A simple game theoretical analysis for incentivizing multi-modal transportation in freight supply chains

A simple game theoretical analysis for incentivizing multi-modal transportation in freight supply chains

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A simple game theoretical analysis for incentivizing multi-modal transportation in freight supply chains Zhuzhu Song, Wansheng Tang, Ruiqing Zhao PII: DOI: Reference:

S0377-2217(19)30900-2 https://doi.org/10.1016/j.ejor.2019.10.048 EOR 16134

To appear in:

European Journal of Operational Research

Received date: Accepted date:

7 January 2019 31 October 2019

Please cite this article as: Zhuzhu Song, Wansheng Tang, Ruiqing Zhao, A simple game theoretical analysis for incentivizing multi-modal transportation in freight supply chains, European Journal of Operational Research (2019), doi: https://doi.org/10.1016/j.ejor.2019.10.048

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Highlights • The incentivizing for offering multi-modal transportation is considered. • Ocean shipping companies have an incentive to offer multi-modal transportation. • Both provide multi-modal transportation is one effective equilibrium. • The effective equilibrium can maximize supply chain profit and social welfare. • The integration efficiency and competitive intensity are important factors.

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A simple game theoretical analysis for incentivizing multi-modal transportation in freight supply chains Zhuzhu Song1 , Wansheng Tang1,∗, Ruiqing Zhao1 College of Management & Economics, Tianjin University, Tianjin 300072, China. [email protected], [email protected], [email protected]

Abstract Multi-modal transportation, as a highly efficient approach, can economize many intermediate links in the supply chain and save social operating costs. However, at present, multi-modal transportation accounts for only a small portion of the total traffic volume, and there are few multi-modal carriers. To analyze the incentives of ocean shipping companies to provide multi-modal transportation, this paper considers a freight supply chain composed of two upstream ocean shipping companies and two downstream railway transportation companies. After depicting a Nash game between the two competing ocean shipping companies in terms of whether to integrate downstream railway transportation services to provide multi-modal transportation, we analyze the performance of the participants in sub-games for each integration strategy. The results indicate that regardless of competitor behavior, ocean shipping companies may have an incentive to provide multi-modal transportation. Although the two ocean shipping companies are unlikely to agree on the optimal strategy, the only effective equilibrium they can achieve is both providing multi-modal transportation. Moreover, in this equilibrium, the supply chain’s profit, consumer utility and social welfare are likely to be maximized. In addition, although the provision of multi-modal transportation will attract more shippers to the market, whether more shippers can ultimately be retained depends on the integration efficiency and competitive intensity. Keywords: Supply chain management; multi-modal transportation; ocean shipping; railway transportation; Nash game 1. Introduction International long-distance freight usually includes ocean shipping, inland railway transportation and other modes of transportation. In traditional transportation, these different transportation modes are carried out separately. The shippers complete the relevant formalities and sign the necessary contracts for every type of transportation. This not only increases the cost of international transportation for shippers but also makes connecting various modes of transportation ∗

Corresponding author: Wansheng Tang ([email protected]).

Preprint submitted to EJOR

November 13, 2019

extremely difficult. Multi-modal transportation, a highly efficient form of transportation organization, represents an integrated service with two or more transportation modes, which enables efficient connection and rapid transshipment between shipping, railways and so forth, minimizes the number of loading changes, improves operational efficiency and considerably reduces transportation costs. In 2017, China’s multi-modal transportation industry entered a period of accelerated development. Relevant policy documents have proliferated, and multi-modal transportation has become a national strategy. COSCO and Sinotrans, as the world’s and China’s leading shipping company, respectively, have corresponding multi-modal transportation services 1 . COSCO’s Wuhan-Chengdu combined rail and water transportation service began operations in 2016, and related services have gradually increased since then 2 . In addition, in 2017, MSC acquired a Russian multi-modal operator to further develop its own multi-modal service 3 . However, at present, multi-modal transportation accounts for only 2.9% of China’s total freight volume, and in 2017, China’s multi-modal transportation volume was 1.368 billion tons. The vast majority of containers are transported through combined shipping and railway transportation. Nevertheless, China’s rail-water transportation volume has long accounted for less than 3% of port container throughput, which indicates a low level of development. Only Yingkou, the main coastal port for rail-water transportation, exhibits a share higher than 10%, and the figures for most ports are less than 5%, far lower than the shares of foreign ports, such as Duisburg 36%, Hamburg 39%, and Bremen 47%.4 Thus, the multi-modal transportation market has considerable growth potential, which needs to be further improved and developed. For shippers, multi-modal transportation reduces many intermediate operational links in the transportation process, which improves their utility from transportation. Therefore, it is obvious that introducing multi-modal transportation will attract more shippers, that is, there will be a significant expansion of shippers’ basic market demand. This is also one of the clearest benefits for carriers that provide multi-modal transportation. However, providing multi-modal transport entails considerable additional integration costs for carriers. On the one hand, there are barriers to entry imposed by the government. The government’s access conditions and price controls on the provision of multi-modal transportation have increased the inputs required for carriers to provide multi-modal transportation. On the other hand, the provision of multi-modal transportation requires service 1

See http://development.coscoshipping.com/col/col1629/index.html and

http://tj.sinotrans.com/col

/col4507/index.html 2 See http://www.cosco-wuhan.com/product/26.html 3 See https://www.joc.com/rail-intermodal/international-rail/europe/msc-pursues-stake-russian-rai l-operator-transcontainer_20171109.html 4 The relevant data are all from “Review and prospect of China’s multi-modal transportation development in 2017” released by the Joint Transportation Branch of China Transportation Association, which can be found at http://www.lyccta.org/newsc-view-386.aspx

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integration with other transportation modes, which extends beyond simple cooperation between different transportation modes. Because multi-modal transportation has the “one ticket system” document standard, it also requires new hub stations, the construction of collection and distribution infrastructure to link different transportation modes, and further standardization and specialization of transportation equipment. All of these factors entail tremendous costs for carriers. In summary, carriers need to decide whether to integrate services to provide multi-modal transportation. In addition, given the fierce competition in the transportation market, if a carrier integrates services to provide multi-modal transportation that attracts more shippers to enter the market, another carrier that has not paid the costs of service integration might win more shippers by reducing its freight rate, which is free-riding behavior. Therefore, it is crucial to study an ocean shipping company’s incentives to provide multi-modal transportation when there is competition between carriers operating the same transportation modes and complementarity between different upstream and downstream transportation modes. Hence, we formulate the following research questions: (i) Under different combinations of integration strategies employed by two ocean shipping companies, how will the upstream ocean shipping companies and the downstream railway transportation companies determine their freight rates? How will the final market shares be distributed among them? (ii) What is the value of multi-modal transportation? What impact will it have on the profits of the participants, the realized shipper demand, and freight rates? (iii) What are the optimal and equilibrium strategies of the two ocean shipping companies? What are the supply chain’s profit and social welfare under an achievable equilibrium strategy? To answer these questions, we consider two upstream ocean shipping companies and two downstream railway transportation companies, as well as shippers that need a combination of upstream and downstream transportation services. Upstream ocean shipping companies can integrate services with downstream railway transportation companies to provide multi-modal transportation; otherwise, upstream and downstream transportation will be carried out independently. Hence, there is a Nash game regarding the integration strategy between two ocean shipping companies. In each sub-game model, ocean shipping companies and railway transportation companies need to make corresponding freight rate decisions. In this paper, we first build the sub-game models of the integration strategy for the two ocean shipping companies under three different combinations, i.e., neither offers multi-modal transportation, only one offers multi-modal transportation, and both offer multi-modal transportation. The results show that in the market with no multi-modal transportation, downstream railway transportation companies always obtain less profits than upstream ocean shipping companies, but when the latter integrate services to provide multi-modal transportation, the opposite is true. However, providing multi-modal transportation does not necessarily enable one ocean shipping company to earn more than the other. In terms of the final market shares, we obtain an interesting conclu-

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sion: Although multi-modal transportation expands basic market demand, this benefit can also be derived by free-riding in separate transportation services and ultimately result in higher shipper demand than multi-modal transportation services. In examining the value of multi-modal transportation, we reach meaningful conclusions. First, regardless of what integration strategy the competitor chooses, providing multi-modal transportation is always beneficial to an ocean shipping company, provided that there is the appropriate competitive intensity and integration efficiency. This means that the ocean shipping company is likely to have incentives to integrate services and provide multi-modal transportation. Moreover, an upstream ocean shipping company and a downstream railway transportation company may simultaneously have incentives to provide multi-modal transportation, which means that service integration is a win-win for the upstream and downstream companies. Second, the provision of multi-modal transportation does not necessarily result in the highest realized shipper demand, which depends on the integration efficiency of the services affected by both the expansion of basic market demand and the integration cost. Finally, in the market where multi-modal transportation and separate transportation coexist, the freight rates of both services are likely to be higher. By exploring the optimal strategy and equilibrium strategy of the two ocean shipping companies, we find that the companies always prefer that only one offer multi-modal transportation in the market so that they can both benefit from service advantages or free riding. However, the two ocean shipping companies can only reach an equilibrium in which both offer multi-modal transportation, which is the only stable equilibrium. Further analysis of this unique equilibrium reveals that supply chain’s profit, consumer utility and social welfare are likely to be simultaneously maximized in this equilibrium. Therefore, this equilibrium in which both ocean shipping companies offer multi-modal transportation can be achieved and benefit all participants as long as the government can constrain competition to an appropriate level and help reduce the cost of service integration. The remainder of this paper is organized as follows. Section 2 reviews the relevant literature. We provide a simple problem description in Section 3. Then, in Section 4, we model the three combinations of integration strategies of the two ocean shipping companies, and the optimal decisions and realized shipper demand and profits of the participants in each case are analyzed. In Section 5, we analyze the value of and incentives to provide multi-modal transportation, including the impact of providing multi-modal transportation on participants’ profits, realized shipper demand and the freight rate; the optimal and equilibrium strategies of the ocean shipping companies; and the supply chain’s profit and social welfare under the equilibrium strategy. In Section 6, some extensions are made to verify the robustness of the main conclusions. This study ends with concluding remarks and avenues for future research in Section 7.

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2. Literature Review Our work is broadly related to three streams of literature: intermodal freight transportation, vertical supply chain integration, and the marketing of transportation services. Next, we compare and contrast our work with these studies to highlight our contributions. 2.1. Intermodal freight transportation Intermodal freight transportation is defined as the movement of cargo from the origin to the destination by several modes of transportation; each of these modes is operated by a different carrier, each with its own independent contract. As this process entails coordination among multiple participants, there are many problems worth studying that consistently attract researchers’ attention (Li and Tayur, 2005; Verma and Verter, 2010; Assadipour et al., 2015). For intermodal freight transportation systems, Crainic et al. (2018) analyze a large set of papers published in scientific journals and conferences from different disciplines. They confirm the multidisciplinary nature of applications to freight transportation, involving computer science, mathematics, transportation engineering, management science, and economics. Specifically, some researchers address empty container repositioning problems in intermodal transportation (Choong et al., 2002; Xie et al., 2017; Kuzmicz and Pesch, 2019). Other researchers consider problems in the intermodal transportation network; for example, Resat and Turkay (2015) present a multi-objective optimization model for integrating different transportation modes in the design and operation of an intermodal transportation network in a geographical region. Baykaso˘glu et al. (2016) present a mixed-integer mathematical programming model for a multi-objective, multi-mode and multi-period sustainable load planning problem. Sarhadi et al. (2017) develop an analytical framework for intermodal rail owners to determine the best defense plan. Considering the intermodal transportation of airlines and high-speed rail, Avenali et al. (2018) study the effects of intermodal transportation on traffic volumes in the transportation network and on the level of congestion at hub airports. There are also studies on problems in other industries using intermodal transportation, which includes B2B e-commerce logistics problems (Xu et al., 2015), medical supplies in response to large-scale disasters (Ruan et al., 2016), and double-stack railcars(Mantovani et al., 2018). However, the above works all study relevant issues in the context of intermodal transportation. A further extension of intermodal transportation is multi-modal transportation, which integrates various modes of transportation. In multi-modal transportation, the entire process of transporting cargo is carried out under a single contract or bill of lading, without any handling of the freight itself when changing modes. Research on multi-modal transportation is limited. SteadieSeifi et al. (2014) present a structured overview of the multi-modal transportation literature from 2005 onward and focus on the traditional strategic, tactical, and operational levels of planning. Bevrani et al. (2017) develop a linear programming model to study multi-modal transportation systems and their 6

capacity assessment. Marufuzzaman and Ek¸sio˘glu (2017) focus on multi-modal supply chain designs for bio-fuel. Yang et al. (2018) develop a multi-modal evacuation model that considers multiple transportation modes and their interactions and captures the proper traffic dynamics. Algaba et al. (2019) analyze the situation involving several transport companies in a multi-modal public transport system. Unlike the previous literature, our paper focuses on carriers’ incentive to integrate services and provide multi-modal transportation. Rather than considering problems related to multi-modal transportation, we study the significance and impact of multi-modal transportation. 2.2. Vertical supply chain integration Different modes of transportation are integrated to provide a unified service, which is similar to the vertical integration of a supply chain. There is considerable research on vertical integration in manufacturing. In Kapoor and Adner (2012), vertically integrated firms have, on average, a faster time to market for new product generation than non-integrated firms. Lin et al. (2014) consider three strategies for each manufacturer under two competing supply chains: forward integration, backward integration, or no vertical integration. Wan and Sanders (2017) evaluate how firms can increase product variety while managing inventory levels and find that vertical integration creates opportunities for information sharing, thereby reducing the uncertainty that may contribute to forecast bias. Vertical integration also exists in a wide range of industries and is the subject of a rich literature, such as car leasing (Pierce, 2012), outsourcing (Grahovac et al., 2015), pharmaceuticals (Kouvelis et al., 2018), and research and development (Lambertini, 2018). The typical aim in vertically integrating a supply chain is to improve efficiency and reduce intermediate links, but whether the integrated enterprise can develop in the long term remains an open question. Helfat and Campo-Rembado (2016) provide a new explanation for why vertically integrated and specialized firms may continue to coexist as industries evolve, especially during periods when conditions unequivocally favor lower-cost, specialized firms. In our paper, we study the integration of different modes of transportation, upstream and downstream, which originally provided complementary transportation services. To provide integrated transportation services, the carrier needs to pay additional costs, but the shipper will benefit from this and thus be attracted to the market. From the perspective of supply chain structure, our research is similar to Wang et al. (2017), who study who canvasses for cargos and whether to hire agents when transportation companies offer one-stop services upstream and downstream. Our paper focuses on whether carriers will integrate services in a competitive environment. 2.3. Marketing of transportation services In contrast to other products, marketing is the first and most important step in carrying out transportation services. A common approach to selling transportation services is an auction, which usually yields a long-term contract for transportation services between large carriers and shippers. 7

The literature on this topic is also very rich and includes Lim et al. (2008), Remli and Rekik (2013), Basu et al. (2015), Xu et al. (2016), Zhang et al. (2019). There are also some studies on the relationship between participants in transportation that establish stylized game models. Lee et al. (2015) study a fractional price-matching contract and find that such a contract will not affect the carrier’s profit but will increase the shipper’s satisfaction. The relationship between the carrier and shipper is also the focus of Song et al. (2017), who investigate two different strategies that carriers use to sell capacity to the shipper. The relationship between different transportation service providers is also worth studying; Wang et al. (2017) examine who should be responsible for canvassing – an ocean shipping company and an inland shipping company – and whether the latter should hire an agent. Song et al. (2018) study the cooperative relationship between the carrier and the port and whether a liner company should conduct pure business cooperation with the port or invest in the port. In the context of empty container repositioning, Song et al. (2019) study the problem of encroachment and canvassing strategy in the marine supply chain. Some studies focus on the pricing of transportation service marketing, such as the pricing algorithm for tactical service scheduling and operational cargo freight allocation in liner shipping (Koza, 2019), route optimization and profit enhancement under quantity-based pricing discounts in the trucking industry (Nowak et al., 2019), and the pricing decision when considering the influence of port congestion (Wang and Meng, 2019). Our paper also examines the relationships between different service providers, but there are several differences between our work and these previous contributions. First, we consider two different modes of transportation, each of which takes on a particular segment of the goods shipment, rather than different participants in the same segment. Second, after the integration of different modes of transportation, a new transportation service is formed, which will attract more shippers. 3. Problem Description Consider a freight transportation service supply chain consisting of two upstream homogeneous ocean shipping companies (OS1 and OS2, he) and two downstream homogeneous railway transportation companies (R1 and R2, she). The two upstream ocean shipping companies compete for shippers that need transportation services; for example, COSCO and MSC compete on their overlapping routes and on overlapping lines for multi-modal transport services. The two downstream railway transportation companies are common in the international market because many countries have private rail companies and they also compete with each other. The upstream and downstream are vertically complementary transportation services. The shippers select the transportation service offered by a given company according to their own utility functions. To characterize the demand functions of competing transportation services, we adopt the utility function of a representative consumer introduced by Ingene and Parry (2004), 8

which has been extensively applied in the fields of marketing and operations management (Cai, 2010; Liu et al., 2014; Wu et al., 2015; Gui et al., 2018). Suppose that the actual demands for transportation services are di , i = 1, 2, . . . , n, respectively; we depict the representative consumer’s utility as U=

n X i=1

(αi di −

n n n X X X d2i )−k di · ( dj ) − Ri di , 2 i=1

j=1,j6=i

(1)

i=1

where αi is the base demand for the competing transportation services; the parameter k (0 6 k < 1) measures the intensity of competition between the transportation services and can represent the degree of substitution between the transportation services; and Ri represents the freight rate charged by the transportation services.

(a) Without

multi-modal (b) One

transportation

party

provides (c) Both

multi-modal transportation

provide

multi-

modal transportation

Figure 1: Market structure

When there is no multi-modal transportation services in the market, the upstream and downstream transportation services are sold separately; that is, shippers may choose any combination of upstream and downstream transportation services. Concretely, as shown in 1(a), OS1 and OS2 first simultaneously determine their freight rates r1 and r2 , and then R1 and R2 simultaneously determine their freight rates p1 and p2 . The shippers can then choose from four combinations of transportation services (i.e., n = 4): option OS1 and R1 and pay freight rate R1 = r1 + p1 , option OS1 and R2 and pay freight rate R2 = r1 +p2 , option OS2 and R1 and pay freight rate R3 = r2 +p1 , and option OS2 and R2 and pay freight rate R4 = r2 + p2 . Furthermore, due to the symmetry and the convenience of handling, we assume that αi = 14 , which means that the total basic market demand is standardized to 1. Alternatively, an upstream ocean shipping company can provide shippers with both upstream and downstream transportation modes by integrating transportation services with a downstream railway transportation company, i.e., multi-modal transportation services. Here, we have two cases: OS1 and R1 are integrated while OS2 and R2 are not, that is, there are simultaneously multi-modal transportation and separate transportation services. Specifically, in this case, the multi-modal transportation service provided by OS1 competes with the transportation services provided by OS2 9

Table 1: Nash game decision

OS1

Separate transportation

Integrated transportation

Separate transportation

SS

IS

Integrated transportation

SI

II

OS2

and R2. As shown in 1(b), OS1 decides to integrate with the transportation service of R1 to provide multi-modal transportation. R1 determines the wholesale price w to sell her transportation service to OS1, and then OS1 determines the freight rate P for the multi-modal transportation service to offer to shippers. However, OS2 and R2, which do not integrate transportation services, still make their own freight rate decisions r2 and p2 . In this case, for Eq. (1), n = 2 and R1 = P , R2 = r2 + p2 . To indicate that the availability of the multi-modal transport service expands the basic market demand, we assume that α1 = demand is standardized to 1 +

θ 2, θ θ−1 2 .

> 1, and α2 =

1 2,

which means that the total basic market

The other case is that OS1 and OS2 each integrate with one of the downstream railway transportation companies, that is, only multi-modal transportation services are available in the market. Obviously, there is now competition between two multi-modal transportation services. As shown in 1(c), both railway transportation companies simultaneously determine the wholesale prices w1 and w2 that they charge the upstream ocean shipping companies for their transportation services. The two ocean shipping companies then simultaneously determine the freight rate P1 and P2 for the multi-modal transportation service. In this case, for Eq. (1), n = 2 and R1 = P1 , R2 = P2 . Multi-modal transport will increase basic market demand; therefore, α1 = α2 = 2θ , which means that the total basic market demand is standardized to θ. In addition, when an upstream ocean shipping company provides multi-modal transportation services, he has to pay a series of additional costs, such as corresponding standardized equipment and operations. To capture this cost, we assume that an ocean shipping company’s unit cost is zero when providing a separate transportation service but is c when providing multi-modal transportation. The cost of downstream railway companies is always standardized to zero. Subsection 6.1 verifies the main conclusions by modeling two ocean shipping companies with different costs of providing multi-modal transportation. In summary, Table 1 depicts a Nash game between the two upstream ocean shipping companies, which are the leaders of the freight transport service supply chain, regarding whether to integrate with the downstream railway transportation service to provide multi-modal transportation service. We assume that the two ocean shipping companies are homogeneous and thus that cases IS and SI are symmetric.

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4. Model In this section, we establish the game model after the upstream ocean shipping companies have made their integration decision, that is, the four cases shown in Table 1 above. By solving the models, the optimal pricing decisions of the ocean shipping companies and railway transportation companies can be obtained in each case. Note that we use ΠC i , i = 1, 2, C = SS, IS, II to represent the profits of the OSi in case C and πiC to represent the profits of the Ri in case C. Before proceeding, we present a simple case as a benchmark in which the players are one ocean shipping company and one railway transportation company to describe the incentives and effects of multi-modal transportation. Proposition 1. When there is a single ocean shipping company and a single railway transportation company, providing multi-modal transportation will have the following characteristics: 1) The provision of multi-modal transportation will bring higher profit to the ocean shipping com√ pany when θ − c > 2 2 − 1, and the railway transportation company can also obtain a higher profit. 2) When the ocean shipping company provides multi-modal transportation, the supply chain’s profit, consumer utility and social welfare can also be improved. The proposition validates the benefits of multi-modal transportation for the entire supply chain, including shippers. This finding also gives theoretical support for the government to promote the development of multi-modal transportation. The following analysis considers competition, which matches reality, and the incentives and effects of multi-modal transportation will be more complex. 4.1. Neither offers multi-modal transportation (case SS) In the absence of multi-modal transportation, the upstream and downstream transportation companies separately decide the relevant freight rates. In this case, there are four combinations of transportation services that shippers can choose from, and the corresponding demands of these four combinations of transportation services can be obtained by maximizing Eq. (1) as follows: 1 2k+1 k k k dSS 1 = 12k+4 − 1+2k−3k2 (r1 +p1 )+ 1+2k−3k2 (r1 +p2 )+ 1+2k−3k2 (r2 +p1 )+ 1+2k−3k2 (r2 +p2 ), 1 k 2k+1 k k dSS 2 = 12k+4 + 1+2k−3k2 (r1 +p1 )− 1+2k−3k2 (r1 +p2 )+ 1+2k−3k2 (r2 +p1 )+ 1+2k−3k2 (r2 +p2 ), 1 k k 2k+1 k dSS 3 = 12k+4 + 1+2k−3k2 (r1 +p1 )+ 1+2k−3k2 (r1 +p2 )− 1+2k−3k2 (r2 +p1 )+ 1+2k−3k2 (r2 +p2 ),

(2)

1 k k k 2k+1 dSS 4 = 12k+4 + 1+2k−3k2 (r1 +p1 )+ 1+2k−3k2 (r1 +p2 )+ 1+2k−3k2 (r2 +p1 )− 1+2k−3k2 (r2 +p2 ). SS Specifically, dSS 1 represents the shipper demand for the transportation services of OS1 and R1; d2

denotes the shipper demand for the transportation services of OS1 and R2; dSS 3 is the shipper demand for the transportation services of OS2 and R1; and dSS 4 expresses the shipper demand for 11

the transportation services of OS2 and R2. According to the sequence of events, the upstream ocean shipping companies first simultaneously decide their freight rates r1 and r2 , and the downstream railway transportation companies then simultaneously decide their freight rates p1 and p2 . Hence, the two-layer Nash game model for these companies is given as follows: SS SS max ΠSS 1 = r1 (d1 + d2 ), r1 >0

SS SS max ΠSS 2 = r2 (d3 + d4 ), r2 >0

(3)

SS s.t. max π1SS = p1 (dSS 1 + d3 ), p1 >0

SS max π2SS = p2 (dSS 2 + d4 ). p2 >0

By solving the two-layer Nash game by backward induction, the optimal decisions of all participants can be obtained, which are summarized in the following proposition. Proposition 2. In case SS, the optimal decisions of the participants, shipper demands, and the optimal profits of the participants are given as follows: (1−k)(1+k) , i = 1, 2, 2(5+6k−3k2 ) 2 (1−k)(3+6k−k companies are pSS∗ = 8(5+6k−3k2 ) ) , i (k+1)(3+6k−k2 ) . 4(3k+1)(5+6k−3k2 )

1) The optimal freight rates of the two ocean shipping companies are riSS∗ = the optimal freight rates of the two railway transportation and these four companies have the same shipper demands

(3+6k−k2 )(k+1)2 (1−k) , 8(3k+1)(3k2 −6k−5)2 (1−k)(k2 −6k−3)2 (k+1) . 32(3k2 −6k−5)2 (3k+1)

2) The ocean shipping companies’ profits ΠSS∗ = i transportation companies’ profits πiSS∗ =

i = 1, 2 and the railway

Because of symmetry, the two companies with the same horizontal dimension ultimately have the same pricing decisions and profits. Due to the complementarity of upstream and downstream transportation services, ocean shipping companies and railway transportation companies ultimately have the same shipper demands. The following corollary can be drawn by comparing the pricing and profits between upstream and downstream transportation companies. Corollary 1. The freight rate and profit of the ocean shipping company are always higher than those of the railway transportation company, and the difference decreases as the competitive intensity k increases. The corollary highlights that although both upstream and downstream transportation companies have the same shipper demand due to the complementarity of the services they provide, the leader-follower relationship leads to different pricing and, in turn, different profits. As leaders, upstream ocean shipping companies have the first-mover advantage of setting higher freight rates, while downstream railway transportation companies can only set lower freight rates than ocean shipping companies to achieve the best shipper demand. Different transportation services are naturally priced differently, followed by transportation costs, transportation distance and other 12

conditions. However, our model ignores these factors, and the different order of moves between the upstream and downstream companies can help characterize differences in modes of transportation. Moreover, Fig. 2 clearly shows the changes in the differences in price and profit between upstream and downstream companies as the competitive intensity k changes. Note that due to symmetry, the corresponding analysis also applies to ΠSS∗ − π2SS∗ and r2SS∗ − pSS∗ 2 2 . As competition intensifies between the same transportation services, both upstream and downstream transportation companies will set lower prices. As the first mover, the upstream ocean shipping company is more affected, which eventually leads to reductions in the difference in price and profit as k increases. Consider an extreme case: When k approaches 1, the competitive intensity is the highest, and different combinations of transportation services become perfect substitutes. The downstream railway transportation company charging a lower price no longer helps competition, so she tends to charge the same freight rate as the upstream ocean shipping company. 0.025 SS∗ ΠSS∗ 1 − π1

r1SS∗ − pSS∗ 1

0.02

0.015

0.01

0.005

0

0

0.2

0.4

0.6

0.8

1

k

Figure 2: The difference in pricing and profit between the ocean shipping company and the railway transportation company

4.2. Only one offers multi-modal transportation (case IS or case SI) In both cases IS and SI, the multi-modal transportation service and the separate transportation service exist simultaneously, that is, one of the two ocean shipping companies and one of the downstream railway transportation companies integrate their transportation services, and then the upstream ocean shipping company provides the multi-modal transportation, while the other two companies still independently offer their own transportation services. Because of symmetry, we can focus on solving case IS and then directly obtain the optimal decisions for case SI. In this case, maximization of the representative shipper utility Eq. (1) can yield the shipper demand for each ocean shipping company as follows: dIS 1 = dIS 2 =

θ−k 2−2k2 1−θk 2−2k2

− +

1 P 1−k2 k P 1−k2

13

+ −

k (r 1−k2 2 1 (r 1−k2 2

+ p2 ), + p2 ).

(4)

Note that dIS 1 represents the shipper demand for the multi-modal transportation service provided by OS1, and dIS 2 denotes the shipper demand for the separate transportation services of OS2 and R2. According to the sequence of events, R1 first maximizes her profit to decide the wholesale price w that she charges OS1; then, OS1 and OS2 maximize each of their profits to simultaneously set their freight rates P and r2 ; finally, R2 maximizes her profit to decide her freight rate p2 . Hence, in this case, there is a three-layer game model among the participants as follows: max π1IS = wdIS 1 , w>0

IS s.t. max ΠIS 1 = (P − c − w)d1 , P >0

IS max ΠIS 2 = r2 d2 ,

(5)

r2 >0

s.t. max π2IS = p2 dIS 2 . p2 >0

By solving the problem by backward induction, the optimal decisions of all participants can be obtained, which are summarized in the following proposition. Proposition 3. In case IS, the optimal decisions of the participants, shipper demands, and the optimal profits of the participants are given as follows: (4−3k2 )(θ−2c)−k , the optimal freight rate of the 4(4−3k2 ) 2 )−θ)(4−3k 2 )−k(3−2k 2 ) multi-modal transportation service provided by OS1 is P IS∗ = ((c+2θ)(2−k , and (4−3k2 )(8−5k2 ) (4−3k2 )(2−k2 )(k−(2c−θ)(4−3k2 )) IS∗ the corresponding shipper demand is d1 = . 8(1−k2 )(4−3k2 )(8−5k2 )

1) The optimal wholesale price of R1 is wIS∗ =

k(2c−θ)(2−k2 )(4−3k2 )+19k4 −50k2 +32 , the optimal freight 4(4−3k2 )(8−5k2 ) 2 )(4−3k 2 )+19k 4 −50k 2 +32 k(2c−θ)(2−k R2 is pIS∗ , and the corresponding shipper demand is 2 = 8(4−3k2 )(8−5k2 ) k(2c−θ)(2−k2 )(4−3k2 )+19k4 −50k2 +32 . 8(1−k2 )(4−3k2 )(8−5k2 )

2) The optimal freight rate of OS2 is r2IS∗ = rate of dIS∗ 2 =

(2−k2 )(6ck2 −3k2 θ−8c−k+4θ)2 , and that of R1 is π1IS∗ = 32(8−5k2 )2 (1−k2 ) 2 2 2 2 2 2 (k(2c−θ)(2−k )(4−3k2 )+19k4−50k2+32)2 (4−3k )(2−k )(6ck −3k θ−8c−k+4θ) ; that of OS2 is ΠIS∗ , and that 2 = 32(1−k2 )(8−5k2 )(4−3k2 )2 32(4−3k2 )2 (8−5k2 )2 (1−k2 ) 2 2 4 2 2 )(4−3k )+19k −50k +32) of R2 is π2IS∗ = (k(2c−θ)(2−k . 64(4−3k2 )2 (8−5k2 )2 (1−k2 )

= 3) The optimal profit of OS1 is ΠIS∗ 1

Only one ocean shipping company provides multi-modal transportation, which breaks the symmetry between the two ocean shipping companies. As a result, the basic market demand from the expansion of multi-modal transportation is unevenly distributed between the two ocean shipping companies. By comparing shipper demand for multi-modal transportation service and separate transportation service in this case, the following corollary can be obtained. Corollary 2. When θ − 2c 6

(1−k)(3k4 −16k3 −26k2 +24k+32) , (4−3k)(k+1)(2−k2 )(4−3k2 )

shipper demand for the separate trans-

IS∗ portation service is higher than that for the multi-modal transportation service (i.e., dIS∗ 1 6 d2 );

otherwise, shipper demand for the multi-modal transportation service is higher than that for the IS∗ separate transportation service(i.e., dIS∗ 1 > d2 ).

14

This corollary reveals an interesting conclusion: The multi-modal transportation service may not always be able to obtain more shipper demand than the separate transportation service. When the expansion of basic market demand generated by the availability of multi-modal transportation is not particularly large, the higher freight rate charged by the multi-modal transportation service weakens its competitive advantage. The high cost also makes the ocean shipping company that provides the multi-modal transportation service further increase his freight rate, yielding him a lower market share than the separate transportation service obtains. As shown in Fig. 3, a higher service integration cost c and lower market expansion θ can help the separate transportation service obtain a higher market share. Furthermore, Fig. 3 shows that the multi-modal transportation service is more likely to secure a higher market share under stronger competition, which means that the multi-modal transportation service has a stronger competitive advantage due to the higher service substitutability. Unlike separate transportation, multi-modal transportation integrates upstream and downstream transportation services and improves the efficiency of the supply chain.

(a) θ = 1.5

(b) c = 0.4

Figure 3: Comparison of market share for multi-modal transportation service and separate transportation service

In this case, the profit distribution between upstream and downstream companies has changed. The following corollary can be drawn by comparing the profits of ocean shipping companies and railway transportation companies. √ Before presenting the results, we define the following notations: k(2−k2 )2 (16−11k2 )−4 2(1−k)2 (k+1)2 (2−k2 )(8−5k2 )3 (4−3k2 ) 1 µ1 = max(0, ), µ2 = (2−k2 )(31k4−90k 2+64)(4−3k 2 ) (k(2 − (2−k2 )(31k4−90k2+64)(4−3k2 ) p k 2 )2 (16−11k 2 )+4 2(1−k)2 (k+1)2 (2−k 2 )(8−5k 2 )3 (4−3k 2 )). Corollary 3. A comparison of profits between participants can obtain the following characteristics:

1) The ocean shipping company that offers the multi-modal transportation service always obtains lower profit than the railway transportation company that he integrates with but higher profit than the other ocean shipping company when θ − 2c > 15

√ 2 2−k2

−

k . 4−3k2

2) The railway transportation company that still provides the separate transportation service always obtains a lower profit than her upstream ocean shipping company but may obtain a higher profit than the other railway transportation company when θ − 2c ∈ (µ1 , µ2 ]. The corollary highlights that companies that provide multi-modal transportation services do not necessarily obtain higher profits than companies that do not. When providing multi-modal transportation entails a high integration cost and the effect is not substantial (i.e., c is large, and θ is small), the competitive advantage of the multi-modal transportation service is very weak, and he even suffers a cost disadvantage. Moreover, the corollary also reveals another interesting implication. Although the upstream ocean shipping company has the right to decide whether to integrate the transportation services to provide multi-modal transportation, after the integration, the downstream railway transportation company can first set the wholesale price, which gives the railway transportation company some advantages and ultimately leads to her securing a higher profit than the upstream ocean shipping company, which is in contrast to the case in which multimodal transportation is not provided. 4.3. Both offer multi-modal transportation (case II) When both upstream ocean shipping companies decide to integrate with a downstream railway transportation company, only multi-modal transportation services are available in the market. In this case, the representative shipper utility Eq. (1) can yield the shipper demand for each ocean shipping company as follows: θ 2(1+k) θ 2(1+k)

dII 1 = dII 2 =

− +

1 P 1−k2 1 k P 1−k2 1

+ −

k P , 1−k2 2 1 P . 1−k2 2

(6)

Note that dII i , i = 1, 2 represent the shipper demand for the multi-modal transportation service provided by the OSi. According to the sequence of events, R1 and R2 first simultaneously maximize their profits to decide the wholesale price wi that they charge OSi; then, OS1 and OS2 simultaneously maximize their profits to determine their freight rates P1 and P2 , respectively. Hence, in this case, there is a two-layer Nash game model among the participants as follows: max π1II = w1 d1 ,

w1 >0

max π2II = w2 d2 ,

w2 >0

s.t. max ΠII 1 = (P1 − c − w1 )d1 ,

(7)

P1 >0

max ΠII 2 = (P2 − c − w2 )d2 . P2 >0

By solving the problem by backward induction, the optimal decisions of all participants can be obtained, which are summarized in the following proposition.

16

Proposition 4. In case II, the optimal decisions of the participants, shipper demands, and the optimal profits of the participants are given as follows: 1) The optimal wholesale prices of the railway transportation companies are wiII∗ = (k+2)(1−k)(θ−2c) , 8−2k−4k2 i = 1, 2, the optimal freight rates of the multi-modal transportation services provided by ocean shipping companies are PiII∗ = dII∗ i

=

(2−k2 )(θ−2c) . 2(1+k)(2−k)(4−k−2k2 )

θ(1−k)(3−k2 )+c(2−k2 ) , (2−k)(4−k−2k2 )

and the corresponding shipper demand is

2) The optimal profits of the ocean shipping companies are ΠII∗ i = and the optimal profits of the railway transportation companies

(1−k)(2−k2 )2 (θ−2c)2 , i = 1, 2, 4(4−k−2k2 )2 (2−k)2 (1+k) 2 )(θ−2c)2 (1−k)(2+k)(2−k are πiII∗ = 4(4−k−2k2 )2 (2−k)(1+k) .

Both ocean shipping companies integrate with a downstream railway transportation company to provide multi-modal transportation, which enables both companies to make the same optimal decisions and obtain the same shipper demands and profits. Consistent with Corollary 3, the integration of transportation services enables downstream railway transportation companies to consistently obtain higher profits than upstream ocean shipping companies. Next, we investigate how this difference in profits can be affected by related factors. Corollary 4. The railway transportation companies always obtain higher profit than the ocean shipping companies, and πiII∗ − ΠII∗ is increasing with respect to θ while decreasing with respect to i c. The more significant the effect of providing multi-modal transportation is, the greater the positive impact on the profits of the railway transportation companies will be. However, when providing multi-modal transportation entails a high integration cost, on the one hand, the ocean shipping companies will increase the freight rate for multi-modal transportation, which reduces shipper demand, and on the other hand, the railway transportation companies have to reduce their wholesale prices to make up for the costs faced by the ocean shipping companies. Both factors reduce the profits that railway transportation companies can obtain from multi-modal transportation. This finding also demonstrates that service integration makes the upstream and downstream transportation companies more affected by one another’s decisions, and they need to jointly face the costs and benefits of service integration. 5. Value and Incentive Analysis of Multi-modal Transportation 5.1. Value of multi-modal transportation In the foregoing corollary, we concluded that in contrast to the case of not providing multi-modal transportation, providing multi-modal transportation means that the upstream ocean shipping companies always obtain lower profits than the downstream railway transportation companies. 17

However, this will not affect the incentives of ocean shipping companies to provide multi-modal transportation. Whether an ocean shipping company has the incentive to provide multi-modal transportation depends on whether offering multi-modal transportation can increase his profits. The value of multi-modal transportation to an ocean shipping company can be obtained by comparing his profits when providing and not providing multi-modal transportation. Before prek senting the results in the following proposition, we define the following notations: ∆1 = 4−3k 2 − √ √ 2 2 2 2 2 3 2 2 2 2 2 3 2 (3k+1)(k −6k−3)(k −2)(1−k) (5k −8) (k+1) 2 (3k+1)(k −6k−3)(k −2)(1−k) (5k −8) (k+1) k , ∆2 = 4−3k , ∆3 = 2+ (3k+1)(k2−2)(3k2−4)(5+6k−3k2 ) (3k+1)(k2 −2)(3k2 −4)(5+6k−3k2 ) √ (k(k−2)(2k2+k−4)+2 2(k−1)(5k2−8))(2k2+k−4)(k−2)(19k4−50k2+32) 1 2 , ∆4 = Γ2 (k2 −2)(3k 2 −4) ((k(k − 2)(2k + k − 4) − Γ2 (k2−2)(3k2−4) √ 2 2(k − 1)(5k 2 − 8))(2k 2 + k − 4)(k − 2)(19k 4 − 50k 2 + 32)); k0 is the value that makes Γ1 equal

to 0 and k1 that can make Γ2 equal to 0; Γ1 = −100k 11 + 500k 10 + 1447k 9 − 2399k 8 − 5748k 7 +

3804k 6 + 9967k 5 − 1519k 4 − 8014k 3 − 1266k 2 + 2304k + 768, Γ2 = 4k 8 − 12k 7 − 215k 6 + 468k 5 + 428k 4 − 1376k 3 + 192k 2 + 1024k − 512.

Proposition 5. Multi-modal transportation has the following characteristics for ocean shipping companies: 1) When the other ocean shipping company does not provide multi-modal transportation, providing multi-modal transportation can generate a higher profit for the ocean shipping company in the following two cases: (i) weak competitive intensity but high integration efficiency, i.e., 0 6 k < k0 and θ − 2c > ∆2 ; (ii) strong competitive intensity but low or high integration efficiency, i.e.,

k0 6 k < 1 and θ − 2c 6 ∆1 or θ − 2c > ∆2 .

2) When the other ocean shipping company provides multi-modal transportation, providing multimodal transportation can bring higher profit to the ocean shipping company in the following two cases: (i) weak competitive intensity but high integration efficiency, i.e., 0 6 k < k1 and θ − 2c > ∆4 ; (ii) strong competitive intensity but medium integration efficiency, i.e., k1 6 k < 1

and ∆4 < θ − 2c 6 ∆3 .

The proposition shows that an ocean shipping company has incentives to integrate services and provide multi-modal transportation regardless of whether the competitor does so. The larger θ is, the greater the basic market demand for the expansion of multi-modal transportation will be, which represents the benefits generated by multi-modal transportation. Combined with the integration cost of multi-modal transportation, θ − 2c can be used to characterize the efficiency of multi-modal transportation. In a market with low competitive intensity, regardless of whether the competitor provides multi-modal transportation, a higher integration efficiency will encourage an ocean shipping company to provide multi-modal transportation. This is because a lower competitive intensity means lower substitutability of service products, and the ocean shipping company can enjoy most of the benefits of market expansion generated by providing multi-modal transportation. 18

However, in a market with high competitive intensity, an ocean shipping company’s incentives to provide multi-modal transportation are different. The shipper market expands in the presence of the multi-modal transportation provided by the ocean shipping company, and the other ocean shipping company that does not provide multi-modal transportation may obtain a higher market share; thus, offering multi-modal transport allows the competitor to free riding. Therefore, the ocean shipping company will offer multi-modal transportation only if the degree to which the competitor can free riding is extremely low (θ − 2c is small) or if it is highly beneficial to himself (θ − 2c is large). When the competitor offers multi-modal transportation, the ocean shipping company can free riding on the competitor. In this case, only a moderate level of integration efficiency can motivate the ocean shipping company to provide multi-modal transportation.

(a) The other ocean shipping company does not pro- (b) The other ocean shipping company provides multivide multi-modal transportation

modal transportation

Figure 4: Value of multi-modal transportation for the ocean shipping company and the railway transportation company

Because the results are similar to those for ocean shipping companies and only slightly different from the baseline, we will not separately describe the value of multi-modal transportation for railway transportation companies. Given the absence of additional relevant parameters, Fig. 4 also shows the analytical comparison results. Regardless of whether the competitor provides multimodal transportation, integrating transportation services to provide multi-modal transportation is a win-win strategy for both ocean shipping companies and railway transportation companies, as shown in the dark area of Fig. 4, while it is a lose-lose strategy in the grey area of Fig. 4. This finding again verifies that the upstream and downstream companies always stand together, and the benefits and costs generated by multi-modal transportation are shared by the two companies. However, due to the uneven distribution of relevant responsibilities and benefits, upstream and downstream companies may still have different preferences, as shown in the white area of Fig. 4. Multi-modal transportation will expand the basic demand in the market, but whether the ship19

per demand will be higher than when there is no multi-modal transportation remains unclear. Let QSS , QIS and QII represent the total shipper demand realized in the following three cases, respectively: there is no multi-modal transportation, only one ocean shipping company provides multi-modal transportation, and both ocean shipping companies provide multi-modal transportation. The relevant conclusions are summarized in the following proposition; see the Appendix for the relevant notation. Proposition 6. The influence of multi-modal transportation on shipper demand has the following characteristics: 1) When the integration efficiency is relatively low, regardless of whether one or two ocean shipping companies provide multi-modal transportation, the realized shipper demand is lower than it is in the absence of multi-modal transportation (max(QIS , QII ) < QSS ); 2) When the integration efficiency is moderate, either the market with multi-modal transportation and separate transportation or the market with only multi-modal transportation will realize higher shipper demand than it is in the absence of multi-modal transportation (QSS < max(QIS , QII )); 3) When the integration efficiency is high, one or two ocean shipping companies provide multimodal transportation can achieve higher shipper demand than that in the absence of multi-modal transportation (QSS < QIS , QSS < QII ). As shown in part (1) of Proposition 6, a lower integration efficiency will result in lower shipper demand in the market when a multi-modal transportation service exists because the existence of multi-modal transportation changes the relationship between upstream and downstream companies and affects the competition between two transportation companies of a given type. Moreover, the limited benefit of multi-modal transportation in this case makes it difficult for firms to compensate for these adverse factors. Therefore, only when the integration efficiency is relatively high can the market with multi-modal transport achieve higher shipper demand, as shown in parts (2) and (3) of Proposition 6. Furthermore, markets where only multi-modal transportation exists may not be able to obtain higher shipper demand than in markets in which both multi-modal transportation and separate transportation exist simultaneously. As shown in Fig. 5, when the integration efficiency is low, we have QII < QIS . Although both ocean shipping companies provide multi-modal transportation, which greatly expands the basic market demand, the low integration efficiency enables them to raise freight rates to compensate for the integration cost, which reduces the realized shipper demand. Finally, Fig. 5 also shows that a higher competitive intensity can make the market with multi-modal transportation better realize higher shipper demand. Strong competition will lead to lower freight rates for participants and ultimately attract more shippers,

20

and this effect is reinforced by the expansion of basic market demand in the presence of multi-modal transportation.

Figure 5: The difference in pricing and profit between ocean shipping companies and railway transportation companies

Proposition 7. The freight rate of multi-modal transportation in case II is always higher than that of separate transportation in the other two cases but may be lower than that of multi-modal transportation in case IS; the freight rate of separate transportation in case IS is always higher than that in case SS. The proposition shows that freight rates are generally raised in markets where multi-modal and separate transportation exist simultaneously. The company that provides multi-modal transportation raises his prices because he pays integration costs and has a large base market demand, while companies that still provide separate transportation services raise prices because they can free ride. Therefore, with both companies providing multi-modal transportation, not only is unilateral free riding eliminated, but the freight rate of multi-modal transportation may also be reduced. 5.2. Optimal and equilibrium strategies for multi-modal transportation Every ocean shipping company faces four possible strategies: neither he nor the competitor provides multi-modal transportation, he provides multi-modal transportation when the competitor does not, he does not provide multi-modal transportation when the competitor does, and he and the competitor both provide multi-modal transportation. Before exploring the equilibrium strategies of the two ocean shipping companies for multi-modal transportation, we first study the optimal strategies of a single ocean shipping company, which are summarized in the following proposition. Proposition 8. When the integration efficiency is relatively low (θ −2c 6

√ 2 2−k2

k − 4−3k 2 ), the opti-

mal strategy of the ocean shipping company is to have the competitor provide multi-modal transportation while he does not; when the integration efficiency is relatively high (θ − 2c >

√ 2 2−k2

−

the optimal strategy is to provide multi-modal transportation while the competitor does not. 21

k ), 4−3k2

Table 2: Ocean shipping companies’ expected payoffs

OS1

Separate transportation

Integrated transportation

Separate transportation

SS∗ ΠSS∗ 1 , Π2

IS∗ ΠIS∗ 1 , Π2

Integrated transportation

SI∗ ΠSI∗ 1 , Π2

II∗ ΠII∗ 1 , Π2

OS2

The proposition indicates that ocean shipping companies always prefer that only one company provides multi-modal transportation in the market, that is, multi-modal transportation and separate transportation services coexist. When the competitor integrates services to provide multimodal transportation, the ocean shipping company can benefit from the expanded base market demand and free riding. As a result, an ocean shipping company will decide to save the integration cost and not provide multi-modal transportation. However, when integration is very efficient, this also means that the basic market demand that integration can generate is high, and direct integration of services to provide multi-modal transportation can benefit him far more than can free riding. Therefore, an ocean shipping company will prefer to provide multi-modal transportation through integrating services. However, because of symmetry, the two ocean shipping companies have exactly the same preferences, which means that they always have difficulty jointly achieving the optimal and equilibrium outcomes. Thus, what are the equilibrium strategies for the two ocean shipping companies? In determining service integration, there is a Nash game between the two ocean shipping companies. To determine whether each ocean shipping company integrates services in equilibrium, we solve the meta-game by using the expected payoffs while accounting for proving multi-modal transportation as determined in the four sub-games, as shown in Table 2. The equilibrium strategies of the two ocean shipping companies are summarized in the following proposition, and the specific values of the relevant notations are shown in the Appendix. In addition, Fig. 6 illustrates these results more vividly, and because there are no other parameters, the results described in the figure are also analytical. Proposition 9. The equilibrium multi-modal transportation strategies for the two ocean shipping companies are as follows: 1) When the intensity of market competition is relatively low (k 6 k2 ), • equilibrium is achieved in case SS or case II with low integration efficiency; • equilibrium is achieved in case II with moderate integration efficiency; • equilibrium is achieved in case SI or case IS with high integration efficiency. 2) When the intensity of market competition is moderate (k2 < k 6 k3 ), 22

• equilibrium is achieved in case II with low integration efficiency; • equilibrium is achieved in case SI or case IS with high integration efficiency. 3) When the intensity of market competition is relatively high (k > k3 ), • equilibrium is achieved in case II with very low, moderate or very high integration efficiency; • equilibrium is achieved in case SS or case II with low integration efficiency; • equilibrium is achieved in case SI or case IS with high integration efficiency. Proposition 9 shows that the competitive intensity k and integration efficiency θ − 2c directly influence the equilibrium strategies of two ocean shipping companies. The former describes the substitutability of service products between ocean shipping companies, which, on the one hand, allows an ocean shipping company to free ride on the expanded basic market demand generated by the multi-modal transportation provided by the other ocean shipping company and, on the other hand, the two ocean shipping companies will suffer from a price war. The latter is a direct factor that measures whether an ocean shipping company benefits from integrating transportation services to provide multi-modal transportation. Combining the above with Fig. 6, we find that under a moderate level of integration efficiency, regardless of what the competition intensity is, the two ocean shipping companies will reach the equilibrium of case II, that is, they will both pursue service integration, and thus, only multimodal transportation services will be available in the final market. However, when the integration efficiency is extremely low or extremely high, the two ocean shipping companies can reach the equilibrium of providing multi-modal transportation only when the competitive intensity is high. The high competitive intensity means that an ocean shipping company benefits less from providing multi-modal transportation and a low degree of free riding by the competitor in the case of low integration efficiency. In the case of high integration efficiency, the ocean shipping company benefits more from providing multi-modal transportation, and the degree of free riding by the competitor is also high. Furthermore, the price war caused by the high competitive intensity adversely affects the profits of ocean shipping companies, which prompts them to provide multi-modal transportation to compensate for the loss. In the gray and white areas in Fig. 6, there are two equilibrium strategies for the two ocean shipping companies. However, the resulting equilibrium is unstable and difficult to achieve in practice and is therefore invalid. Thus, we will focus on the supply chain’s profit and consumer utility under the only and effective equilibrium, case II. 5.3. Supply chain profit and social welfare Because the two ocean shipping companies can reach a stable equilibrium only in case II, we need to consider the supply chain’s profit and social welfare in this case. Define the supply chain’s profit 23

Figure 6: Equilibrium multi-modal transportation strategies for two ocean shipping companies

as the sum of the profits of the two ocean shipping companies and the two railway transportation companies involved. The following proposition can then be obtained. Proposition 10. The supply chain’s profit in case II will be the highest in the following two cases: (i) weak competitive intensity but high integration efficiency, i.e., 0 6 k < k4 and θ − 2c > ∆5 ; (ii)

strong competitive intensity but moderate integration efficiency, i.e., k4 6 k < 1 and ∆5 < θ − 2c 6 ∆6 . The proposition shows that the highest profit for the entire supply chain can be achieved

when both ocean shipping companies provide multi-modal transportation. Recall the previous discussion that service integration improves the position of downstream railway transportation companies. Although railway transportation companies no longer obtain profits directly from shippers by selling transportation services, their ability to set the wholesale price enables them to transition out of their previously subordinate status where they were completely controlled by upstream ocean shipping companies, thereby improving their profits. As shown in Fig. 7(a), when market competition is less intense, the two ocean shipping companies obtain limited benefits from free riding. A higher integration efficiency ensures that ocean shipping companies can always benefit from providing multi-modal transportation, thus generating higher supply chain profits. Next, we compare consumer utility under the different strategies, as defined in Eq. (1). Proposition 11. The consumer utility in case II will be the highest when θ − 2c > ∆7 . Moreover, ∆6 > ∆7 , which means that consumer utility is maximized when the supply chain’s profit is maximized. Proposition 11 highlights that consumer utility can be maximized when both ocean shipping companies provide multi-modal transportation, and this can be achieved simultaneously with the highest supply chain profit. For a single shipper, the fiercer the competition between the two 24

(a) Supply chain’s profit

(b) Consumer utility

Figure 7: Supply chain’s profit and consumer utility

ocean shipping companies is, the lower the freight rate will be, which increases the shipper’s utility. Moreover, Proposition 7 shows that the freight rate of multi-modal transportation is higher in case II, which means that the shipper pays higher costs. However, the provision of multi-modal transportation expands the basic market demand and eventually leads to more shippers being served, which greatly improves overall consumer utility. Thus, as shown in Fig. 7(b), a moderate competitive intensity k and integration efficiency θ − 2c mean that consumer utility is maximized in case II.

Figure 8: Supply chain’s profit and social welfare are optimal under the equilibrium strategy

Social welfare is equal to the sum of supply chain profit and consumer utility, and thus, the highest social welfare is achieved in case II. As stated in Proposition 11, the dark area in Fig. 7(a) is not only where the supply chain profit is the highest but also where consumer utility and social welfare are the highest. Fig. 8 can be obtained by combining the equilibrium strategies of the two ocean shipping companies and social welfare. In the dark area of Fig. 8, both ocean shipping com25

panies can reach the equilibrium of both providing multi-modal transportation, and social welfare is also the highest in this case. This finding suggests that the government can constrain the competition between transportation companies to a moderate level and lower the threshold for providing multi-modal transportation, among other factors, to reduce the ocean shipping companies’ cost of service integration and ensure that the integration efficiency is moderate. 6. Extensions 6.1. Heterogeneous ocean shipping companies This subsection extends the models to case in which the two ocean shipping companies have different integration costs. Specifically, OS1 faces unit cost c1 , while OS2 faces unit cost c2 . By solving and comparing the profits (see Appendix B), we find that our main conclusions remain qualitatively unchanged. In particular, it may always be profitable for an ocean shipping company to offer multi-modal transportation, regardless of whether the competitor does the same. Combined with the subgraph in Figure 1 of Appendix B, the equilibrium that the two ocean shipping companies reach in providing multi-modal transportation may also maximize the supply chain’s profit, consumer utility, and social welfare. In addition, the asymmetry between the two ocean shipping companies gives rise to some new conclusions. First, the two ocean shipping companies will also achieve other equilibria, which depend on the cost relationship between them. When an ocean shipping company has a cost advantage, the equilibrium will tend to feature only one ocean shipping company to provide multi-modal transportation. This conforms to the principle of the optimal allocation of resources. Second, other equilibria achieved by the two ocean shipping companies, such as IS and SI, can also maximize the supply chain’s profit, consumer utility, and social welfare, but equilibrium SS does not. This finding also proves that the provision of multi-modal transportation always benefits society. 6.2. Only one downstream railway transportation company This subsection considers the case in which there is only one railway transportation company. After solving and analyzing, we find that our main conclusions remain qualitatively unchanged (see Appendix B for the proof). Specifically, first, the provision of multi-modal transportation will result in an increase in the final realization of shipper demand. However, due to the monopoly position, the downstream railway transportation company can always obtain a higher profit than the upstream ocean shipping companies, regardless of whether multi-modal transport is provided. Second, providing multi-modal transportation always has the potential to generate a higher profit for ocean shipping companies. Finally, both provide multi-modal transportation (case II), which is an equilibrium that the two ocean shipping companies can reach given an appropriate integration

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advantage and competitive intensity. This equilibrium may achieve higher supply chain profit, consumer utility, and social welfare under certain conditions. 7. Conclusion and Future Research Multi-modal transportation is an efficient system that can effectively coordinate different modes of transportation to economize on many intermediate operational links. However, at present, the annual volume of multi-modal transportation accounts for only a small share of total transportation, meaning that there are considerable opportunities for development. One factor obstructing the development of multi-modal transportation is that there are currently few carriers providing such services. To study the incentives of ocean shipping companies to provide multi-modal transportation, we consider a freight supply chain that includes two upstream ocean shipping companies and two downstream railway transportation companies. After verifying the benefit of multi-modal transportation in the absence of competition, introducing competition makes it possible to derive more specific and meaningful insights that can be summarized as follows. First, the provision of multi-modal transportation will change the status of upstream and downstream companies, which will benefit downstream companies and generate higher profits for them than upstream companies. However, offering multi-modal transportation does not necessarily enable an upstream ocean shipping company to outstrip the competitor. Moreover, multi-modal transportation may not be able to increase the final realization of shipper demand. Second, despite the above-mentioned disadvantages of providing multi-modal transportation, an ocean shipping company may have incentives to provide it at a certain competitive intensity and integration efficiency, regardless of the competitor’s actions. Moreover, the two upstream and downstream companies are likely to agree on their preferences with respect to the provision of multi-modal transportation. Finally, the effective equilibrium strategy that the two ocean shipping companies can reach is to integrate services and provide multi-modal transportation, but this is not their optimal strategy. In addition, this equilibrium strategy is also able to maximize both supply chain profit and social welfare. This paper analyzes the incentives of ocean shipping companies to provide multi-modal transportation and offers some meaningful managerial insights for the rapid development of multi-modal transportation. However, due to a series of simplifications in our stylized model, this paper has limitations. We do not account for uncertainty in shipper demand, which is very common in the transportation market. Incorporating uncertain demand would make our problems more complex and represents a direction for future research. In addition, in our paper, upstream companies buy downstream companies to provide multi-modal transportation; however, in practice, there are various ways to integrate upstream and downstream services, such as sharing profits and costs. These avenues are worthy of further study. 27

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