.t. Q_{bm}\ge 0$$

$$\underset{Q_{bh}}{max} {\pi }_b^h=P_{hs}\left(Q_{bh}-\lambda P_{hs}\right)+Q_{bh}\left(D-Q_{bh}-\delta Q_{bm}\right)$$

(11)

$$s.t. Q_{bh}\ge 0$$

$Q_{bh}\left(D-Q_{bh}-\delta Q_{bm}\right)$ denotes the product sales profit of the high-tech manufacturer. Next, we consider the supplier’s patent licensing decision: the supplier determines the licensing price $w_b$ to maximize his profit, that is,

$$\underset{w_b}{max} {\pi }_b^S=w_b{Q}_{bm}$$

(12)

$$s.t. w_b\ge 0$$

Solving the four optimization problems above yields the equilibrium decisions and profits of each party. See Lemma 1.

Lemma 1. 

Under the benchmark model, the equilibrium decisions and profits of all supply chain members are shown in

Table 2. The equilibrium decisions and profits of all supply chain members under benchmark model.

Variable	Equilibrium
$\mathrm{Patent} \mathrm{licensing} \mathrm{price} (w_b^{*}$)	${\displaystyle \frac{\left(2\left(\delta -2\right)\lambda +1\right)D}{2-8\lambda }}$
$\mathrm{Common} \mathrm{manufacturer}’\mathrm{s} \mathrm{output} (Q_{bm}^{*}$)	${\displaystyle \frac{\lambda D}{2\left(\delta +2\right)\lambda -1}}$
$\text{High-tech} \mathrm{manufacturer}’\mathrm{s} \mathrm{output} (Q_{bh}^{*}$)	${\displaystyle \frac{2\lambda D\left(\left(\delta +4\right)\lambda -1\right)}{\left(4\lambda -1\right)\left(2\left(\delta +2\right)\lambda -1\right)}}$
$\mathrm{Common} \mathrm{manufacturer}’\mathrm{s} \text{after-sales} \mathrm{service} \mathrm{price} (P_{ms}^{*}$)	${\displaystyle \frac{D}{4\left(\delta +2\right)\lambda -2}}$
$\text{High-tech} \mathrm{manufacturer}’\mathrm{s} \text{after-sales} \mathrm{service} \mathrm{price} (P_{hs}^{*}$)	${\displaystyle \frac{D\left(\left(\delta +4\right)\lambda -1\right)}{\left(4\lambda -1\right)\left(2\left(\delta +2\right)\lambda -1\right)}}$
$\mathrm{Profit} \mathrm{of} \mathrm{supplier} ({\pi }_b^{S*}$)	${\displaystyle \frac{D^2\left(2\left(\delta -2\right)\lambda +1\right)}{\left(2-8\lambda \right)\left(4\left(\delta +2\right)\lambda -2\right)}}$
$\mathrm{Profit} \mathrm{of} \mathrm{common} \mathrm{manufacturer} ({\pi }_b^{m*}$)	${\displaystyle \frac{D^2\lambda \left(8\left(\delta \left(\delta +4\right)+2\right){\lambda }^2-4\left(\delta \left(\delta +6\right)+2\right)\lambda +4\delta +1\right)}{4\left(4\lambda -1\right){\left(1-2\left(\delta +2\right)\lambda \right)}^2}}$
$\mathrm{Profit} \mathrm{of} \text{high-tech} \mathrm{manufacturer} ({\pi }_b^{h*}$)	${\displaystyle \frac{D^2\lambda {\left(\left(\delta +4\right)\lambda -1\right)}^2}{\left(4\lambda -1\right){\left(1-2\left(\delta +2\right)\lambda \right)}^2}}$

.

Referring to Singh and Vives (1984) [21] and applying Lemma 1, we obtain the consumer surplus in the benchmark model as follows:

$$C{S}_b=D{Q}_{bm}+D{Q}_{bh}-{\displaystyle \frac{\left({Q_{bm}}^2+2\delta Q_{bm}{Q}_{bh}+{Q_{bh}}^2\right)}{2}}-P_{bm}{Q}_{bm}-P_{bh}{Q}_{bh}+{\displaystyle \frac{{\left(Q_{ms}\right)}^2+{\left(Q_{hs}\right)}^2}{2\lambda }}$$

(13)

$D{Q}_{bm}+D{Q}_{bh}-\left({Q_{bm}}^2+2\delta Q_{bm}{Q}_{bh}+{Q_{bh}}^2\right)/2-P_{bm}{Q}_{bm}-P_{bh}{Q}_{bh}$ denotes the consumer surplus from the product, and $\left({\left(Q_{ms}\right)}^2+{\left(Q_{hs}\right)}^2\right)/\left(2\lambda \right)$ denotes the consumer surplus from the after-sales service. Equation (13) can be simplified as follows:

$$C{S}_b={\displaystyle \frac{D^2\lambda \left(4\lambda \left(4\left(\delta \left(5\delta +24\right)+20\right){\lambda }^2-\left(\delta +10\right)\left(3\delta +2\right)\lambda +2\delta -5\right)+5\right)}{8{\left(1-4\lambda \right)}^2{\left(1-2\left(\delta +2\right)\lambda \right)}^2}}$$

Proof of Lemma 1. 

In the benchmark model, let $\partial {\pi }_b^m/\partial P_{ms}=0$, yield its first-order conditional solution:

$$P_{ms}={\displaystyle \frac{Q_{bm}}{2\lambda }}$$

since ${\partial }^2{\pi }_b^m/\partial {P_{ms}}^2=-2\lambda <0$, the above first-order condition solution is optimal.

Using a similar proof method as above, we obtain the following:

$$P_{hs}^{*}={\displaystyle \frac{Q_{bh}}{2\lambda }}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}$$

$$Q_{bm}^{*}={\displaystyle \frac{2\lambda \left(D-\delta Q_{bh}-w_b\right)}{4\lambda -1}}$$

(14)

$$Q_{bh}^{*}={\displaystyle \frac{2\lambda \left(D-\delta Q_{bm}\right)}{4\lambda -1}}\hspace{1em}\hspace{1em}$$

(15)

Combining (14) and (15) yields the following:

$$Q_{bm}^{*}={\displaystyle \frac{2\left(2\delta {\lambda }^{2}D-4{\lambda }^{2}D+\lambda D+4{\lambda }^2{w}_b-\lambda w_b\right)}{4{\delta }^2{\lambda }^2-16{\lambda }^2+8\lambda -1}}$$

$$Q_{bh}^{*}={\displaystyle \frac{2\lambda \left(2\delta \lambda D-4\lambda D+D-2\delta \lambda w_b\right)}{4{\delta }^2{\lambda }^2-16{\lambda }^2+8\lambda -1}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}$$

Using a similar proof method as above, we obtain the following:

$$w_b^{*}={\displaystyle \frac{\left(2\left(\delta -2\right)\lambda +1\right)D}{2-8\lambda }}$$

By simple substitution, we can obtain the equilibrium decision, profit, and consumer surplus in Lemma 1. □

4.2. Model After the SDE

The high-tech manufacturer will be forced out of the market if it fails to respond to the SDE in time. If it cooperates with the common manufacturer to reshape the supply chain, it can regain part of the profit.

4.2.1. High-Tech Manufacturer Is Squeezed out of the Market

Using backward induction, we first consider the after-sales service pricing decision of the common manufacturer. Given the supplier’s patent licensing price $w_n$ and the output $Q_{np}$ of the common manufacturer, it determines the service price $P_{ns}$ to maximize its profit ${\pi }_n^m$, that is,

$$\underset{P_{ns}}{max} {\pi }_n^m=P_{ns}\left(Q_{np}-\lambda P_{ns}\right)+Q_{np}\left(\left(1+\phi \right)D-Q_{np}-w_n\right)$$

(16)

$$s.t. P_{ns}\ge 0$$

$P_{ns}\left(Q_{np}-\lambda P_{ns}\right)$ and $Q_{np}\left(\left(1+\phi \right)D-Q_{np}-w_n\right)$ denote the after-sales service profit and the product sales profit of the common manufacturer, respectively. We then analyze the output decision of the common manufacturer. Given the supplier’s patent licensing price $w_n$, it determines the output to maximize its profit ${\pi }_n^m$, that is,

$$\underset{Q_{np}}{max} {\pi }_n^m=P_{ns}\left(Q_{np}-\lambda P_{ns}\right)+Q_{np}\left(\left(1+\phi \right)D-Q_{np}-w_n\right)$$

(17)

$$s.t. Q_{np}\ge 0$$

We then consider the supplier’s decision on the patent licensing price: it sets the licensing price $w_n$ to maximize its profit ${\pi }_n^S$, that is,

$$\underset{w_n}{max} {\pi }_n^S=w_n{Q}_{np}$$

(18)

$$s.t. w_n\ge 0$$

Solving the two optimization problems above yields the equilibrium decisions and profits of each party. See Lemma 2.

Lemma 2. 

After the high-tech manufacturer exits the market, the equilibrium decisions and profits of all supply chain members are shown in

Table 3. The equilibrium decisions and profits of all supply chain members after the high-tech manufacturer exits the market.

Variable	Equilibrium
$\mathrm{Patent} \mathrm{licensing} \mathrm{price} (w_n^{*}$)	${\displaystyle \frac{\left(1+\phi \right)D}{2}}$
$\mathrm{Common} \mathrm{manufacturer}’\mathrm{s} \mathrm{output} (Q_{np}^{*}$)	${\displaystyle \frac{\left(1+\phi \right)\lambda D}{4\lambda -1}}$
$\mathrm{Common} \mathrm{manufacturer}’\mathrm{s} \text{after-sales} \mathrm{service} \mathrm{price} (P_{ns}^{*}$)	${\displaystyle \frac{\left(1+\phi \right)D}{8\lambda -2}}$
$\mathrm{Profit} \mathrm{of} \mathrm{supplier} ({\pi }_n^{S*}$)	${\displaystyle \frac{{\left(1+\phi \right)}^2\lambda D^2}{8\lambda -2}}$
$\mathrm{Profit} \mathrm{of} \mathrm{common} \mathrm{manufacturer} ({\pi }_n^{m*}$)	${\displaystyle \frac{{\left(1+\phi \right)}^2\lambda D^2}{16\lambda -4}}$

.

After the SDE, the consumer surplus under the scenario where the high-tech manufacturer exits the market is given as follows:

$$C{S}_n={\displaystyle \frac{{Q_{np}}^2}{2}}+{\displaystyle \frac{{Q_{ns}}^2}{2\lambda }}$$

(19)

Equation (19) can be simplified as follows:

$$C{S}_n=D^2{\left(1+\phi \right)}^2\lambda \left(4\lambda +1\right)/\left(8{\left(1-4\lambda \right)}^2\right)$$

Proof of Lemma 2. 

Using a proof similar to that of Lemma 1, Lemma 2 can also be proven. □

4.2.2. The High-Tech Manufacturer Regains Part of Its Profit by Cooperating with the Common Manufacturer

Using backward induction, we first analyze the after-sales service pricing decisions of the common and high-tech manufacturers. Given the patent licensing price $w_d$ of the high-tech manufacturer and the output decision $Q_{dp}$ of the common manufacturer, the common manufacturer chooses the after-sales service price $P_{ds}$ to maximize its profit ${\pi }_d^m$, that is,

$$\underset{P_{ds}}{max} {\pi }_d^m=P_{ds}\left(Q_{dp}-\lambda P_{ds}\right)+Q_{dp}\left(2D-Q_{dp}-w_d\right)-\tau$$

(20)

$$s.t. P_{ds}\ge 0$$

We then consider the output decision of the common manufacturer. Given the patent licensing price $w_d$ set by the high-tech manufacturer, it chooses the output $Q_{dp}$ to maximize its profit ${\pi }_d^m$, that is,

$$\underset{Q_{dp}}{max} {\pi }_d^m=P_{ds}\left(Q_{dp}-\lambda P_{ds}\right)+Q_{dp}\left(2D-Q_{dp}-w_d\right)-\tau$$

(21)

$$Q_{dp}\ge 0$$

Finally, we consider the patent licensing decision of the high-tech manufacturer, that is,

$$\underset{w_d}{max} {\pi }_d^h=w_d{Q}_{dp}-\tau$$

(22)

$$s.t. w_d\ge 0$$

Solving the three optimization problems above yields the equilibrium decisions of the two manufacturers. See Lemma 3.

Lemma 3. 

After the two manufacturers cooperate, the equilibrium decisions and profits of each party are are shown in

Table 4. The equilibrium decisions and profits of all supply chain members after the two manufacturers cooperate.

Variable	Equilibrium
$\mathrm{Patent} \mathrm{licensing} \mathrm{price} (w_d^{*}$)	$D$
$\mathrm{Common} \mathrm{manufacturer}’\mathrm{s} \mathrm{output} (Q_{dp}^{*}$)	${\displaystyle \frac{2\lambda D}{4\lambda -1}}$
$\mathrm{Common} \mathrm{manufacturer}’\mathrm{s} \text{after-sales} \mathrm{service} \mathrm{price} (P_{ds}^{*}$)	${\displaystyle \frac{D}{4\lambda -1}}$
$\mathrm{Profit} \mathrm{of} \mathrm{common} \mathrm{manufacturer} ({\pi }_d^{m*}$)	${\displaystyle \frac{\lambda D^2}{4\lambda -1}}-\tau$
$\mathrm{Profit} \mathrm{of} \text{high-tech} \mathrm{manufacturer} ({\pi }_d^{h*}$)	${\displaystyle \frac{2\lambda D^2}{4\lambda -1}}-\tau$

.

When the two manufacturers cooperate, the resulting consumer surplus is as follows:

$$C{S}_d={\displaystyle \frac{{Q_{dp}}^2}{2}}+{\displaystyle \frac{{Q_{ds}}^2}{2\lambda }}$$

(23)

Equation (23) can be simplified as follows: $C{S}_d=D^2\lambda \left(4\lambda +1\right)/\left(2{\left(1-4\lambda \right)}^2\right)$.

Proof of Lemma 3. 

Using a proof similar to that of Lemma 1, Lemma 3 can also be proven. □

4.2.3. Comparison of Cooperative and Non-Cooperative Strategies

Proposition 1. 

Compared with the non-cooperative case, cooperation not only increases the common manufacturer’s output (i.e., $Q_{dp}^{*}>Q_{np}^{*}$) and after-sales service price (i.e., $P_{ds}^{*}>P_{ns}^{*}$) but also raises the patent licensing price (i.e., $w_d^{*}>w_n^{*}$) and consumer surplus (i.e., $C{S}_d>C{S}_n$).

The rationale behind Proposition 1 is as follows. After cooperation, the high-tech manufacturer licenses its patents to the common manufacturer. The latter then supplies both products and after-sales service to the market. Most consumers who previously purchased from the former shift to the latter, leading to an increase in the latter’s output under the cooperative setting. To safeguard its profit, the high-tech manufacturer typically does not offer a reduced licensing price out of goodwill; instead, it tends to set a higher fee, increasing the cost burden on the common manufacturer. To offset the resulting profit loss, the common manufacturer raises the service price. Cooperation also enhances consumer trust in the brand, thereby increasing consumer surplus. Proposition 1 provides a key managerial insight: even when seeking cooperation, a rival prioritizes its own profit. Therefore, when considering a cooperative proposal from a competitor, firms should carefully evaluate the potential downsides.

Proof of Proposition 1. 

Since

$$Q_{np}^{*}-Q_{dp}^{*}={\displaystyle \frac{\left(\phi -1\right)\lambda D}{4\lambda -1}}\le 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}$$

$$w_n^{*}-w_d^{*}={\displaystyle \frac{\left(\phi -1\right)D}{2}}\le 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}$$

$$P_{ns}-P_{ds}={\displaystyle \frac{D\left(\phi -1\right)}{8\lambda -2}}<0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}$$

$$C{S}_n-C{S}_d={\displaystyle \frac{D^2\left(\phi -1\right)\left(\phi +3\right)\lambda \left(4\lambda +1\right)}{8{\left(1-4\lambda \right)}^2}}\le 0$$

$Q_{np}^{*}\le Q_{dp}^{*}$, $w_n^{*}\le w_d^{*}$, $P_{ns}^{*}<P_{ds}^{*}$, and $C{S}_n\le C{S}_d$ can be proved. □

Proposition 2 is obtained by comparing the common manufacturer’s profit under the cooperative and non-cooperative strategies.

Proposition 2. 

When the cooperation cost is high (i.e., $\tau \ge {\tau }_0$), the common manufacturer prefers non-cooperation strategy (i.e., ${\pi }_d^{m*}<{\pi }_n^{m*}$). When the cost is low (i.e., $\tau <{\tau }_0$), the decision further depends on the customer transfer rate. A high transfer rate (i.e., $\phi >{\phi }_0$) leads to non-cooperation (i.e., ${\pi }_d^{m*}<{\pi }_n^{m*}$), while a low transfer rate (i.e., $\phi \le {\phi }_0$) results in cooperation (i.e., ${\pi }_d^{m*}\ge {\pi }_n^{m*}$), where ${\tau }_0=3D^2\lambda /\left(16\lambda -4\right)$ and ${\phi }_0=2\sqrt{D^2\lambda \left(-4\tau \lambda +\tau +D^2\lambda \right)}/\left(D^2\lambda \right)-1$.

Figure 4 illustrates the conclusion of Proposition 2. Intuitively, after the SDE, the common manufacturer—who gains market dominance—would be expected to reject any cooperation proposed by the high-tech manufacturer. However, Proposition 2 reveals a counterintuitive threshold effect: cooperation arises when both the cooperation cost and customer transfer rate are sufficiently low.

The rationale is twofold. When the transfer rate is low, the common manufacturer captures only a limited share of the high-tech manufacturer’s customers under the non-cooperative strategy. In contrast, cooperation via patent licensing allows access to the rival’s loyal customer base, thereby expanding market reach. A low cooperation cost further facilitates this partnership. As a result, cooperation can yield higher profits than monopolistic dominance.

Conversely, if either the cooperation cost or the transfer rate is high, the common manufacturer prefers to remain a monopolist. This leads to a double-threshold decision structure: cooperation occurs when both thresholds are met, making the strategy mutually beneficial.

To verify the robustness and practical relevance of Proposition 2, we conduct a numerical example using realistic synthetic data calibrated to the smartphone industry (see Figure 5). The parameters are $\lambda =0.6$, $D=800$ USD, and $c=\mathrm{150,000}$ USD. The results confirm Proposition 2: these findings demonstrate that the theoretical conclusions remain valid under plausible real-world conditions.

Proof of Proposition 2. 

$${\pi }_n^{m*}-{\pi }_d^{m*}={\displaystyle \frac{4\tau \left(4\lambda -1\right)+D^2\left(\phi -1\right)\left(\phi +3\right)\lambda }{16\lambda -4}}$$

let ${\pi }_n^{m*}-{\pi }_d^{m*}=0$, yields: ${\phi }_0={\displaystyle \frac{2\sqrt{D^2\lambda \left(D^2\lambda -4\tau \lambda +\tau \right)}}{D^2\lambda }}-1$, when $\tau <{\displaystyle \frac{3D^2\lambda }{4(4\lambda -1)}}$, ${\phi }_0$ satisfies $0<\phi <1$. Thus, when $\tau <{\displaystyle \frac{3D^2\lambda }{4\left(4\lambda -1\right)}}$ and $\phi \le {\phi }_0$, ${\pi }_d^{m*}\ge {\pi }_n^{m*}$; when $\tau <{\displaystyle \frac{3D^2\lambda }{4\left(4\lambda -1\right)}}$ and $\phi >{\phi }_0$, ${\pi }_d^{m*}<{\pi }_n^{m*}$; when $\tau \ge {\displaystyle \frac{3D^2\lambda }{4(4\lambda -1)}}$, ${\pi }_d^{m*}<{\pi }_n^{m*}$. □

Proposition 3. 

If the cooperation cost is high (i.e., $\tau \ge {\tau }_1$), the supply chain system achieves a higher profit under the non-cooperative strategy (i.e., ${\pi }_d<{\pi }_n$). If the cooperation cost is low (i.e., $\tau <{\tau }_1$), the comparison of supply chain profits depends on the customer transfer rate. When the transfer rate is high (i.e., $\phi >{\phi }_1$), the non-cooperative strategy yields a higher system profit (i.e., ${\pi }_d<{\pi }_n$); in contrast (i.e., $\phi \le {\phi }_1$), the cooperative strategy leads to a higher profit (i.e., ${\pi }_d\ge {\pi }_n$), where ${\tau }_1=9D^2\lambda /\left(32\lambda -8\right)$, ${\phi }_1=2\sqrt{D^2\lambda \left(-8c\lambda +2c+3D^2\lambda \right)}/\left(\sqrt{3}{D}^2\lambda \right)-1$, ${\pi }_d={\pi }_d^{m*}+{\pi }_d^{h*}$, ${\pi }_n={\pi }_n^{S*}+{\pi }_n^{m*}$.

Figure 6 visually illustrates the conclusion of Proposition 3. The underlying economic intuition concerns how cooperation reshapes market coverage and reallocates profits under different parameter conditions. When the customer transfer rate is low, few consumers shift to the common manufacturer under the non-cooperative strategy. In contrast, cooperation enables the common manufacturer to access the high-tech manufacturer’s loyal customer base, thereby expanding its market potential and improving profitability. Meanwhile, the high-tech manufacturer secures substantial profit through patent licensing, supported by a relatively high licensing price. Consequently, the supply chain system profit under cooperation may exceed that under non-cooperation. However, this advantage depends critically on the cooperation cost. Only when the cost is sufficiently low can the gains from collaboration outweigh its burden. Thus, Proposition 3 highlights a threshold effect: cooperation outperforms non-cooperation only when the cooperation cost falls below a certain level, allowing both parties to realize potential synergy.

Proof of Proposition 3. 

Using a proof similar to that of Proposition 2, Proposition 3 can also be proven. □

Corollary 1. 

${\eta }_1>{\eta }_0$  and $c_1>c_0$.

Figure 7 is derived from Figure 4 and Figure 6 and visually illustrates the insights of Corollary 1, which reveals the misalignment between the common manufacturer’s optimal strategy and the supply chain system optimum. The shaded area in the figure highlights the region where such distortion occurs. The source of this misalignment lies in two opposing forces: the limited relative advantage of the cooperation strategy for the common manufacturer and the profit erosion caused by the patent licensing payment to the high-tech manufacturer. In the cooperative setting, the high-tech manufacturer tends to charge a relatively high licensing price, thereby extracting part of the common manufacturer’s profit. Consequently, in the shaded region, although cooperation yields a higher supply chain system profit, the common manufacturer may still prefer non-cooperation due to reduced individual gain. Corollary 1 suggests that although the supply chain system has a higher tolerance for cooperation cost, the common manufacturer’s willingness to bear such cost ultimately determines whether cooperation is feasible. This yields a managerial implication: the high-tech manufacturer should prioritize partnering with large-scale competitors who have stronger cost tolerance to ensure successful supply chain reshaping.

Proof of Corollary 1. 

Using a proof similar to that of Proposition 2, Corollary 1 can also be proven. □

5. Model Comparison

Proposition 4 is derived by comparing the common manufacturer’s output before and after the SDE.

Proposition 4. 

Compared with the benchmark model before the SDEs, the SDEs increase not only the patent licensing price (i.e., $w^{*}>w_b^{*}$) but also the common manufacturer’s output and after-sales service price (i.e., $Q_p^{*}>Q_{bm}^{*}$; $P_{ns}^{*}>P_{ms}^{*}$), where

$$w^{*}=\left\{\begin{array}{l}{w}_d^{*},\phi \le {\phi }_0\\ w_n^{*},\phi >{\phi }_0\end{array}\right., Q_p^{*}=\left\{\begin{array}{l}{Q}_{dp}^{*},\phi \le {\phi }_0\\ Q_{np}^{*},\phi >{\phi }_0\end{array}\right., P_s^{*}=\left\{\begin{array}{l}{P}_{ds}^{*},\phi \le {\phi }_0\\ P_{ns}^{*},\phi >{\phi }_0\end{array}\right.$$

The reason is that, following the SDE, customer transfer arises in both cooperative and non-cooperative cases, expanding the market potential for the common manufacturer. Consequently, the common manufacturer’s output increases. To secure their own profit, the high-tech manufacturer or the supplier imposes a higher patent licensing fee. The resulting profit loss for the common manufacturer is compensated by raising the price of after-sales services.

Proof of Proposition 4. 

When $\phi \le {\phi }_0$

$${\displaystyle \frac{Q_{dp}^{*}}{Q_{bm}^{*}}}-1={\displaystyle \frac{\delta }{4\lambda -1}}+\delta +1>0$$

$$\hspace{1em}{w}_d^{*}-w_b^{*}={\displaystyle \frac{D\left(2\left(\delta +2\right)\lambda -1\right)}{8\lambda -2}}>0$$

$$P_{ds}^{*}-P_{ms}^{*}={\displaystyle \frac{\delta }{4\lambda -1}}+\delta +1>0$$

when $\phi >{\phi }_0$

$$Q_{np}^{*}={\displaystyle \frac{\left(1+\phi \right)\lambda D}{4\lambda -1}}, Q_{bm}^{*}={\displaystyle \frac{\lambda D}{2\left(\delta +2\right)\lambda -1}}$$

where $\left(1+\phi \right)\lambda D>\lambda D$ and $4\lambda -1<2\left(\delta +2\right)\lambda -1$. Thus, $Q_{np}^{*}>Q_{bm}^{*}$.

$$w_n^{*}-w_b^{*}={\displaystyle \frac{D\left(2\delta \lambda +\phi \left(4\lambda -1\right)\right)}{8\lambda -2}}>0$$

$$P_{ns}^{*}={\displaystyle \frac{\left(1+\phi \right)D}{8\lambda -2}}, P_{ms}^{*}={\displaystyle \frac{D}{4\left(\delta +2\right)\lambda -2}}$$

where $\left(1+\phi \right)D>D$, $8\lambda -2<4\left(\delta +2\right)\lambda -2$, so $P_{ns}^{*}>P_{ms}^{*}$. Therefore, $Q_p^{*}>Q_{bm}^{*}$, $w^{*}>w_b^{*}$, $P_s^{*}>P_{ms}^{*}$. □

By comparing the common manufacturer’s profit before and after the SDE, we derive Proposition 5.

Proposition 5. 

The affect of SDEs on the common manufacturer’s profit are shown in

Table 5. The effects of the SDE on the profit of common manufacturer.

Condition	Effects on the Profit of Common Manufacturer
$\phi <{\phi }_2$
$D<D_1$	${\pi }^{m*}<{\pi }_b^{m*}$
$D_1\le D\le D_2$
$\tau \le {\tau }_2$	${\pi }^{m*}\ge {\pi }_b^{m*}$
$\tau >{\tau }_2$	${\pi }^{m*}<{\pi }_b^{m*}$
$D>D_2$	${\pi }^{m*}\ge {\pi }_b^{m*}$
$\phi >{\phi }_2$
$D<D_1$	${\pi }^{m*}<{\pi }_b^{m*}$
$D\ge D_1$	${\pi }^{m*}\ge {\pi }_b^{m*}$

${\pi }^{m*}=\left\{\begin{array}{l}{\pi }_d^{m*},\phi \le {\phi }_0\\ {\pi }_n^{m*},\phi >{\phi }_0\end{array}\right.$ ${\pi }_b^{m*}$ and ${\pi }^{m*}$ represent the profits of the common manufacturer before and after the SDE, respectively; ${\pi }_d^{m*}$ and ${\pi }_n^{m*}$ represent the profits of common manufacturer under cooperative and non-cooperative strategies, respectively.

.

Figure 8 illustrates the insights of Proposition 5, which uncovers a key economic intuition: when the market potential is sufficiently large, or the cooperation cost is relatively low, the common manufacturer can achieve higher profits after the SDE. This result stems from two mechanisms. Under cooperation, a low collaboration cost allows the common manufacturer to serve the rival’s former customers at minimal expense, thereby boosting profit. Under non-cooperation, the common manufacturer becomes the sole product provider in the market. In this case, greater market potential directly translates into increased demand and revenue. Therefore, Proposition 5 reveals that SDEs do not necessarily reduce profit. Under specific conditions, the SDE may create opportunities for the common manufacturer to improve performance—either through cost-effective collaboration or by capitalizing on monopolistic market access.

Proof of Proposition 5. 

Proposition 5 can be proved similarly by applying the same method used in Proposition 4. □

Proposition 6. 

Compared with the benchmark model before the SDE, when the cooperation cost is high (i.e., $\tau \ge {\tau }_0$), the high-tech manufacturer’s profit reduced after the SDE (i.e., ${\pi }^{h*}<{\pi }_b^{h*}$). When the cooperation cost is low (i.e., $\tau <{\tau }_0$), the effect also depends on the customer transfer rate. If the transfer rate is high (i.e., $\phi >{\phi }_0$), its profit still decreases (i.e., ${\pi }^{h*}<{\pi }_b^{h*}$); if the transfer rate is low (i.e., $\phi \le {\phi }_0$), the SDE instead increases its profit (i.e., ${\pi }^{h*}>{\pi }_b^{h*}$), where

$${\pi }^{h*}=\left\{\begin{array}{l}{\pi }_d^{h*},\phi \le {\phi }_0\\ {\pi }_n^{h*},\phi >{\phi }_0\end{array}\right.$$

Notably, after the SDE, the high-tech manufacturer is forced to exit the market. While this intuitively suggests a loss in profit, the outcome may be counterintuitive. If both the cooperation cost and the customer transfer rate are low, the high-tech manufacturer may instead earn higher profit by licensing its patents to the competitor.

Proof of Proposition 6. 

Proposition 6 can be proved similarly by applying the same method used in Proposition 4. □

6. The Impact of After-Sales Service on the Common Manufacturer’s Strategic Decisions

Using a similar proof, it is easy to show that when neither manufacturer provides after-sales services, the common manufacturer will reject the high-tech manufacturer’s cooperation request (i.e., ${\pi }_d^{M*}<{\pi }_n^{M*}$) if the cooperation cost is high (i.e., $\tau \ge {\tau }_3$) or if the cost is low (i.e., $\tau <{\tau }_3$) but the customer transfer rate is high (i.e., $\phi >{\phi }_3$); otherwise (i.e., $\tau <{\tau }_3$ and $\phi \le {\phi }_3$), it will accept the cooperation (i.e., ${\pi }_d^{M*}\ge {\pi }_n^{M*}$), where the superscript $M$ denotes the common manufacturer in the absence of after-sales service, and ${\phi }_3=\left(2\sqrt{D^2-4c}-D\right)/D$ ${\tau }_3=3D^2/16$.

Proposition 7 is derived by comparing the dominance regions of the cooperation strategy for the common manufacturer under the models with and without after-sales service.

Proposition 7. 

Compared with the scenario without after-sales service, the presence of after-sales service expands the dominance region for the common manufacturer’s cooperation strategy (i.e., ${\phi }_0>{\phi }_3$), where ${\phi }_0=2\sqrt{D^2\lambda \left(-4\tau \lambda +\tau +D^2\lambda \right)}/\left(D^2\lambda \right)-1$  and ${\phi }_3=\left(2\sqrt{D^2-4c}-D\right)/D$.

Figure 9 visualizes the result of Proposition 7. The presence of after-sales services for both manufacturers expand the dominance region of the cooperation strategy. This expansion is driven by the fact that after-sales revenue enhances the common manufacturer’s tolerance for cooperation cost.

7. Supply Chain Reshaping Decisions Under a Generalized Customer Transfer Rate

In this section, we generalize the customer transfer rate from $\xi =1$ to $\phi <\xi \le 1$ based on the main model. After the SDE, under the cooperation strategy, the common manufacturer penetrates the customer base of the high-tech manufacturer. As competition disappears, more customers shift to the former. Therefore, the market potential it faces increases from $D$ to $\left(1+\xi \right)D$, where $\phi <\xi \le 1$. Its profit function under the cooperation strategy becomes the following:

$$\underset{P_{gs}}{max} {\pi }_g^m=P_{gs}\left(Q_{gp}-\lambda P_{gs}\right)+Q_{gp}\left(\left(1+\xi \right)D-Q_{gp}-w_g\right)-\tau$$

The subscript $g$ denotes the supply chain reshaping model under a generalized customer transfer rate, yielding Proposition 8.

Proposition 8. 

When the cooperation cost is high (i.e., $\tau \ge {\tau }_4$), the common manufacturer prefers non-cooperation (i.e., ${\pi }_g^{m*}<{\pi }_n^{m*}$). When the cost is low (i.e., $\tau <{\tau }_4$), the decision further depends on the customer transfer rate. A high transfer rate (i.e., $\phi >{\phi }_4$) leads to non-cooperation (i.e., ${\pi }_g^{m*}<{\pi }_n^{m*}$), while a low transfer rate (i.e., $\phi \le {\phi }_4$) results in cooperation (i.e., ${\pi }_g^{m*}\ge {\pi }_n^{m*}$), where ${\tau }_4=\lambda \left(D\xi +D-6\right)\left(D\xi +D+2\right)/\left(16\lambda -4\right)$ and

$${\phi }_4=\left\{\begin{array}{l}1, \tau <{\displaystyle \frac{\lambda \left(\lambda \left(D^2\left(D\xi +D-6\right)\left(D\xi +D+2\right)-64\right)+32\right)-4}{4D^2\lambda \left(4\lambda -1\right)}}\\ {\displaystyle \frac{\sqrt{D^2\lambda \left(\tau \left(4-16\lambda \right)+\lambda \left(D\xi +D-6\right)\left(D\xi +D+2\right)\right)}}{D^2\lambda }}-1, \tau \ge {\displaystyle \frac{\lambda \left(\lambda \left(D^2\left(D\xi +D-6\right)\left(D\xi +D+2\right)-64\right)+32\right)-4}{4D^2\lambda \left(4\lambda -1\right)}}\end{array}\right.$$

Proposition 8 shows that the previous counterintuitive conclusion (i.e., Proposition 2) still holds when the customer transfer rate is generalized from $\xi =1$ to $\phi <\xi \le 1$. After the SDE, cooperation for supply chain reshaping yields higher profit for the common manufacturer when both the cooperation cost and customer transfer rate are low. In addition, Proposition 2 is essentially a special case of Proposition 8 when the customer transfer rate is $\xi =1$. These results demonstrate the robustness of the model developed in this study.

8. Discussion and Implications

8.1. Discussion

The results reveal a novel mechanism where a high-tech manufacturer can regain profits through patent licensing after market exit caused by sudden disruptive events (SDEs). The model also highlights a misalignment between private incentives and system-wide efficiency: although cooperation improves supply chain system’s profit, it may not always maximize individual firms’ payoffs. These findings provide new insights into strategic decision-making and supply chain reshaping under SDE.

8.2. Managerial Implications

Our results have several practical implications. First, patent licensing enables high-tech manufacturers forced to exit the market due to SDEs to recover part of their profit, providing a viable response to disruption. Second, the common manufacturer’s decision to accept licensing depends critically on cooperation cost and customer transfer rate—two key parameters that managers should evaluate when initiating licensing partnerships. Third, the model provides a theoretical explanation for real-world behavior. For example, Huawei, after facing U.S. sanctions, exited the 5G smartphone market and strategically licensed its patents to OPPO and Samsung to maintain profit—an approach aligned with our findings. Lastly, the study underscores the need for policymakers to promote collaborative mechanisms such as licensing, especially during disruption-induced market realignments.

9. Conclusions

This study develops a multi-stage game-theoretic model to investigate how a high-tech manufacturer can reshape the supply chain through patent licensing after SDEs. The results show that cooperation via licensing can, under certain conditions, increase the common manufacturer’s output, after-sales service price, and the supply chain system’s profit compared to the non-cooperative case. Interestingly, SDEs may even enhance the high-tech manufacturer’s profit despite market exit, demonstrating that disruptions can serve as both a challenge and an opportunity for strategic collaboration.

We integrate supply chain reshaping and after-sales service into a unified analytical framework under disruption and identify a patent-licensing-driven recovery mechanism, bridging the gap between patent strategies and service decisions in disrupted supply chains. The findings provide guidance for high-tech firms to leverage licensing as a post-disruption recovery tool and for policymakers to design cooperative frameworks enhancing supply chain resilience.

Unlike existing models that separately consider supply chain coordination or patent strategies, our unified approach captures the interplay between patent licensing and after-sales services under disruption. This integration fills a critical gap in the literature and provides a novel lens for understanding strategic collaborations when high-tech firms face forced market exit.

Our model relies on simplifying assumptions such as linear demand, symmetric information, binary strategy choices, and fixed cooperation costs. Future research can extend this work by incorporating nonlinear demand, asymmetric information, and variable cost structures. In addition, exploring multi-agent cooperation mechanisms and alternative forms of intellectual property (e.g., know-how, trade secrets) can further enrich the understanding of post-disruption collaboration strategies.