Market Entry or Outsourcing? Game Analyzing Coastal Piggybacking Within Horizontal Competition

Abstract

The shipping industry employs various strategies for outsourcing between freight forwarders and ocean shipping (OS) companies, including consignment and turnkey strategies. Freight forwarders often have a competitive edge in cargo canvassing, but many OS companies still engage in this practice. With China’s new policy liberalizing coastal shipping rights, OS companies are presented with two coastal shipping tactics: coastal transition and coastal piggyback (CPB). The interaction between OS companies and freight forwarders in the context of this policy change raises important strategic questions. This study examines the coastal piggyback business model within a three-tier shipping supply chain, involving a freight forwarder and two competing OS companies (OS1, which does not qualify for the coastal piggyback policy, and OS2, which does) using game theory. Through game analysis, we find that CPB may represent a myopic equilibrium. Specifically, when the freight forwarder’s cargo-canvassing capability is higher than a certain threshold, CPB is not advantageous for OS2’s market entry. Conversely, if the freight forwarder’s capability is relatively low, both OS companies can benefit from CPB. Additionally, OS companies enter the market when entry costs are low and avoid it when costs are high. With moderate costs, their strategy depends on the other OS company’s actions. Interestingly, the forwarder can deter market entry by enhancing cargo canvassing and adjusting outsourcing tactics. Notably, OS companies’ market entry may boost the forwarder’s payoffs in a horizontally competitive supply chain. Furthermore, this research examines the economic sustainability of coastal piggyback policy by analyzing its impacts on the profitability of all supply chain members.

1. Introduction

The recent liberalization of coastal piggyback (CPB) shipping policies has emerged as a transformative force in global maritime logistics. CPB—permitting foreign vessels to transport international trade containers between domestic ports without requiring transshipment through local carriers—marks a significant departure from traditional cabotage restrictions. China formally implemented this policy in 2022, for example, Maersk’s pioneering shipment from Shanghai’s Yangshan Port to Tianjin Port.1 Other maritime nations have adopted diverse approaches, ranging from full liberalization in Singapore to partial acceptance in the European Union and outright prohibition in the United States under the Jones Act. This policy shift introduces stringent qualification requirements, allowing only select ocean shipping (OS) companies that meet specific operational benchmarks, such as fleet size and safety records, to participate. Consequently, market asymmetries emerge. For example, while industry giants like Maersk and COSCO qualify, competitors such as APL and KLINE face exclusion, fundamentally reshaping competitive dynamics within shipping supply chains. For industry stakeholders, CPB presents both opportunities and challenges: Qualified OS companies gain access to new revenue streams through domestic route expansion, but this may come at the cost of disrupting traditional freight-forwarding partnerships. Meanwhile, freight forwarders benefit from potential cost reductions through streamlined logistics yet face fierce competition from OS companies that use vertically integrating downstream inland shipping (IS) transportation. The above observation raises the first crucial question of this paper: Is coastal piggybacking universally beneficial across different market contexts? How does its impact vary in shaping the profitability of different supply chain members?

OS companies not only gain advantages from downstream expansion enabled by the coastal piggyback policy but also have the potential to strategically move into upstream canvassing segments. Leading carriers such as Maersk, through its logistics arm Maersk Logistics & Services, and CMA CGM, via CEVA Logistics, are increasingly pursuing vertical integration across freight forwarding, warehousing, and end-to-end supply chain management. By internalizing cargo-canvassing functions traditionally handled by freight forwarders, OS companies can capture higher profit margins and exert greater control over logistics operations. However, this expansion significantly transforms their relationship with freight forwarders, shifting from cooperation to a more complex dynamic of co-opetition, which can directly impact revenue streams. Additionally, as Xu et al. [1] highlight, OS companies must carefully consider the substantial costs associated with market entry when expanding upstream. A thorough evaluation of both financial implications and strategic benefits is essential before deciding to enter either the downstream or upstream market. This raises the second critical question: Should OS companies actively encroach on the upstream market, and how does market entry affect freight forwarders?

To navigate the competitive pressures posed by OS companies’ vertical integration, forwarders strategically adopt two distinct outsourcing approaches: the turnkey strategy (single OS provider managing end-to-end transport, e.g., Maersk Line’s integrated services) and the consignment strategy (splitting ocean and inland shipping among specialists, e.g., DHL’s multi-carrier collaborations). However, these choices carry strategic implications for OS market encroachment. A turnkey partnership may inadvertently accelerate OS companies’ downstream expansion by deepening their service integration, whereas consignment strategies could deter encroachment by maintaining forwarders’ control over inland segments. This interplay raises our third research question: What is the optimal outsourcing strategy for the freight forwarder? Could changes in outsourcing defer OS companies’ market entry?

To address the above questions, this study employs a game-theoretic model to examine a three-tier supply chain with a freight forwarder, two competing OS companies (OS1 lacking coastal piggyback qualification versus OS2 with full CPB qualification), and several potential IS companies. As Stackelberg leaders, OS companies determine market entry first, followed by the forwarder’s outsourcing strategy and coastal shipping tactic. This investigation faces three key research challenges: (i) given the complex different equilibrium configurations, solving sequentially for operational, outsourcing, and market-entry decisions, (ii) simultaneously incorporating both vertical and horizontal competition within a three-tier supply chain, and (iii) accounting for asymmetric competitive capabilities among supply chain members. Our primary objectives are to (i) develop a game-theoretic framework that captures the strategic interactions between policy-enabled market access and logistics outsourcing decisions, (ii) identify the conditions under which different outsourcing strategies create value for forwarders while influencing OS encroachment patterns, and (iii) provide managerial insights for industry practitioners navigating this transformed competitive landscape.

This study makes several contributions. First, it pioneers the analysis of equilibrium strategies for CPB and service outsourcing in an encroached shipping supply chain. Second, it reveals that CPB may be a short-sighted equilibrium, particularly when the freight forwarder has a significant cargo-canvassing advantage, making it less favorable for OS2’s market entry. Third, unlike the traditional view that OS company market entry reduces freight forwarder revenue, this study shows that in a horizontally competitive supply chain, OS companies’ market entry can benefit the freight forwarder. Fourth, the forwarder’s cargo-canvassing advantage may deter OS company encroachment but also limit its CPB benefits. Lastly, this study establishes CPB’s economic sustainability as threshold-driven: A freight forwarder’s canvassing capacity dictates “triple-win” gains or systemic “triple-loss” risks, necessitating dynamic market reassessment for enduring value. Hybrid governance—turnkey outsourcing for scale and elastic contracts for flexibility—curbs carrier dominance while amplifying resilience, aligning CPB’s efficiency with sustainable supply chain objectives. These insights reframe green logistics strategies through contractual innovation and power-balancing mechanisms critical for operational and environmental stewardship.

The remainder of this paper is structured as follows: Section 2 reviews relevant literature. Section 3 describes the model setting. Section 4 presents optimal coastal shipping and outsourcing equilibrium decisions. Section 5 analyzes OS companies’ market-entry strategies. Section 6 examines CPB value. Section 7 provides an extension of the differential market sizes of competing OS companies. Section 8 summarizes findings and future research directions.

2. Literature Review

The literature relevant to this paper includes the following three main streams: market entry, shipping outsourcing, and coastal shipping policy.

2.1. Market Entry

In the shipping industry, numerous studies explore the market entry of supply chain members. Part of the literature examines the impact of encroachment on the revenue of supply chain members [2,3,4,5,6,7]. Wang et al. [8] examine the incentives of OS and IS firms to solicit goods, and they find that when OS firms canvass for goods without a bargaining agent, a “win-win” situation arises, whereas IS firms canvassing for goods leads to a “prisoner’s dilemma”. In the context of relocating empty containers, Song et al. [9] introduce liner company market entry into the existing model, finding it beneficial to liner companies but detrimental to freight forwarders. Additionally, other works analyze the strategy of providing container capacity reservations on e-commerce platforms. Zhang et al. [7] developed a game theory model involving two logistics service providers to discuss online logistics market entry. Peng and Wang [10] explore container capacity-sharing strategies of competing shipping companies on third-party e-commerce platforms, showing that cooperation by sharing idle container capacity leads to a win-win situation. Xu et al. [6] examine the impact of corporate social responsibility (CSR) activities on entry strategies of new entrant carriers, accommodation strategies of ports, and social welfare in centralized and decentralized shipping supply chains, while analyzing the effects of pricing modes and CSR investment costs on competitive dynamics. Li et al. [3] employ a game theory model to explore the strategic interplay between ocean shipping (OS) companies’ market encroachment and blockchain technology adoption, revealing how encroachment costs, blockchain implementation expenses, and market demand shape decisions.

Compared with the game theory model under this topic, the game theory model in this paper has the following characteristics. First, it pioneers the analysis of equilibrium strategies for CPB and service outsourcing in an encroached shipping supply chain. Second, we simultaneously incorporate both vertical and horizontal competition within a three-tier supply chain. Third, this study considers asymmetric competitive capabilities and finds that OS companies’ market entry can benefit the freight forwarder. Lastly, unlike the traditional view that OS company market entry reduces freight forwarder revenue, we find the forwarder’s cargo-canvassing advantage may deter OS company encroachment but also limit its CPB benefits.

2.2. Shipping Outsourcing

Scholars in shipping outsourcing research explore various aspects, including contract mechanisms, transportation models, cooperation strategies, and market dynamics. Contract mechanisms focus on revenue-sharing contracts and forward freight agreements [11,12,13,14]. Liu and Wang [11] find that alliances between dual carriers reduce competition, lower port service costs, and weaken port monopolies. They propose a combined contract mechanism to align interests and create mutually beneficial outcomes. Qiu and Lam [15] highlight that shared transportation services between inland ports and shippers significantly enhance profitability. Ma et al. [16] developed a multimodal transportation system involving public transit operators, freight forwarders, and freight companies, assessing profit variations in a non-cooperative framework. Peng et al. [17] formulated a bilevel optimization game between the O2O parcel service provider and the on-demand mobility provider, demonstrating that properly priced outsourcing yields savings in PSP cost and improves OMP profit. Xu et al. [18] examine the “guaranteed delivery” model in outsourced logistics, analyzing freight consolidation for long-haul and mixed hauls. Cooperative models are widely studied [14,19,20,21,22,23,24,25]. Tan et al. [23] investigate competition and alliance strategies between ocean carriers and inland shippers, suggesting a “what-if” entry threat mechanism. Xu et al. [24] examine platform market entry and price-matching among liner companies and asymmetric firms, concluding that smaller forwarders are more likely to adopt price-matching strategies. Lee et al. [21] derive oil-well facilities’ best outsourcing response and the logistics provider’s optimal pricing via a Stackelberg pricing game, thereby informing shipping, collaboration, and outsourcing decisions.

Relevant research concerns decisions by freight forwarders in purchasing services and the impact of OS companies entering downstream cargo handling markets [5,26,27]. Wang et al. [5] find that minimal effort in cargo handling by forwarders benefits stakeholders, although OS company entry tends to disadvantage forwarders. Zhang et al. [26] argue that OS companies lacking a significant consolidation advantage may still benefit from market entry, potentially to the detriment of freight forwarders. This paper shifts focus to the balance between OS market entry and freight forwarders’ service outsourcing, finding that service outsourcing can effectively deter OS market entry.

2.3. Coastal Shipping

Literature on coastal shipping schemes mainly focuses on route planning and system optimization [28,29]. Yu et al. [29] examine an inland empty container transportation system comprising sea and inland container terminals. Wang et al. [8] propose that freight forwarders adopt a ‘one-stop’ strategy to purchase all transportation services from OS companies, who in turn purchase inland transportation from IS companies, or a ‘two-stop’ strategy to separately purchase ocean and inland transportation from OS and IS companies, respectively. Zhang et al. [30] explore hinterland transportation schemes, finding that cooperating with competing HS companies is always optimal due to lower hinterland transportation costs. Liu and Zhang [31] analyze equilibrium interactions in a shipping supply chain where logistics service providers select AI upgrades and service-expansion portfolios, and cargo agents set outsourcing tactics under scenarios with or without a CPB policy. However, existing literature seldom considers the inland shipping options chosen by ocean shipping companies.

Building on the coastal piggyback policy from the Ministry of Transport, this paper explores coastal shipping options for OS companies and analyzes the influence of different schemes on supply chain members. This study makes two key contributions. First, it provides a more realistic context by discussing coastal shipping decisions of OS companies and their impact on supply chain members within an encroaching supply chain structure. Second, contrary to most studies suggesting OS company market entry harms freight forwarders’ revenue, our findings indicate that in a horizontally competitive supply chain environment, OS companies’ market entry may increase freight forwarders’ revenue. Moreover, CPB by OS companies could benefit competitors, creating a ‘triple win’ scenario. These insights offer practical guidance for decision-making in encroaching supply chains with horizontal competition.

3. Modeling Assumptions and Models

We consider a three-tier shipping supply chain consisting of a freight forwarder (F), two competing ocean shipping companies (OSi, i∈{1,2}), and inland shipping companies (IS). Figure 1 illustrates this structure. The freight forwarder arranges cargo canvassing and procures transportation services from tier-2 ocean (OS1, OS2) and tier-3 coastal shipping providers (IS), optimizing supply chain efficiency. Additionally, OS companies show potential willingness to encroach on the freight forwarding market. Inspired by China’s shipping policy, we explore the impact of CPB policy on the forwarder and OS companies.

3.1. Decision Sequence

This paper examines strategic market-entry decisions and tactical outsourcing choices [5,9]. Market entry represents a foundational strategic decision that fundamentally reshapes a firm’s competitive position, long-term goals, and supply chain architecture. These high-level choices determine an organization’s future trajectory and survival in the marketplace. Only after establishing this strategic direction can firms effectively address operational considerations like outsourcing, which serves to optimize distribution networks, improve efficiency, and enhance service quality within the established strategic framework. This hierarchy of decision-making is demonstrated in industry practice: Maersk Group’s 2009 strategic move into freight forwarding preceded and necessitated PKP Cargo’s 2015 operational adjustments to its outsourcing models. The Stackelberg leadership model appropriately reflects this sequence, with maritime companies as first-movers setting market-entry strategies, while freight forwarders subsequently adapt their outsourcing tactics accordingly. This framework is detailed in Figure 2.

Stage 1: Strategy of Market Entry. Each OS company evaluates its approach to the downstream cargo-canvassing market, choosing between non-market entry (N) or market entry (E). Non-market entry maintains the company’s traditional role as an ocean carrier, serving a dedicated forwarder. Market entry, however, involves actively entering the downstream market, engaging multiple forwarders, and influencing freight flow. This creates vertical cooperation and horizontal competition with forwarders, incurring incremental costs $X_i$ for advertising, sales networks, websites, and training [9,27,32]. Four strategies emerge: no entry (NN), single entry (EN/NE), or both entering (EE).

Stage 2. Outsourcing and coastal shipping tactics. The forwarder selects between a turnkey contract (T) with an OS company or a consignment contract (C) with both an OS and an IS company. The turnkey option streamlines logistics, while the consignment option offers cost and service flexibility. This setup results in four outsourcing combinations: TT, CC, TC, and CT. OS1 companies, like APL and KLINE2, cannot use the coastal piggyback policy, only coastal transition. OS2 companies, like MAERSK and OOCL3, can choose between coastal transition tactic (t) and CPB tactic (p) under China’s new shipping policy.

Stage 3. Ordering decision. Initially, the IS companies propose inland shipping service fees ($v_F$ or $v_i$) to the forwarder or to OSi companies within the consignment framework. For turnkey services, IS companies offer $v_i$ exclusively to OSi companies. Subsequently, each OS company announces ocean shipping fees $w_i$ for the forwarder. The forwarder then determines freight order quantities ($q_{Fi}$) for OSi companies. Finally, OSi companies decide on encroaching freight order quantities ($q_{OSi}$) if they choose to enter. This sequence, which gives OS companies a strategic advantage by setting capacities after observing forwarder orders, is well-recognized in the market-entry literature [33,34].

3.2. Demand Function

As commonly practiced in the operations management literature [5,8,35,36], the inverse demand functions for each scenario are specified as follows:

In

Table 1. Inverse demand functions for potential scenarios.

Scenarios	Forwarder’s Freight Prices for OS1&OS2	Freight Price of the Entrant OS1	Freight Price of The Entrant OS2
NN	$p_{F1}=1+k-q_{F1}-\gamma q_{F2}$$;$ $p_{F2}=1+k-q_{F2}-\gamma q_{F1}$;	_	_
EN	$p_{F1}=1+k-q_{F1}-q_{OS1}-\gamma q_{F2};$ $p_{F2}=1+k-q_{F2}-\gamma (q_{F1}+q_{OS1})$;	$p_{OS1}=1-q_{OS1}-q_{F1}-\gamma q_{F2}$;	_
NE	$p_{F1}=1+k-q_{F1}-\gamma (q_{F2}+q_{OS2})$$;$ $p_{F2}=1+k-q_{F2}-q_{OS2}-\gamma q_{F1}$;	_	$p_{OS2}=1-q_{OS2}-q_{F2}-\gamma q_{F1}$;
EE	$p_{F1}=1+k-q_{F1}-q_{OS1}-\gamma (q_{F2}+q_{OS2})$$;$ $p_{F2}=1+k-q_{F2}-q_{OS2}-\gamma (q_{F1}+q_{OS1})$;	$p_{OS1}=1-q_{OS1}-q_{F1}-\gamma (q_{F2}+q_{OS2})$;	$p_{OS2}=1-q_{OS2}-q_{F2}-\gamma (q_{F1}+q_{OS1})$.

, we employ an assumption that the potential shipping market of the OS1/OS2 company is 1/$a$ ($a>1$) to capture the limited open right of coastal shipping. In maritime practice, it is natural that a shipping company with a larger market size is more qualified to obtain the “flag of convenience”; hence, the assumption $a>1$ has practical sense. By arithmetical manipulation, $a$ can be normalized as 1, and we verify this robustness by studying a general $a$ in Section 7. We denote the coefficient $\gamma$ as the degree of demand substitution [5,37], which is influenced by differences in services offered by OS companies, such as shipping space, transportation time, and information update speed. $\gamma$ ranges from 0 to 1, with $\gamma =1$ indicating complete substitution for OS companies’ services. In the freight business, shippers typically prefer forwarders due to more professional and comprehensive services compared to OS companies. To illustrate the incumbent forwarder’s advantage in cargo canvassing over entrant ocean shipping companies, we assume $k$ represents the forwarder’s extra capacity in cargo canvassing [5,38]. In our model, $k$ is an exogenous variable where $k>0$. To simplify computational complexity, we consider homogeneous vertical competition between the forwarder and OS companies as perfect competition (Arya et al. [33]). Additionally, for simplicity, we normalize each firm’s operational costs to zero (Dong et al. [39]).

Given positive returns on freight orders and supply chain members, we assume $k\in (0,\overline{k}]$, where $\overline{k}=\mathrm{m}\mathrm{i}\mathrm{n}\left\{{\mathrm{a}\mathrm{r}\mathrm{g}}_k\right\{q^{\ast }=0\left\}\right\}$. Optimal solutions are denoted with an asterisk (*) and summarized in

Table 2. Notations.

Notations	Descriptions
$k$	$\mathrm{Cargo}-\mathrm{canvassing} \mathrm{capability} \mathrm{of} \mathrm{the} \mathrm{forwarder}, k\in (0,\overline{k}]$.
$X_i$	$\mathrm{Market}-\mathrm{entry} \cos \mathrm{t} \mathrm{of} \mathrm{the} \mathrm{OS}i \mathrm{company}, X_i>0$$\mathrm{and} i\in \left\{\mathrm{1,2}\right\}$.
$\gamma$	$\mathrm{Degree} \mathrm{of} \mathrm{demand} \mathrm{substitution} \mathrm{between} \mathrm{OS} \mathrm{companies}, \gamma \in \left(\mathrm{0,1}\right]$.
$p_{\iota }$	$\mathrm{The} \mathrm{freight} \mathrm{price} \mathrm{of} \mathrm{the} \mathrm{forwarder} \mathrm{or} \mathrm{OS} \mathrm{company}, \iota \in \{F_1,F_2,O{S}_1,O{S}_2\}$.
$q_{\iota }$	The freight order quantity of the forwarder or the OSi company.
$w_i$	The service fee charged by the OSi company for ocean shipping.
$v_{\sigma }$	$\mathrm{The} \mathrm{inland} \mathrm{shipping} \mathrm{service} \mathrm{fee} \mathrm{for} \mathrm{the} \mathrm{forwarder} \mathrm{or} \mathrm{the} \mathrm{OS}i \mathrm{company}, \sigma \in \{F,\mathrm{1,2}\}$.
${\Pi }_{IS\sigma }$	The profit of the IS company.
${\Pi }_{\mathit{OS}i}$	The profit of the OSi company.
${\Pi }_F$	The profit of the forwarder.

Note: If superscripts $xy$ are added to the above notations, they refer to the solutions in the case $y$ of scenario $x$, where $x\in \{NN,EN,NE,EE\}$ and $y\in \{CC,TC,CT,TT\}$. Here, $N/E$ denotes non-market entry/market entry and $T/C$ denotes turnkey/consignment service; The subscript $z\in \{t,p\}$, where $t/p$ denotes coastal transition/coastal piggyback.

.

3.3. Model Formulations

We present the optimal tactical decisions under the various market-entry strategy combinations of the two OS companies, i.e., scenarios NN, EN, NE, EE. In each scenario, four potential configurations of the forwarder’s outsourcing tactic are further incorporated, including the selection of turnkey or consignment service delivery to two OS companies, i.e., TT, TC, CT, and CC. Notably, the OS2 company is unique in coastal shipping tactics and necessitates opting for coastal transition (t) or coastal piggyback (p) when implementing the market-entry strategy or executing the turnkey service.

3.3.1. Scenario NN

Both OS companies in this model operate traditionally, providing only transport services to the freight forwarder. The freight forwarder, in turn, selects the outsourcing strategy for each OS company, resulting in four potential strategic combinations: consignment service delivery to both OS companies (case NNCC); turnkey service delivery to OS1 only (case NNTC); turnkey service delivery to OS2 only (case NNCT); and turnkey service delivery to both OS companies (case NNTT).

The channel structures are illustrated in Figure 3. The freight forwarder can outsource both ocean and inland shipping to OS companies. In a turnkey approach, the forwarder pays an OS provider who contracts the IS company for inland costs. Under consignment, the forwarder pays separate fees to the OS and IS companies. Notably, if the turnkey service is given to OS2, it can choose between coastal transition (t) and coastal piggyback (p).

In this scenario, the cost parameter $C_{Fi}^{NN}(w_i,v_F)$ and price parameter $C_{OSi}^{NN}(w_i,v_i)$ are specified as follows: (i) Under a consignment contract, $C_{Fi}^{NN}=w_i+v_F$ is the total outsourcing cost paid by the forwarder to the OSi company and exclusive IS company, and $C_{OSi}^{NN}=w_i$ is the ocean shipping price charged by the OSi to the forwarder, respectively. (ii) Under a turnkey contract, $C_{Fi}^{NN}=w_i$ is the total outsourcing cost paid by the forwarder to the OSi company, and $C_{OSi}^{NN}=w_i-v_i/C_{OSi}^{NN}=w_i$ is the ocean shipping price charged by the OSi to the forwarder in coastal transition/coastal piggyback, respectively. Moreover, the quantity parameter $Q_F^{NN}\left(q_{Fi}^{NN}\right)$ depends on the combination of OS companies’ contract types, where $Q_F^{NN}=q_{F1}^{NN}+q_{F2}^{NN}$ in case CC, $Q_F^{NN}=q_{Fi}^{NN}$ in case CT/TC, and $Q_F^{NN}=0$ in case TT.

The forwarder’s expected payoff is given by ${\Pi }_F^{NN}={\sum }_{i=1}^2[p_{Fi}^{NN}-C_{Fi}^{NN}(w_i,v_F\left)\right]q_{Fi}^{N\mathrm{N}}$, and the OSi company’s expected payoff can be written as ${\Pi }_{OS1}^{NN}=C_{OS1}^{NN}(w_1,v_1)q_{F1}^{NN}$. The potential payoff of the forwarder’s exclusive IS company is ${\Pi }_{I{S}_F}^{NN}=v_F^{NN}{Q}_F^{NN}\left(q_{Fi}^{NN}\right)$, and the potential payoff of the OSi company’s exclusive IS company is ${\Pi }_{ISi}^{NN}=v_i^{NN}{q}_{Fi}^{NN}$.

3.3.2. Scenario EN

Unlike the previous scenario, with OS1’s market entry, both the forwarder and OS1 simultaneously canvass for cargo in the downstream market, creating dual channels. Similarly, OS2 has two coastal shipping options under the turnkey service. The channel structure is shown in Figure 4.

In this scenario, the price parameter $C_{IS1}^{EN}\left(v_1\right)$ is specified as follows: $C_{IS1}^{EN}=v_1/C_{IS1}^{EN}=0$ is the ocean shipping price charged by the IS1 company to the OS1 company in coastal transition/coastal piggyback, respectively. Moreover, the quantity parameter $Q_{Fi}^{EN}(q_{Fi}^{EN},q_{OSi}^{EN})$ depends on the combinations of the OSi company’s contract type and market entry scenario, where $Q_{Fi}^{EN}=q_{Fi}^{EN}+q_{OSi}^{EN}/Q_{Fi}^{EN}=q_{Fi}^{EN}$ in the turnkey contract under a market-entry/non-market-entry scenario, $Q_{Fi}^{EN}=q_{OSi}^{EN}/Q_{Fi}^{EN}=0$ in the consignment contract under a market-entry/non-market-entry scenario.

The forwarder’s expected payoff is given by ${\Pi }_F^{EN}={\sum }_{i=1}^2[p_{Fi}^{EN}-C_{Fi}^{EN}(w_i,v_F\left)\right]q_{Fi}^{EN}$, and the OSi company’s expected payoff can be written as ${\Pi }_{OS1}^{EN}=C_{OS1}^{EN}(w_1,v_1)q_{F1}^{EN}+[p_{OS1}^{EN}-C_{IS1}^{EN}(v_1\left)\right]q_{OS1}^{\mathrm{E}N}-X_1$ and ${\Pi }_{OS2}^{EN}=C_{OS2}^{EN}(w_2,v_2)q_{F2}^{EN}$. The potential payoff of the forwarder’s exclusive IS company is ${\Pi }_{I{S}_F}^{EN}=v_F^{EN}{Q}_F^{EN}\left(q_{Fi}^{EN}\right)$, and the potential payoff of the OSi company’s exclusive IS company is ${\Pi }_{ISi}^{EN}=v_i^{EN}{Q}_{Fi}^{EN}(q_{Fi}^{EN},q_{OSi}^{EN})$.

3.3.3. Scenario NE

In the NE scenario, OS1 provides transportation services for freight forwarders exclusively, while OS2 will additionally solicit cargo from downstream markets, incurring the market-entry cost $X_2$. Considering the forwarder’s outsourcing strategies and the OS companies’ coastal shipping tactics, we examine cases NECC, NETC, NECT, and NETT, as illustrated in Figure 5.

Similarly, as OS2 encroaches, both the forwarder and OS2 simultaneously canvass for cargo in the downstream market, creating dual channels. Regardless of the outsourcing service provided by the forwarder to OS2, the company can still select coastal shipping services due to its encroaching channel.

In this scenario, the price parameter $C_{IS2}^{NE}\left(v_2\right)$ is specified as follows: $C_{IS2}^{NE}=v_2/C_{IS2}^{NE}=0$ is ocean shipping price charged by the IS2 company to the OS2 company in coastal transition/coastal piggyback, respectively. Similarly, the forwarder’s expected payoff is given by ${\Pi }_F^{NE}={\sum }_{i=1}^2[p_{Fi}^{NE}-C_{Fi}^{NE}(w_i,v_F\left)\right]q_{Fi}^{NE}$, and the OSi company’s expected payoff can be written as ${\Pi }_{OS1}^{NE}=C_{OS1}^{NE}(w_1,v_1)q_{F1}^{NE}$ and ${\Pi }_{OS2}^{NE}=C_{OS2}^{NE}(w_2,v_2)q_{F2}^{NE}+[p_{OS2}^{NE}-C_{IS2}^{NE}(v_2\left)\right]q_{OS2}^{NE}-X_2$. The potential payoff of the forwarder’s exclusive IS company is ${\Pi }_{I{S}_F}^{NE}=v_F^{NE}{Q}_F^{NE}\left(q_{Fi}^{NE}\right)$, and the potential payoff of the OSi company’s exclusive IS company is ${\Pi }_{ISi}^{NE}=v_i^{NE}{Q}_{Fi}^{NE}(q_{Fi}^{NE},q_{OSi}^{NE})$.

3.3.4. Scenario EE

In this scenario, both the OS companies provide shipping services to the freight forwarder and compete with the forwarder on the market. Considering the forwarder’s outsourcing tactics, we analyze the cases EECC, EETC, EECT, and EETT, as illustrated in Figure 6.

The two OS companies are directly involved in cargo transportation, which forms a three-channel supply chain structure. Apart from this, OS2 has the capability to select coastal shipping services as it enters the market. In this scenario, the forwarder’s expected payoff is given by ${\Pi }_F^{EE}={\sum }_{i=1}^2[p_{Fi}^{EE}-C_{Fi}^{EE}(w_i,v_F\left)\right]q_{Fi}^{EE}$, and the OSi company’s expected payoff can be written as ${\Pi }_{OSi}^{EE}=C_{O\mathrm{S}i}^{EE}(w_i,v_i)q_{Fi}^{EE}+[p_{OSi}^{EE}-C_{ISi}^{EE}(v_i\left)\right]q_{OSi}^{EE}-X_i$. The potential payoff of the forwarder’s exclusive IS company is ${\Pi }_{I{S}_F}^{EE}=v_F^{EE}{Q}_F^{EE}\left(q_{Fi}^{EE}\right)$, and the potential payoff of the OSi company’s exclusive IS company is ${\Pi }_{ISi}^{EE}=v_i^{EE}{Q}_{Fi}^{EE}(q_{Fi}^{EE},q_{OSi}^{EE})$.

4. Coastal Shipping and Service Outsourcing Tactics

In this section, we first lay the groundwork for our analysis, detailing the game process and computing the companies’ trade profits based on the ordering decisions. Next, we investigate the equilibrium outcomes of the coastal shipping tactics by comparing the profit variations in the OS2 company between coastal transition and CPB. Building on this, we then determine the forwarder’s equilibrium outcomes for service outsourcing tactics.

4.1. Preliminaries

We now derive the forwarder’s optimal order quantities for either the OS company, the OS companies’ ocean shipping prices, the IS companies’ inland shipping prices, and the resulting trade profits. The derivations are identical for the outsourcing combined cases of the four scenarios; thus, we take case EETC-p as an example to illustrate the game structure and ordering decisions, which maximally embody the traits of different combined cases.

In this case, the forwarder resorts to the turnkey contract to the OS1 company and the consignment contract to the OS2 company, leading to the expected profit of the forwarder, given by ${\Pi }_{F-p}^{EETC}=(p_{F1-p}^{EETC}-w_{1-p}^{EETC})q_{F1-p}^{EETC}+(p_{F2-p}^{EETC}-w_{2-p}^{EETC}-v_{F-p}^{EETC})q_{F2-p}^{EETC}$. The OS1 company has no choice but coastal transition, whilst the OS2 company embraces the coastal piggyback policy, and two OS companies’ expected profits can be written as ${\Pi }_{OS1-p}^{EETC}=(w_{1-p}^{EETC}-v_{1-p}^{EETC})q_{F1-p}^{EETC}+(p_{OS1-p}^{EETC}-v_{1-p}^{EETC})q_{OS1-p}^{EETC}-X_1$ and ${\Pi }_{OS2-p}^{EETC}=w_{2-p}^{EETC}{q}_{F2-p}^{EETC}+p_{OS2-p}^{EETC}{q}_{OS2-p}^{EETC}-X_2$, respectively. Correspondingly, the expected profits of IS companies are ${\Pi }_{I{S}_F-p}^{EETC}=v_{F-p}^{EETC}{q}_{F2-p}^{EETC}$ and ${\pi }_{IS1-p}^{EETC}=v_{1-p}^{EETC}(q_{F1-p}^{EETC}+q_{OS1-p}^{EETC})$.

Using backward induction, we detail this outline in four steps. In the fourth step, each OS company anticipates the forwarder’s freight order and the IS company’s service price, then determines the optimal order quantity $q_{OSi-p}^{EETC}$. The optimal order quantity functions in response to a given pair of ocean freight prices are shown as follows:

$$\left\{\begin{array}{l}{q}_{OS1-p}^{EETC}(q_{Fi-p}^{EETC},v_{1-p}^{EETC})=\left(2-\gamma -2v_{1-p}^{EETC}-(2-{\gamma }^2)q_{F1-p}^{EETC}-\gamma q_{F2-p}^{EETC}\right)/(4-{\gamma }^2)\\ q_{OS2-p}^{EETC}\left(q_{Fi-p}^{EETC}\right)=\left(2-\gamma +\gamma v_{1-p}^{EETC}-\gamma q_{F1-p}^{EETC}-(2-{\gamma }^2)q_{F2-p}^{EETC}\right)/(4-{\gamma }^2)\end{array}\right.;$$

(1)

In the third step, the freight forwarder anticipates the freight prices of OS and IS companies and determines the optimal order quantity $q_{Fi-p}^{EETC}$. The optimal order quantity in response to a given pair of ocean freight prices is then calculated as follows:

$$\left\{\begin{array}{l}{q}_{F1-p}^{EETC}(w_{i-p}^{EETC},v_{F-p}^{EETC},v_{1-p}^{EETC})={\displaystyle \frac{1-\gamma +k(2-\gamma -{\gamma }^2)+\gamma v_{F-p}^{EETC}+(1-{\gamma }^2)v_{1-p}^{EETC}-(2-{\gamma }^2)w_{1-p}^{EETC}+\gamma w_{2-p}^{EETC}}{2(1-{\gamma }^2)}}\\ q_{F2-p}^{EETC}(w_{i-p}^{EETC},v_{F-p}^{EETC})={\displaystyle \frac{1-\gamma -k\gamma +k(2-{\gamma }^2)-(2-{\gamma }^2)v_{F-p}^{EETC}+\gamma w_{1-p}^{EETC}-(2-{\gamma }^2)w_{2-p}^{EETC}}{2(1-{\gamma }^2)}}\end{array}\right.;$$

(2)

In the second step, each OS company determines the optimal freight price $w_{i-p}^{EETC}$ based on the best-response order quantity. The optimal ocean freight price functions in response to a given pair of inland freight prices are provided as follows:

$$\left\{\begin{array}{l}{w}_{1-p}^{EETC}(v_{F-p}^{EETC},v_{1-p}^{EETC})=\left(\begin{array}{l}18-9\gamma -20{\gamma }^2+8{\gamma }^3+5{\gamma }^4-2{\gamma }^5+k\left(3-2{\gamma }^2-\gamma (2-{\gamma }^2)\right)\\ (4-{\gamma }^2)-(8\gamma -6{\gamma }^3+{\gamma }^5)v_{F-p}^{EETC}-(18-17{\gamma }^2+6{\gamma }^4-{\gamma }^6)v_{1-p}^{EETC}\end{array}\right)/(4-{\gamma }^2)(9-7{\gamma }^2+{\gamma }^4)\\ w_{2-p}^{EETC}(v_{F-p}^{EETC},v_{1-p}^{EETC})=\left(\begin{array}{l}\left(18-20{\gamma }^2+5{\gamma }^4+k(12-11{\gamma }^2+2{\gamma }^4\right)-k\gamma (8-6{\gamma }^2+{\gamma }^4)\\ -(12-11{\gamma }^2+2{\gamma }^4)v_{F-p}^{EETC}-\gamma (9-8{\gamma }^2+2{\gamma }^4)(1-v_{1-p}^{EETC})\end{array}\right)/(4-{\gamma }^2)(9-7{\gamma }^2+{\gamma }^4)\end{array}\right.$$

(3)

In the first step, given the best-response freight prices, either IS company determines the optimal service price $v_{F-p}^{EETC}$ and $v_{1-p}^{EETC}$, respectively.

4.2. Equilibrium Outcome of Coastal Shipping Tactic

So far, we have presented optimal ordering decisions in four scenarios. We now examine the equilibrium tactic of the coastal shipping service, where the OS1 company must deliver via coastal transition, but the OS2 company has the privilege to embrace the coastal piggyback policy. The comparative outcomes of OS2 company’s profits in different coastal shipping tactics are summarized in the following proposition.

Proposition 1. 

Coastal piggyback is more profitable for the OS2 company in the coastal shipping service.

Proposition 1 states that OS2 will always choose the coastal piggyback service, regardless of market entry and outsourcing scenarios. CPB consistently offers better service prices and freight orders, making it the optimal shipping tactic whenever OS2 can select a coastal shipping service.

We further shed light on the effect of CPB on the OS2 company’s freight order and service price. $C_{OS2-t}<C_{OS2-p}$ shows that when the OS2 company chooses the coastal piggyback service, the service price is higher than that under the coastal transition service. This is because under the coastal piggyback policy, the OS2 company can avoid the extra service cost of outsourcing inland transportation to an IS company, which leads to the positive “Price effect”. In addition, it can be seen from  $q_{F2-t}<q_{F2-p}$ and $q_{OS2-t}<q_{OS2-p}$ that the order under CPB is higher than that under the coastal transition, which implies that the implementation of the coastal piggyback policy may further attract the goods originally transshipped in overseas ports to gather in China’s coastal ports, bringing a positive “Cargo effect”. For instance, the global shipping giant, Maersk, believes that the implementation of CPB policy could expand market options for foreign trade routes and shorten the transport time of goods. Maersk has indicated plans to apply for more routes and ships to engage in this business in the future. In summary, CPB positively impacts service prices by reducing them and increasing freight orders.

4.3. Equilibrium Outcome of Service Outsourcing Tactic

When OS2 is involved in coastal shipping services, CPB is temporarily the optimal tactic. On this basis, we further elaborate on the equilibrium tactics of the forwarder’s service outsourcing.

Proposition 2 

(Equilibrium tactic of service outsourcing).

(i) 

Scenario NN: The forwarder prefers turnkey for the OS2 company and is indifferent to outsourcing tactic for the OS1 company (i.e., NNTT/NNCT);

(ii) 

Scenario EN: The forwarder always prefers turnkey for the OS2 company, whereas he/she prefers consignment for the OS1 company (i.e., ENCT) if  $k\in (0,{\overline{k}}_{EN}]$ and prefers turnkey (i.e., ENTT) otherwise;

(iii) 

Scenario NE: The forwarder prefers consignment for both OS companies (i.e., NECC) if  $k\in (0,{\overline{k}}_{NE}]$, whereas he/she prefers turnkey for the OS2 company if  $k\in ({\overline{k}}_{NE},\overline{k}]$, and is indifferent to outsourcing tactics for the OS1 company (i.e., NETT/NECT);

(iv) 

Scenario EE: The forwarder unanimously prefers consignment/turnkey for both OS companies (i.e., EECC/EETT) if  $k\in (0,{\overline{k}}_{EE}^1]/k\in ({\overline{k}}_{EE}^2,\overline{k}]$, whereas he/she only prefers consignment for the OS1 company (i.e., EECT) if $k\in ({\overline{k}}_{EE}^1,{\overline{k}}_{EE}^2]$.

The thresholds above are ${\overline{k}}_{EN}={\mathrm{a}\mathrm{r}\mathrm{g}}_k\{{\pi }_{F-p}^{ENCT}={\pi }_{F-p}^{ENTT}\}$, ${\overline{k}}_{NE}={\mathrm{a}\mathrm{r}\mathrm{g}}_k\{{\pi }_F^{NECC}={\pi }_{F-p}^{NETT}\}$, ${\overline{k}}_{EE}^1={\mathrm{a}\mathrm{r}\mathrm{g}}_k\{{\mathsf{\pi }}_{F-p}^{EECC}={\pi }_{F-p}^{EECT}\}$, and ${\overline{k}}_{EE}^2={\mathrm{a}\mathrm{r}\mathrm{g}}_k\{{\pi }_{F-p}^{EETT}={\pi }_{F-p}^{EECC}\}$.

Note: The two symbols in brackets, respectively, represent the change trend of the OS1/2 company’s outsourcing adopted by the forwarder. Taking (+, −) as an example, “+” means that the outsourcing adopted by the forwarder to the OS1 company has changed, and “−” means that the outsourcing adopted by the forwarder to the OS2 company has not changed.

Proposition 2 outlines the forwarder’s tactical preferences in outsourcing selection. Specifically, as shown in Figure 7, when neither OS company encroaches on the market, the forwarder always opts for a turnkey contract with OS2 but remains indifferent regarding the outsourcing contract for OS1. This conclusion can be explained by examining the two income sources for the forwarder. On the one hand, when the forwarder resorts to a turnkey contract for the OS2 company, the forwarder can also enjoy the benefits of the lower service price ($C_{2-p}^{NNTT*}=C_{2-p}^{NNCT*}<C_2^{NNTC*}<C_2^{NNCC*}$) and higher freight order ($q_{F2-p}^{NNTT*}=q_{F2-p}^{NNCT*}>q_{F2}^{NNTC*}>q_{F2}^{NNCC*}$) brought by the coastal piggyback service adopted by the OS2 company, thus obtaining higher profit. On the other hand, although the coastal piggyback service reduces the forwarder’s freight order for the OS1 company ($q_{F1-p}^{NNTT*}=q_{F1-p}^{NNCT*}=q_{F1}^{NNCC*}<q_{F1}^{NNTC*}$), the increase in the forwarder’s order for the OS2 company is greater than the decrease in the forwarder’s freight order for the OS1 company, that is, $q_{F2}$ plays a leading role in the profit of the forwarder. Therefore, the forwarder always resorts to a turnkey contract for the OS2 company.

With OS1’s market entry, the forwarder always chooses a turnkey contract with OS2. The forwarder’s cargo-canvassing capacity influences the outsourcing choice for OS1. This increases orders for OS2, decreases orders for OS1, and enhances the forwarder’s profit. In differing scenarios, the forwarder chooses OS2’s outsourcing contract post-market entry. The turnkey contract boosts OS2’s orders, but market entry weakens the coastal piggyback’s cargo effect, especially with low forwarder cargo-canvassing capacity. Without significant canvassing, consignment, or turnkey choice, OS2 has little profit impact. OS2 benefits from the coastal piggyback service under turnkey, improving freight and market orders, reducing OS1’s orders under turnkey versus consignment. The forwarder prefers consignment contracts for both OS companies without a clear market advantage. The EE scenario’s outsourcing equilibrium mirrors the NE scenario, with consignment (turnkey) for OS1 under low (high) canvassing capacity, similar to the EN scenario.

We emphasize that when OS2 stays out of canvassing, the forwarder prefers turnkey outsourcing to capture CPB scale benefits, whereas OS1 is managed with more elastic contracts. Such differentiated contracting mitigates single-carrier dominance and enhances supply chain resilience—an essential pillar of sustainable operations.

5. Market-Entry Strategy

To this point, we have analyzed forwarder payoffs and identified equilibrium outsourcing decisions. Next, we investigate market-entry strategy, examining its effects on OS companies and forwarders. By exploring market-entry behavior, we aim to understand how these strategies shape competitive interactions and influence outcomes in the outsourcing framework.

5.1. Equilibrium Outcomes of Market-Entry Strategy

In this section, we analyze the equilibrium market-entry strategy for each OS company. Building on the outsourcing equilibrium outcomes discussed in the previous section, we compare the payoffs for each OS company under the market-entry strategy (E) versus the non-market-entry strategy (N). For instance, if the equilibrium strategy is EECC for a specific value of $k\in (0,{\overline{k}}_{EE}^1]$, it must hold that both ${\pi }_{OS1-p}^{EECC*}>{\pi }_{OS1-p}^{NECC*}$ and ${\pi }_{OS2-p}^{EECC*}>{\pi }_{OS2-p}^{ENCT*}$. This condition defines a combined interval for the market-entry costs of each OS company, represented as $\{X_1<{\overline{X}}_1^1,X_2<{\overline{X}}_2^1\}$. Based on the equilibrium decision for forwarder’s service outsourcing, the equilibrium market-entry strategies for the OS companies are formalized in Proposition 3.

Proposition 3 

(OS companies’ market-entry equilibrium strategies).

Both OS companies persist in market entry if  $\{X_1\le {\overline{X}}_1^m,X_2\le {\overline{X}}_2^m\}$; Only OS1 persists in market entry if  $\{X_1\le {\overline{X}}_1^n,X_2>{\overline{X}}_2^m\}$; Only OS2 persists in market entry if  $\{X_1>{\overline{X}}_1^m,X_2\le {\overline{X}}_2^n\}$; Both OS companies forgo market entry if $\{X_1>{\overline{X}}_1^n,X_2>{\overline{X}}_2^n\}$, Where ${\overline{X}}_1^1={\mathit{arg}}_X\{{\pi }_{OS1-p}^{EECC*}={\pi }_{OS1-p}^{NECC*}\}$, ${\overline{X}}_2^1={\mathit{arg}}_X\{{\pi }_{OS2-p}^{EECC*}={\pi }_{OS2-p}^{ENCT*}\}$, ${\overline{X}}_1^2={\overline{X}}_1^4={\overline{X}}_1^{14}={\overline{X}}_1^{16}={\mathit{arg}}_X\{{\pi }_{OS1-p}^{ENCT*}={\pi }_{OS1-p}^{NNTT*}\}$, ${\overline{X}}_2^2={\overline{X}}_2^4={\overline{X}}_2^6={\overline{X}}_2^8={\mathit{arg}}_X\{{\pi }_{OS2-p}^{NECC*}={\pi }_{OS2-p}^{NNTT*}\}$, ${\overline{X}}_1^3={\overline{X}}_1^5={\mathit{arg}}_X\{{\pi }_{OS1-p}^{EECT*}={\pi }_{OS1-p}^{NECC*}\}$, ${\overline{X}}_2^3={\overline{X}}_2^{13}={\mathit{arg}}_X\{{\pi }_{OS2-p}^{EECT*}={\pi }_{OS2-p}^{ENCT*}\}$, ${\overline{X}}_1^4={\mathit{arg}}_X\{{\pi }_{OS1-p}^{ENCT*}={\pi }_{OS1-p}^{NNTT*}\}$, ${\overline{X}}_2^5={\overline{X}}_2^{11}={\mathit{arg}}_X\{{\pi }_{OS2-p}^{EECT*}={\pi }_{OS2-p}^{ENTT*}\}$, ${\overline{X}}_1^6={\overline{X}}_1^8={\overline{X}}_1^{10}={\overline{X}}_1^{12}={\mathit{arg}}_X\{{\pi }_{OS1-p}^{ENTT*}={\pi }_{OS1-p}^{NNTT*}\}$, ${\overline{X}}_1^7={\mathit{arg}}_X\{{\pi }_{OS1-p}^{EETT*}={\pi }_{OS1-p}^{NECC*}\}$, ${\overline{X}}_2^7={\overline{X}}_2^9={\mathit{arg}}_X\{{\pi }_{OS2-p}^{EETT*}={\pi }_{OS2-p}^{ENTT*}\}$, ${\overline{X}}_1^9={\overline{X}}_1^{15}={\mathit{arg}}_X\{{\pi }_{OS1-p}^{EETT*}={\pi }_{OS1-p}^{NETT*}\}$, ${\overline{X}}_2^{10}={\overline{X}}_2^{12}={\overline{X}}_2^{14}={\overline{X}}_2^{16}={\mathit{arg}}_X\{{\pi }_{OS2-p}^{NETT*}={\pi }_{OS2-p}^{NNTT*}\}$, ${\overline{X}}_1^{11}={\overline{X}}_1^{13}={\mathit{arg}}_X\{{\pi }_{OS1-p}^{EECT*}={\pi }_{OS1-p}^{NETT*}\}$, ${\overline{X}}_2^{15}={\mathit{arg}}_X\{{\pi }_{OS2-p}^{EETT*}={\pi }_{OS2-p}^{ENCT*}\}$.

Proposition 3 outlines equilibrium strategies for OS companies’ market entry based on entry costs. Four strategic combinations are market entry, non-market entry, opposite strategies, and identical strategies. Figure 8 indicates that companies either encroach or refrain in Regions I and II. One company’s strategy influences the other’s, resulting in opposite and identical strategies.

Theoretically, each OS company will independently and rationally select either an opposite or identical strategy in response to its counterpart’s decision, as reflected in Regions III and IV, respectively. Intuitively, an OS company is likely to choose to encroach if its market-entry cost is sufficiently low, as the additional payoff from market entry must outweigh the associated costs. Notably, each company’s market-entry strategy is contingent upon the behavior of its counterpart when the market-entry cost falls within a specific range. This opposite equilibrium strategy emerges from the competitive dynamics between the OS companies, where only one entrant OS company can remain profitable in the market.

5.2. Analysis of Market-Entry Performance

Having detailed the market-entry equilibrium strategy, we now delve into the performance implications of market entry for both OS companies and forwarders. By examining profit variations, we assess how different market-entry scenarios impact the financial outcomes and strategic positions of these entities.

5.2.1. Market-Entry Performance on OS Companies

Corollary 1 

(Market-entry performance on OS companies).

Every OS company benefits from market entry unless the forwarder has strong cargo-canvassing capabilities:  ${\overline{X}}_1^7<0$ if $k\in ({\overline{k}}_{EE}^2,\overline{k}]$; otherwise,  ${\overline{X}}_1^m>0$, ${\overline{X}}_2^m>0$, ${\overline{X}}_1^n>0$, ${\overline{X}}_2^n>0$. Where ${\overline{X}}_1^7={\mathit{arg}}_X\{{\pi }_{OS1-p}^{EETT}={\pi }_{OS1-p}^{NECC}\}$.

Corollary 1 indicates that market-entry thresholds are nearly always non-negative. In simpler terms, once market entry occurs, the OSi company’s revenue falls within specific thresholds, $X_i<{\overline{X}}_i^m$ or $X_i<{\overline{X}}_i^n$. Remarkably, regardless of the intensity of vertical competition, the OSi company’s market-entry strategy remains unaltered when the forwarder has insufficient cargo-canvassing capability  $k\in (0,{\overline{k}}_{EE}^2]$. However, when $k\in ({\overline{k}}_{EE}^2,\overline{k}]$, OS1’s market-entry strategy is entirely reversed; this implies that as the forwarder’s cargo-canvassing capability increases, the OS company’s market-entry cost threshold decreases, thus reducing the likelihood of market entry. Once this threshold drops to zero, it leads to a market entry-restricted zone, making it unwise for the OS company to encroach on the shipping market. Our findings demonstrate that the size of freight forwarders’ cargo capacity is an essential component in deterring OS company entry. The theoretical finding that OS companies profit from encroachment when forwarders lack canvassing advantage aligns with Maersk’s strategic expansion. After acquiring Damco in 2018, Maersk integrated its logistics arm to directly serve SMEs, leveraging its global network. This vertical integration increased Maersk’s logistics EBIT by 47% in 2022 (Maersk Annual Report 2022). Conversely, Hapag-Lloyd’s failed “Quick Quotes” platform in 2019 demonstrates how high canvassing capability deters encroachment.

5.2.2. Market-Entry Performance on the Forwarder

In this section, we will assess the impact of market entry on forwarders’ revenues. Specifically, we explore whether the forwarder can increase his/her payoff by encouraging OS companies to encroach.

Proposition 4 

(Market-entry performance on the forwarder).

In the presence of OS2’s entry, the forwarder can benefits from OS1’s entry if  $k\in ({\overline{k}}_{Fi},\overline{k}]$, otherwise the forwarder is always not able to benefit:  ${\pi }_{F-p}^{EETT*}>{\pi }_{F-p}^{NECC*}$ if  $k\in ({\overline{k}}_{F1},\overline{k}]$, ${\pi }_{F-p}^{EETT*}>{\pi }_{F-p}^{NETT*}$ if $k\in ({\overline{k}}_{F2},\overline{k}]$, ${\pi }_{F-p}^{EEy*}\le {\pi }_{F-p}^{NEy*}$ otherwise; ${\pi }_{F-p}^{EEy*}\le {\pi }_{F-p}^{ENy*}$, ${\pi }_{F-p}^{ENy*}<{\pi }_{F-p}^{NNy*}$, ${\pi }_{F-p}^{NEy*}<{\pi }_{F-p}^{NNy*}$, Where ${\overline{k}}_{F1}={\mathit{arg}}_k\{{\pi }_{F-p}^{EETT*}={\pi }_{F-p}^{NECC*}\}$, ${\overline{k}}_{F2}={\mathit{arg}}_k\{{\pi }_{F-p}^{EETT*}={\pi }_{F-p}^{NETT*}\}$ and $y\in \{TT, TC, CT, CC\}$.

Proposition 4 reveals that OS companies’ market entry can enhance forwarder profitability under two conditions: advanced cargo-canvassing capabilities and OS2’s entry introducing a competitive dynamic. This competition creates a negative channel effect by capturing market share but also a positive wholesale price effect as OS1 lowers fees to attract orders. Despite OS1’s negative impacts, the new entrant can improve the forwarder’s payoff through competitive pricing. These findings challenge the traditional view that market entry worsens conditions under competition, suggesting that a competitive supply chain and OS market entry can benefit forwarders.

6. Value of Coastal Piggyback

It should be noted that the result in Section 5 reflects the market-entry equilibrium of OS companies based on the equilibrium of CPB. We will further investigate the revenues of the supply chain members with a variety of coastal shipping modes to analyze the value of CPB.

6.1. The Impacts on OS Companies

Proposition 5 

(The impact of CPB on OS companies).

CPB may be a myopic equilibrium: If, and only if, $k\in (0,{\overline{k}}_1]/k\in ({\overline{k}}_2,\overline{k}]$, compared with coastal transition, an OS1/OS2 company can obtain more/less payoff with CPB, where ${\overline{k}}_1={arg}_k\{{\overline{X}}_{1-p}^6={\overline{X}}_{1-t}^6\}$, ${\overline{k}}_2={arg}_k\{{\overline{X}}_{2-p}^2={\overline{X}}_{2-t}^2\}$.

Proposition 5 outlines the market-entry thresholds for OS companies under two coastal shipping services. Regardless of the scenario, OS2 favors CPB for its positive cargo and price effects, squeezing OS1’s market. However, under certain conditions ($k\in (0,{\overline{k}}_1]$), OS1’s profit with CPB exceeds that with coastal transitions, suggesting a potential “win-win” situation. A real-world example supporting this conclusion can be observed in the competitive operation between CMA CGM (OS2) and Hapag-Lloyd (OS1) in the Mediterranean trade lane.4 CMA CGM introduced coastal piggyback services using short-sea shipping to connect North African ports (e.g., Tangier) with Southern European hubs, reducing reliance on costly inland trucking. While this initially encroached on Hapag-Lloyd’s market share, the efficiency gains expanded total demand, benefiting both OS companies.

Moreover, as confirmed by Figure 9, which depicts the change in the OS2 company’s market-entry threshold with CPB and coastal transition, when $k\in ({\overline{k}}_2,\overline{k}]$, the OS2 company can obtain more encroaching payoff with coastal transition. Specifically, when the freight forwarder’s cargo-canvassing capability is small, CPB is always more favorable to the OS2 company, while as the cargo-canvassing capability increases, a surprising result generated shows that coastal transition becomes the key countermeasure for the OS2 company to make market entry more profitable. In other words, CPB may be a myopic equilibrium, whereas coastal transition is better in the long run.

6.2. The Impacts on the Forwarder

We delve into the impact of CPB on forwarders by comparing the profits of forwarders under different coastal shipping services, which are described in Proposition 6.

Proposition 6 

(The impact of CPB on the forwarder).

(i) 

Profit: ${\pi }_{F-t}^{EECC}>{\pi }_{F-p}^{EECC}/{\pi }_{F-t}^{NECC}>{\pi }_{F-p}^{NECC}$ if $k\in ({\overline{k}}_3,\overline{k}]/k\in ({\overline{k}}_4,\overline{k}]$, otherwise ${\pi }_{F-t}<{\pi }_{F-p}$;

(ii) 

Service price (cost): $C_{OS1-t}^{EECC}<C_{OS1-p}^{EECC}$ ($C_{Fi-t}^{EECC}<C_{Fi-p}^{EECC}$) and $C_{OS1-t}^{NECC}<C_{OS1-p}^{NECC}$ ($C_{Fi-t}^{NECC}<C_{Fi-p}^{NECC}$), otherwise $C_{OS1-t}>C_{OS1-p}$ ($C_{Fi-t}>C_{Fi-p}$);

(iii) 

Freight order: $q_{F1-t}^{EECC}<q_{F1-p}^{EECC}$ and $q_{F1-t}^{NECC}<q_{F1-p}^{NECC}$, otherwise $q_{F1-t}>q_{F1-p}$; $q_{OS1-t}^{ENTT}<q_{OS1-p}^{ENTT}$, otherwise $q_{OS1-t}>q_{OS1-p}$; ${\sum }_{i=1}^2{q}_{Fi-t}^{EECC}>{\sum }_{i=1}^2{q}_{Fi-p}^{EECC}$ and ${\sum }_{i=1}^2{q}_{Fi-t}^{NECC}>{\sum }_{i=1}^2{q}_{Fi-p}^{NECC}$, otherwise ${\sum }_{i=1}^2{q}_{Fi-t}<{\sum }_{i=1}^2{q}_{Fi-p}$.

The thresholds above are ${\overline{k}}_3={arg}_k\{{\pi }_{F-t}^{EECC}={\pi }_{F-p}^{EECC}\}$, ${\overline{k}}_4={arg}_k\{{\pi }_{F-t}^{EECC}={\pi }_{F-p}^{NECC}\}$.

From part (i), CPB benefits the freight forwarder by reducing service costs and increasing orders. OS2’s avoidance of extra inland shipping costs lowers the forwarder’s expenses. Although it reduces cooperation orders with OS1, the positive effect on OS2 outweighs this, increasing the forwarder’s orders.

In the following analysis, we integrate the impact of CPB on all three supply chain members, illustrated in Figure 10. As indicated in Propositions 5 and 6, CPB is beneficial to OS1 and detrimental to OS2 if $k\in (0,{\overline{k}}_1]$ and $k\in ({\overline{k}}_2,{\overline{k}}_{NE}]$, respectively. Meanwhile, it negatively affects the forwarder if $k\in ({\overline{k}}_3,\overline{k}]$ or $k\in ({\overline{k}}_4,\overline{k}]$. By combining the value effects of CPB in each region, we find that in Region A or D, CPB yields positive or negative impacts for all three members, resulting in a “Triple win” or “Triple lose” scenario. In Region B, CPB no longer benefits the forwarder but continues to benefit the two OS companies, creating a “win-win” scenario. Conversely, Region C is characterized as a “single win,” where CPB benefits either OS1 or OS2.

Our analysis shows that coastal piggyback effects depend on the forwarder’s cargo-canvassing capability. When the forwarder lacks a significant advantage, CPB by OS2 benefits all parties. However, as the forwarder’s capability increases, they do not benefit from the coastal piggyback’s price and order effects, potentially leading to a “Triple-lose” scenario. Thus, forwarders with limited canvassing capability perform better with CPB, while OS companies should avoid it if the forwarder has a strong advantage. For example, when COSCO (OS2) launched a barge-based piggyback network Yangtze River Delta, it reduced reliance on trucking for regional cargo. Small forwarders gained 25% of cost savings by using this service, while COSCO increased its Yangtze market share (SINOTRANS Annual Report 2021); Notably, competitor OOCL (OS1) also benefited as the improved logistics efficiency expanded total regional trade volume. Thus, CPB creates mutual gains for all parties. We discuss how CPB can create either “triple-win” or “triple-lose” outcomes for the two carriers and the freight forwarder, depending on the forwarder’s canvassing-capacity threshold. This warns practitioners that short-term cost advantages may not translate into long-term sustainable value unless market structures are continuously assessed.

7. Extension: OS Companies Have Differentiated Market Sizes

Our preceding analytical framework has operated under the simplifying assumption of symmetric market scales for both ocean shipping providers. We now generalize this approach to incorporate heterogeneous market conditions, where OS1 maintains a baseline market presence (normalized to 1) while OS2 operates at a relative scale of $a$ (where $a>1$). This asymmetry parameter serves dual analytical purposes: First, it captures the degree of market imbalance between the competing OS companies; Second, it enables rigorous testing of our core findings’ robustness under varying competitive conditions.

Proposition 7. 

With the differentiated market size, i.e.,$a\in (1,\overline{a}]$.

(i) 

Equilibrium tactics of coastal shipping: CPB is more profitable to the OS2 company in the coastal shipping service.

(ii) 

Equilibrium tactic of service outsourcing: (a) In scenario NN, the forwarder prefers turnkey for the OS2 company and is indifferent to the outsourcing tactic for the OS1 company (i.e., NNTT/NNCT); (b) In scenario EN, the forwarder always prefers turnkey for the OS2 company, whereas he/she prefers consignment for the OS1 company (i.e., ENCT) if $k\in (0,{\widehat{k}}_{EN}]$ and prefers turnkey (i.e., ENTT) otherwise; (c) In scenario NE, the forwarder prefers consignment for both OS companies (i.e., NECC) if  $k\in (0,{\widehat{k}}_{NE}]$, whereas he/she prefers turnkey for the OS2 company if  $k\in ({\widehat{k}}_{NE},\overline{k}]$, and is indifferent to outsourcing tactics for the OS1 company (i.e., NETT/NECT); (d) In scenario EE, the forwarder unanimously prefers consignment/turnkey for both OS companies (i.e., EECC/EETT) if  $k\in (0,{\widehat{k}}_{EE}^1]$/$k\in ({\widehat{k}}_{EE}^2,\overline{k}]$, whereas he/she only prefers consignment for the OS1 company (i.e., EECT) if $k\in ({\widehat{k}}_{EE}^1,{\widehat{k}}_{EE}^2]$.

The main conclusions in Proposition 7 are similar to those in Proposition 1–2 in the basic model. The similarities are mainly reflected in the following two aspects: (i) For coastal shipping services, the OS2 company always tends to choose CPB because he/she can enjoy the cargo effect and price effect, which is similar to the result of Proposition 1. (ii) For the service outsourcing decision, when the OS2 company does not encroach on the market, the freight forwarder tends to adopt the turnkey service for him/her, and the choice of outsourcing for the OS1 company will be affected by his/her encroachment strategy and the forwarder’s cargo-canvassing capability. When OS2 engages in market encroachment, the freight forwarder may opt for consignment services, particularly when lacking significant cargo-canvassing capabilities. Building upon the established service-outsourcing equilibrium results, we subsequently analyze the optimal encroachment strategies for OS companies within this framework, as formally presented in Proposition 8.

Proposition 8. 

Encroachment equilibrium with the differentiated market size, i.e., $a\in (1,\overline{a}]$. Given any threshold combination $\mathrm{\Omega }(a,k)$, both OS companies persist with encroachment if $\{X_1\le {\widehat{X}}_1^m,X_2\le {\widehat{X}}_2^m\}$, only OS1 persists with encroachment if $\{X_1\le {\widehat{X}}_1^n,X_2>{\widehat{X}}_2^m\}$, only OS2 persists with encroachment if $\{X_1>{\widehat{X}}_1^m,X_2\le {\widehat{X}}_2^n\}$, and both OS companies forgo encroachment if $\{X_1>{\widehat{X}}_1^n,X_2>{\widehat{X}}_2^n\}$.

To enhance understandings, this proposition begins by analyzing how encroachment costs influence the strategic decisions of OS firms. Mirroring the insights of Proposition 3, when encroachment costs are sufficiently low (i.e., $X_i\le {\widehat{X}}_i^m$), every OS company will invariably choose to encroach (i.e., $X_i>{\widehat{X}}_i^n$). Conversely, if these costs exceed a certain level, firms will uniformly abstain from encroachment. In intermediate cost scenarios, however, each company’s decision hinges on its competitor’s strategy—either aligning with or diverging from it. As previously noted, equilibria emerge when both firms adopt identical strategies: either mutual encroachment (EE) or mutual non-encroachment (NN). These outcomes arise when both companies act in unison. In contrast, asymmetric equilibria (EN or NE) occur when one firm encroaches while the other refrains, reflecting opposing strategic choices. Further analysis of encroachment performance yields key insights, which are elaborated in the subsequent corollary. Notably, the interplay between cost structures and competitive dynamics shapes these equilibria, highlighting the strategic interdependence between firms.

Corollary 2. 

Encroachment performance on OS companies and forwarder.

(i) 

${\widehat{X}}_1^7<0$ if $k\in ({\widehat{k}}_{EE}^2,\overline{k}]$; otherwise, ${\widehat{X}}_1^m>0$, ${\widehat{X}}_2^m>0$, ${\widehat{X}}_1^n>0$, ${\widehat{X}}_2^n>0$;

(ii) 

${\pi }_{F-p}^{EETT\ast }>{\pi }_{F-p}^{NECC\ast }$ if $k>{\widehat{k}}_{F1}$, ${\pi }_{F-p}^{EETT\ast }>{\pi }_{F-p}^{NETT\ast }$ if $k>{\widehat{k}}_{F2}$; otherwise, ${\pi }_{F-p}^{EEy\ast }\le {\pi }_{F-p}^{NEy\ast }$ and ${\pi }_{F-p}^{EEy\ast }\le {\pi }_{F-p}^{ENy\ast }$;

(iii) 

${\pi }_{F-p}^{ENTT\ast }>{\pi }_{F-p}^{NNTT\ast }$ if $k>{\widehat{k}}_{F3}$; otherwise ${\pi }_{F-p}^{ENy\ast }<{\pi }_{F-p}^{NNy\ast }$ and ${\pi }_{F-p}^{NEy\ast }<{\pi }_{F-p}^{NNy\ast }$. Where $y\in \{TT,TC,CT,CC\}$.

Corollary 2 (i) examines the encroachment thresholds for OS companies and yields two key findings. First, encroachment is generally beneficial for both OS firms when the freight forwarder lacks a strong cargo-canvassing advantage. However, if the forwarder possesses a significant competitive edge in cargo canvassing, encroachment becomes detrimental to OS1, resulting in a negative post-encroachment payoff below the threshold (i.e., $k>{\widehat{k}}_{EE}^2$). This occurs because the additional revenue from encroachment fails to offset its associated costs. A second insight reveals that a forwarder with sufficiently strong cargo-canvassing capabilities can effectively deter encroachment by its exclusive OS company, as established in the base model.

Corollary 2 (ii) demonstrates a similarly favorable outcome: OS1’s encroachment can enhance the forwarder’s payoff, but only if the forwarder’s cargo-canvassing capability exceeds a critical threshold (i.e., $k>{\widehat{k}}_{F1}$/$k>{\widehat{k}}_{F2}$). Notably, part (iii) uncovers an unexpected result—even when OS2 refrains from encroaching, OS1’s encroachment may still benefit the forwarder. This occurs because OS2’s substantial market potential boosts freight demand, compensating for the negative effects of OS1’s encroachment. Thus, when competing OS firms have asymmetric market power, encroachment by one can improve the forwarder’s profitability, irrespective of whether the dominant OS company encroaches.

8. Conclusions

8.1. Main Conclusions

In shipping operations, freight forwarders typically outsource transportation tasks to OS companies through consignment or turnkey strategies. Despite the forwarder’s cargo-canvassing advantage, OS companies often engage in cargo canvassing themselves. With China’s new policy liberalizing coastal shipping rights, OS2 can choose between coastal transition (t) or coastal piggyback (p). We studied CPB businesses within a three-tier supply chain involving a freight forwarder and two competing OS companies. As Stackelberg leaders, OS companies decide on market entry first. The forwarder, as the follower, then determines service outsourcing and OS2’s coastal shipping tactic. By comparing equilibrium profits, we examine the balance between market entry and outsourcing, discussing CPB effects on supply chain members.

First, OS companies enter the market when entry costs are low and avoid it when costs are high. With moderate costs, their strategy depends on other OS companies’ actions. Analyzing market-entry cost thresholds shows that OS companies gain an advantage when the freight forwarder’s cargo-canvassing capacity is limited but fare worse when forwarders excel at market acquisition. Thus, forwarders can deter market entry by enhancing cargo canvassing and adjusting outsourcing tactics. Interestingly, in a horizontally competitive supply chain, OS companies’ market entry can boost forwarders’ payoffs.

If OS2 does not encroach, the forwarder always opts for a turnkey contract with OS2 due to coastal piggyback benefits. The forwarder is indifferent to non-encroaching OS1’s outsourcing options but chooses consignment or turnkey for OS1 based on cargo-canvassing capability. Once OS2 encroaches, the forwarder prefers a consignment contract with OS2 if lacking cargo-canvassing advantage, as consignment’s positive transportation price effect outweighs the coastal piggyback’s cargo effect.

Finally, OS2 always chooses CPB if possible, enjoying lower service prices and higher freight orders. However, CPB could be short-sighted if the forwarder has significant cargo-canvassing capability, potentially benefiting OS2’s competitors and creating a “triple-win” scenario. As cargo-canvassing capacity grows, the forwarder benefits less from CPB, limiting their development.

8.2. Managerial Implications

For OS companies, evaluating market-entry costs carefully is crucial. For example, Amazon entered the logistics market by leveraging low entry costs and its vast distribution network, but when costs and risks become significant, a more cautious approach is necessary. CPB strategies should consider the freight forwarder’s cargo-canvassing capabilities; similar to how DHL collaborates with regional logistics providers to optimize services. For freight forwarders, in scenario NN (no encroachment), forwarders should focus on turnkey contracts to leverage CPB benefits while building their cargo-canvassing capabilities; In EN (only OS2 encroaches), consignment contracts with OS2 are favorable when forwarders have limited canvassing advantages, as the transportation price effect becomes significant; In NE (only OS1 encroaches), forwarders should flexibly choose between consignment and turnkey contracts based on their canvassing strength, emphasizing service differentiation to counter competition. In EE (both OS1 and OS2 encroach), forwarders must adopt dynamic strategies balancing price effects and canvassing capacity while fostering collaboration with both OS companies to mitigate competition and explore joint opportunities. These insights highlight adaptable approaches to navigating diverse encroachment scenarios for forwarder managers.

8.3. Contributions and Limitations

This research provides insights into the strategic interplay between market entry and outsourcing in a three-tier supply chain, contributing to supply chain management and game theory literature. By applying the Stackelberg game model, it offers a framework for analyzing decision-making processes. These findings guide policymakers in liberalizing coastal shipping rights and help industry practitioners optimize strategies, improving profitability and competitiveness. For example, Kuehne and Nagel’s strategic decisions illustrate leveraging supply chain capabilities to enhance market positioning.

This study has several limitations. First, the model assumes deterministic demand and symmetric information among supply chain members, neglecting potential market uncertainties and information asymmetry that could influence strategic decisions. Second, the analysis focuses primarily on economic incentives (e.g., profit maximization) while overlooking non-monetary factors such as regulatory constraints, environmental policies, or long-term partnerships that may affect encroachment and outsourcing choices. Third, the game-theoretic framework simplifies competition dynamics by treating OS companies’ market sizes and capabilities as exogenous, whereas in practice, these factors could evolve endogenously through adaptive strategies or technological advancements. Fourth, while the theoretical model provides important insights, empirical validation is needed; future research could employ case studies of coastal piggyback implementation (e.g., Maersk’s China routes) or econometric analysis of shipping company performance data to test the model’s predictions and enhance its practical relevance.