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Application of game theory to analyze the competition and cooperation scenarios among container terminals in Northern Vietnam
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Original Article
Application of game theory to analyze the competition and cooperation scenarios among container terminals in Northern Vietnam Minh Duc Nguyen a , S. June Kim b,∗ a b
Vietnam Maritime University, Viet Nam Korea Maritime & Ocean University, South Korea
a r t i c l e
i n f o
Article history: Received 10 April 2019 Received in revised form 26 August 2019 Accepted 28 August 2019 Keywords: Northern Vietnam Container terminals Game theory Handling charges
a b s t r a c t Northern Vietnam plays an important role in Vietnam’s national economy. In recent years, the sea-port industry in the area has witnessed an impressive development and fierce competition especially among local container terminals. Under the pressure of competition, local container ports are competing through attractive handling charges. The paper applies a Bertrand-Nash game model to estimate the equilibrium handling charges and equilibrium market share of each container terminal in the area. The game can be divided into non-cooperative game and cooperative game. Under the cooperative game, three different scenarios are considered. The game results will verify the implication of price competition among local container terminals and present the outcome of each coalitional scenario for further discussion. © 2019 The Authors. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction The seaport industry in Northern Vietnam has witnessed an impressive development in recent years. From 2005 to 2016, both the number of berth and total berth length doubled in figure while the area of the container yard in the whole region increased more than three times. However, the rising number of players and the slowing down of throughput growing rates hardened the competitiveness in the area. Through the period of 2000 to 2012, the supply was always higher than the demand and the gap was even greater since 2012. After 2017, the competition in the area was forecasted to be tougher than when the Lach Huyen International Container Terminal began its operation. The list of local container terminals is presented in Table 1. Under the pressure of competition, local container terminals are competing through attractive handling charges. This situation benefits only foreign shipping lines while local terminals lose profit to reinvest for improving their service quality. Therefore, it
∗ Corresponding author at: c.314, Division of Navigation Science, Korea Maritime & Ocean Univ., 727 Taejong-no, Yeongdo-gu, Busan 49112, South Korea. E-mail addresses: [email protected] (M.D. Nguyen), [email protected] (S.J. Kim). Peer review under responsibility of the Korean Association of Shipping and Logistics, Inc.
is necessary to perform analyses on the topic of handling charges and various cases of cooperation among local terminals for better mutual benefits. The purpose of the research is to fulfil the two major targets: firstly, to verify competition situation between the local container terminals and the statement that their handling charges are lower than the equivalent level and secondly, to suggest a scenario of cooperation between numbers of local container terminals which can generate the highest mutual benefit. The two targets would be reached by applying a game theoretical model to generate equivalent handling charges and profit under scenarios of cooperation and non-cooperation. Some parameters used in the model will also contribute to solve the given questions. The paper consists of five sections including Introduction section followed by Literature review to present the application of game theory in the field of port competition. The game model specification is then presented in the 3rd section under non-cooperative game and cooperative game and different scenarios. Input parameters to solve the model are the next part required before the game results can be generated. Implication and Conclusion is the last section to conclude the whole paper.
2. Literature review The first important text in game theory was “Theory of Games and Economic Behavior” published by Von Neuman and
https://doi.org/10.1016/j.ajsl.2019.08.001 2092-5212 © 2019 The Authors. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).
Please cite this article in press as: M.D. Nguyen and S.J Kim. Application of game theory to analyze the competition and cooperation scenarios among container terminals in Northern Vietnam. The Asian Journal of Shipping and Logistics (2019), https://doi.org/10.1016/j.ajsl.2019.08.001
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2 Table 1 Container terminals in Northern Vietnam. No. Terminals
Throughput 2016 (1000 TEUs)
1 Haiphong – Chua Ve 270 788 2 Haiphong – Tan Vu 3 Dinh Vu 722 4 Nam Hai 255 464 5 Nam Hai Dinh Vu 293 6 Hai An 245 7 PTSC Dinh Vu 240 8 Doan Xa 9 Green Port 280 10VIP Green Port 350 11Saigon New Port (SNP) 223 120 12Transvina 12 13Cai Lan International Container Terminal (CICT) N/A 14Quang Ninh Source: Vietnam Port Association (2017).
Morgenstern (1944). In the book, game theory was mostly considered from the perspective of mathematics. From that publication, game theory has extended further, especially under the contribution of Nash (1950, 1953). It was in the 1970s that game theory, as a way of analyzing strategic situations, began to be applied in all sorts of diverse areas including economics, politics, international relations, business, and biology (Carmichael, 2005). Game theory is described by Roger (1991) as “the study of mathematical models of conflict and cooperation intelligent rational decision makers.” Hutton (1996) describes game theory as “an intellectual framework for examining what various parties to a decision should do given their possession of inadequate information and different objectives.” In the topic of port competition, game theory has been widely recognized as an important tool. Zan (1999) used a bi-level Stackelberg game to capture the flow of foreign trade containers in order to investigate the behaviour of port users in transshipment ports. Anderson et al. (2008) developed a game theoretic best response framework for understanding how competitor ports will respond to the development of a given port and how the given port will respond. Bae Min Ju (2013), in his thesis, applied a two-stage game approach to analyze container transshipment port competition. Ishii, Lee, Texuka, and Chang (2013) developed a non-cooperative game model under stochastic demand to explain inter-port competition under demand uncertainty and derive a unique equilibrium. The competition between the port of Busan and Kobe is used as the case study. Park, Han, and Lu (2010) applied Counot Model–Quantity competition and Bertrand Model-Quantity competition to examine the response of ports under other ports’ demand and profit. In the topic of price competition among ports, game theory is also commonly applied. Han, Park, and Ahn (2012) built game models to analyze port price strategies and competition for transshipment containers between the Busan and Shanghai ports. In this research, the authors used a utility function to measure a customer’s satisfaction based on transport cost, port charges, service quality, and time. Zhang, Yang, and Wang (2010) developed a Bertrand price competition model in both the cases of cooperation and non-cooperation to study the price competition between the container ports of Hong Kong and Shenzhen. The paper analyses the solution of Nash equilibrium and raises strategies to solve the vicious competition in the price war of the two ports. Saeed and Larsen (2010) developed non-cooperative and cooperative game models to examine the equilibrium price of container terminals in one port. Park and Suh (2015) applied the model developed by Saeed and Larsen (2010) to solve the equilibrium price of container terminals in port of Busan in both non-cooperative and co-operative games.
There is no literature review on the topic of game theoretical approach to competition among container terminals in Northern Vietnam. There is also no previous research analyzing different cases of cooperation between local terminals. The paper, therefore, is the first research dealing with the cooperation among local container terminals from the perspective of handling charges. 3. The game model specification 3.1. Utility and demand for container terminal services The structure of Bertrand game is used to describe the game for container terminals in Northern Vietnam. All the container terminals are assumed to provide similar services to containers but at different charges. Customers or service users (here, shipping lines and consignors) will have to decide the container terminal which can maximize their satisfaction. In other words, container terminals will be chosen depending on the utility that they offer to users. The utility function of terminal ‘i’ (i = 1,2,3. . .12) can be presented as follows (Saeed and Larsen, 2010): Ui = ai + b(pi + OUCi)
(1)
Where: Ui is utility of terminal i ai is a derived constant which can be estimated in different ways b is price coefficient at container terminals. b can be estimated in different ways pi is handling charge of container terminal i OUCi stands for other users’ costs which are users’ additional costs beside the handling charges. The OUC can consist of the waiting cost of vessels during their stay at port, the inland transportation cost. Kaselimi, Notteboom, and Saeed (2011) describe the other users’ costs by the following formulation: OUCi = COi + f (X i/CAP i)
(2)
Where: COi is inland transportation cost which is fixed and independent to the volume of containers handled. f(Xi/CAPi) is a function of vessels’ waiting cost which commonly increases when the volume of the containers handled increases. Xi is the volume of containers handled by terminal i. CAPi stands for the capacity of terminal i. The market share of terminals is expressed by the following formulation according to Malchow and Kanafani (2004): Qi =
eU i
13
i=1
(3)
eUi
Where: Qi is the market share of terminal i The total demand of all the container terminals in Northern Vietnam can be denoted by X and expressed by the following formulation (Saeed and Larsen, 2010): X = AeLS
(4)
Where: A and are constants and 0 < < 1 LS is log sum and determined by: LS = ln
13
eU i
(5)
i=1
The demand of 1 container terminal, therefore, can be expressed by: Xi = XQi
(6)
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The profit of container terminal ‘i’ in Northern Vietnam can be defined based on the volume of containers handled as follows: ˘i = Xi(pi − ci)
(7)
Where: i is the profit of container terminal i ci is the marginal cost per TEU of container terminal i in handling cargo Before the games are modelled, it is necessary to assume some conditions to validate the model:
3
(17) can be substituted to (12) to gain: 1 + [b(Qi + 1 − Qi )](pi − ci ) = 0
(18)
Or: 1 b(Qi + 1 − Qi )
pi = Ci −
(19)
Eq. (19) is the price response function of container terminal i. 3.3. Cooperative game
- All the container terminals offer similar services but they are not exact substitutes to each other. - The total demand for the container terminal services of the whole area is fixed when the handling charge of each terminal changes. - The costs which occur in the same amount like inland transportation, berthing charge, port charge, and wharf charge, regardless of the location of the container terminals, will not be considered in the model because the utility model deals with customers’ behaviour which depends on the difference of cost of service. - When a terminal reduces its handling charge, users will choose to move their containers to this terminal. - The users’ selection will depend on only the cost while other kinds of conditions or agreements are out of scope. 3.2. Non-cooperative game Under the non-cooperative game, each container terminal will compete with others independently to maximize their own profit. Therefore, the Bertrand Nash equilibrium can be characterized by the following condition: ∂˘i =0 ∂pi
(8)
According to Eqs. (4) and (6): Xi = XQi = AeLS Qi
(9)
Subsequently: ˘i = AeLS Qi (pi − ci )
Scenario 1: The 4 container terminals of Vinalines cooperate together and the other terminals operate independently. Scenario 2: The 4 container terminals of Vinalines cooperate together and the other similar cooperation is set up between Nam Hai and Nam Dinh Vu, and between Green Port and VIP Green Port. The other terminals work independently. Scenario 3: There are 3 similar coalitions set up between terminals operated by the same operator. Those coalitions are between Chua Ve and Tan Cang Dinh Vu, Nam Hai and Nam Hai Dinh Vu, and Green Port and VIP Green Port.
(10)
Therefore, Eq. (8) becomes: ∂˘i ∂[AeLSQi(pi − ci)] = =0 ∂pi ∂pi
(11)
Eq. (11) can be differentiated to become: AeLS Qi +
Among all container terminals in Northern Vietnam, there are 6 container terminals which are owned by Vinalines with the percentage of share-holding varying from 51% to 100%. They are Chua Ve, Tan Cang Dinh Vu, Doan Xa, Dinh Vu, Quang Ninh, and Cai Lan International Container Terminal. However, the two container terminals in Quang Ninh province, including CICT and Quang Ninh, show a very low level of performance in recent years and will be eliminated. Furthermore, Chua Ve and Tan Cang Dinh Vu are the two terminals of Haiphong Port Join Stock Company (HPC). Similarly, Nam Hai and Nam Hai Dinh Vu are also operated by the same operator named Gemadept Corporation. Green Port and VIP Green Port are the two container terminals operated by Vietnam Container Shipping Join Stock Company (Viconship). Therefore, in a co-operative game, one can assume some coalitional scenarios as follows:
∂(AeLSQi) (pi − ci ) = 0 ∂pi
(12) ˘=
By handling Eq. (12) by logarithm: ln(AeLS Qi ) = ln A + LS + ln Qi
4
˘i =
i=1
(13)
By taking the derivative of Eq. (13) by pi: ∂ ln(AeLSQi) ∂ ln A + ∂ ln(LS) + ∂Ui − ∂LS ∂pi
In each case, the objective of the coalition is to maximize the total profit of all the members. This study will consider the scenario 1 first and the other cases are similar in terms of mathematical expression. In the scenario 1, the total profit of the 4 members is presented by Eq. (20) below:
(14)
∂LS ∂LS +b− ∂p ∂p
∂˘ = ∂p1
(15)
∂(AeLS Q1 ) ∂(AeLS Q2 ) (p1 − c1 ) + AeLS Q1 + (p2 − c2 ) ∂p1 ∂p1 ∂(AeLS Q4 ) ∂(AeLS Q3 ) (p3 − c3 ) + (p4 − c4 ) ∂p1 ∂p1
(21)
According to Eq. (17): (16)
∂(AeLS Q1 ) = AeLS Q1 [b(Q1 + 1 − Q1 ] ∂p1
(22)
And
(16) can be substituted to (15) to gain: ∂ ln(AeLSQi) LS Ae Qi [b(Qi + 1 − Qi )] ∂pi
(20)
In respect of the first terminal, by taking derivative of the total profit by p1:
+
And
∂LS ∂eU eU xb = ∂ ln eU = = = Qb ∂p eU eU
(pi − ci )Xi
i=1
Because ln(A) is a constant, then: ∂ ln(LS) + ∂Ui − ∂LS =
4
(17)
∂(AeLS Q2 ) (p2 − c2 ) = AeLS Q2 [b(Q1 − Q1 ](p2 − c2 ) ∂p1
(23)
Please cite this article in press as: M.D. Nguyen and S.J Kim. Application of game theory to analyze the competition and cooperation scenarios among container terminals in Northern Vietnam. The Asian Journal of Shipping and Logistics (2019), https://doi.org/10.1016/j.ajsl.2019.08.001
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Therefore: ∂˘ = ∂p1
AeLS Q1 [b(Q1 + 1 − Q1 ](p1 − c1 ) + AeLS Q1 +AeLS Q2 [b(Q1 − Q1 ](p2 − c2 ) +AeLS Q3 [b(Q1 − Q1 ](p3 − c3 ) +AeLS Q4 [b(Q1
(24)
Qi =
− Q1 ](p4 − c4 ) = 0
(25)
+Q3 [b( − 1](p3 − c3 ) + Q4 [b( − 1](p4 − c4 ) = 0 Or: c1 − {1 + Q2 [b( − 1)](p2 − c2 ) + Q3 [b( − 1)](p3 − c3 ) +Q4 [b( − 1)](p4 − c4 )}/[b(Q1 + 1 − Q1 ]
(26)
A similar transformation is applied to the three other terminals, and the price response function of those container terminals is as follows: c2 − {1 + Q1 [b( − 1)](p1 − c1 ) + Q3 [b( − 1)](p3 − c3 ) +Q4 [b( − 1)](p4 − c4 )}/[b(Q2 + 1 − Q2 ] p3 =
c3 − {1 + Q1 [b( − 1](p1 − c1 ) + Q2 [b( − 1](p2 − c2 ) +Q4 [b( − 1)](p4 − c4 )}/[b(Q3 + 1 − Q3 ]
p4 =
13
eUi
Ui = ln Qi + ln
[b(Q1 + 1 − Q1 ](p1 − c1 ) + 1 + Q2 [b( − 1](p2 − c2 )
p2 =
eUi
i=1
Finally:
p1 =
The average utility, handling charge, and OUC of all container terminals in Northern Vietnam from 2011 to 2016 are presented in Table 2 as the input of the linear regression. In this table, Eq. (3) is solved by logarithm as follows in order to calculate the utility of each terminal:
c4 − {1 + Q1 [b( − 1)](p1 − c1 ) + Q2 [b( − 1)](p2 − c2 ) +Q3 [b( − 1)](p3 − c3 )}/[b(Q4 + 1 − Q4 ]
(27)
(28)
(29)
The other scenarios have similar price response functions. 4. Input parameters and the game results In order to set the pricing rule by the users, the Nash equilibrium for the Bertrand game will be implemented. Before that, the necessary parameters are defined. The parameters ai and b are used in the utility function as expressed in Eq. (1). Saeed and Larsen (2010) and Munim, Saeed, and Larsen (2017) define these parameters by assuming based on personal experience while Park and Suh (2015) use linear regression to estimate. All the authors consider that a change in terminal service charge will not affect the total demand profoundly but demand of individual terminals might change. Therefore, the value of is quite low and can be assumed by the value (0.01). In this research, the value of is fixed by 0.01. In order to determine the ai value, a1 = a2 = a3 = . . . = a14 = a is assumed. The values of a and b will be determined by linear regression.
⇒ ln Qi = ln
i=1
eUi
eUi
i=1
eUi
or (30)
Where ln = eU i is denoted by LS, LS = 15.24 i=1 Here, the total throughput of container terminals in Northern Vietnam is used as a proxy variable of total utility. The linear regression analysis returns the value of a as 15.79 and b as −0.078. The input to solve the game is presented in Table 3 in Appendix A. The game results of different scenarios are also presented respectively in Tables 4–7 in Appendix A. The calculated results of the non-cooperative and cooperative game reveal the following points that one can learn from the case of container terminals in Northern Vietnam. The current handling charges offered by container terminals in Northern Vietnam are at a significantly low level than the equilibrium price. This result is conformable with the fact that container terminals in the area are competing fiercely with each other and a common strategy to attract customers is offering a better price than competitors. Under this condition, only foreign shipping lines earn benefit from the price competition policy and local terminals lose profit which can be used to reinvest for better performance. This situation is harmful to the local port industry and should be changed. The value of b in the utility function (Eq. 3.1) which is determined by linear regression also reflects the elasticity of local container terminals’ utilities to handling charges. In comparison with the b value in other areas, the b value in Northern Vietnam is −0.078, the b value in Busan is −0.046 according to Park and Suh (2015), the b value in Greek Port is −0.056 according to Polydoropoulou and Litinas (2007), and the b value in port of Karachi, Pakistan is −0.05 according to Saeed and Larsen (2010). It implies that the container terminals in Northern Vietnam are more sensitive to change of handling charges than the mentioned areas. This implication is also confirmable with the current situation of handling charges in the area. The value of b in the case of container terminals in Northern Vietnam also implies that terminals’ market share can be increased significantly by reducing users’ costs. Besides the handling charge, the other user cost is also an important factor that impacts the decision of customers. Investments in improving cargo handling speed, therefore, become critical. In the case of cooperative game, Scenario 1, all the four container terminals of Vinalines show better results in profit. This increase of profit is caused by the increase of equilibrium hand-
Table 2 Input data to estimate parameters a and b. Terminals
Utility
Handling charge (USD/TEU)
OUC (USD/TEU)
Total cost (USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
12.49796 13.56904 13.37651 12.38018 12.4408 13.03943 12.57971 12.40081 12.53434 12.75747 12.30672 11.68705
35 33 33 37 33 33 36 37 33 33 33 36
3.939213 4.187564 6.62151 7.661986 7.109182 4.072414 6.201712 6.209939 5.207364 3.691217 12.90142 3.874874
38.93921 37.18756 39.62151 44.66199 40.10918 37.07241 42.20171 45.20994 38.20736 36.69122 45.90142 39.87487
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ling charges rather than expansion of throughput. The reason is because the 2 leading terminals named Tan Vu and Dinh Vu have already taken full advantage of capacity, and increase in throughput will return a significant increase in vessels’ waiting cost. The considerable increase of profit in cooperation game opens a potential coalitional strategy to given terminals. It also implies that the two terminals, Tan Vu and Dinh Vu, have a potential chance of increasing market share and profit if those terminals are invested in to expand the capacity. In addition and in the case of the cooperative game, Scenario 1, not only the four container terminals of Vinalines record better profit but also all the other container terminals in the area do the same result. It implies a positive impact of the coalitional strategies of the four terminals to the whole local market. Under all the scenarios of coalition, the profit of terminals is higher than the case where they operate independently. However, among those coalitional scenarios, the highest results of equilibrium profit can be found in Scenario 2, with Scenario 3 and the lowest equilibrium profit being found in Scenario 1. This implies that the more players join a coalition, the better the results are for all the container terminals in the area.
5
its operation in a very near future. The competition among container terminals in the area will be more difficult and, therefore, which terminals cannot keep up with the trend will be eliminated. Coalition under scenario 1 is a potential scenario that Vinalines’ terminals can apply to increase all the members’ profit. However, while the equilibrium handling charges and profit increase, the overall market share of Vinalines’ terminals slightly decreases. As a result, not only fixing appropriate level of handling charges, but other policies are also required to increase the utility of those terminals. In summary, the paper applies a Bertrand-Nash game model to estimate the equilibrium handling charges and equilibrium market share of each container terminal in the area. The game can be divided into non-cooperative game and cooperative game. Under the cooperative game, the three different scenarios are considered. The game results will verify the implication of price competition among local container terminals and present the outcome of each coalitional scenario for further discussion.
5. Implications and conclusion Conflict of interest According to the game results, there are some implications which can be suggested to related parties. The current handling charges offered by container terminals in Northern Vietnam are lower than the equilibrium handling charges in case each terminal competes independently. However, the bargaining power is currently in the hand of foreign shipping lines and all the terminals in the area need a representative organization to set the handling charges at higher level. Vietnam Port Association (VPA) and Vietnam Maritime Administration (Vinamarine) are organizations which should be in charge to issue appropriate policies. In such case, the equilibrium price in this study can be taken as reference. Various synchronized policies should be applied by terminal operators to improve terminals’ services both in the perspective of shipping lines and shippers. From the perspective of shipping lines, terminals’ competitive advantages, which should be considered, are the handling charges, vessels’ facilities and services, and cargo handling speed, among others. From the perspective of shippers, the terminals’ competitive advantages, which should be considered, are cargo value added services, distribution costs, and storage services, to name some. The general purpose is to increase the terminals’ utility which directly impacts the terminals’ market share. Lach Huyen International Container Terminal is expected to begin
The authors declare no conflicts of interest.
Uncited references Blancas Mendivil, Isbell, and Isbell (2015) and Verhoeff (1981).
Acknowledgement This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A6A3A01081098).
Appendix A.
Table 3 Input parameters for the game models. a b Total demand (TEUs)
15.79 −0.078 0.01 4,190,000
Terminals
Capacity (,000 TEUs)
Current market share
Current handling charge
Marginal cost (USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
550 1000 500 250 150 500 250 250 350 550 250 250
0.064439 0.188067 0.155131 0.057279 0.060859 0.11074 0.069928 0.058473 0.066826 0.083532 0.053222 0.02864
35 33 33 37 33 33 36 37 33 33 33 36
29 25 25 29 27 25 29 27 25 25 27 27
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6 Table 4 The results of non-cooperative game. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.06443 0.18806 0.15513 0.05727 0.06085 0.11074 0.06992 0.05847 0.06682 0.08353 0.05322 0.02864
35 33 33 37 33 33 36 37 33 33 33 36
0.0808 0.1198 0.1136 0.0619 0.0689 0.1128 0.0731 0.0698 0.0845 0.1076 0.0539 0.0533
42.83 41.27 39.39 42.55 40.65 39.37 42.71 40.66 38.89 39.28 40.43 40.42
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,014
4,716,943 7,478,392 7,066,469 3,497,309 3,940,632 6,996,437 4,210,711 3,995,031 4,946,924 6,593,619 3,016,163 2,985,802
Table 5 The results of cooperative game, Scenario 1. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.0644 0.1880 0.1551 0.0572 0.0608 0.1107 0.0699 0.0584 0.0668 0.0835 0.0532 0.0286
35 33 33 37 33 33 36 37 33 33 33 36
0.0758 0.1181 0.1119 0.0604 0.0701 0.1089 0.0752 0.0711 0.0867 0.1138 0.0543 0.0538
45.11 41.04 40.94 44.08 40.67 41.26 42.74 40.68 38.91 39.33 40.44 40.43
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,014
5,116,568 7,937,218 7,473,644 3,816,386 4,015,139 7,419,292 4,329,309 4,075,395 5,053,127 6,832,859 3,057,828 3,027,417
Table 6 The results of cooperative game, Scenario 2. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.06443 0.18806 0.15513 0.05727 0.06085 0.11074 0.06992 0.05847 0.06682 0.08353 0.05322 0.02864
35 33 33 37 33 33 36 37 33 33 33 36
0.0783 0.1243 0.1167 0.0617 0.0681 0.1065 0.0773 0.0726 0.081 0.1037 0.0551 0.0546
45.32 41.23 41.1 44.18 42.72 42.51 42.77 40.7 42.16 42.13 40.46 40.45
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,010
5,354,217 8,452,860 7,872,465 3,924,379 4,485,529 7,813,575 4,459,924 4,167,458 5,823,932 7,443,036 3,107,497 3,077,010
Table 7 The results of cooperative game, Scenario 3. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.06443 0.18806 0.15513 0.05727 0.06085 0.11074 0.06992 0.05847 0.06682 0.08353 0.05322 0.0286
35 33 33 37 33 33 36 37 33 33 33 36
0.0771 0.1205 0.1227 0.0631 0.067 0.1142 0.0756 0.0714 0.0795 0.1004 0.0545 0.0539
44.93 40.93 39.48 42.57 42.61 40.61 42.75 40.69 42.06 42.03 40.45 40.44
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,014
5,146,171 8,042,977 7,444,356 3,587,759 4,382,195 7,469,354 4,355,505 4,095,583 5,682,771 7,164,112 3,071,375 3,035,303
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References Anderson, C. M., Park, A., Chang, Y. T., Yang, C. H., Lee, T. W., & Luo, M. (2008). A game-theoretic analysis of competition among container port hubs: The case of Busan and Shanghai. Maritime Policy & Management, 35(1), 5–26. Bae Min Ju. (2013). A game theoretic approach to analyzing container transshipment port competition. Thesis submitted for the degree of master of engineering department of Industrial and system of engineering. Department of Industrial and Engineering, National University of Singapore. Blancas Mendivil, L. C., Isbell, J., & Isbell. (2015). Efficient logistics: A key to Vietnam’s competitiveness (English). Directions in development; Countries and regions. Washington, D.C.: World Bank Group. Han, X. U., Park, G. K., & Ahn, T. Y. (2012). On the application of game theory to the competition among major ports in North East Asia for transshipment cargoes. Journal of Korean Institute of Intelligent Systems, 22(2), 261–266. Ishii, M., Lee, P., Texuka, K., & Chang, Y. (2013). A game theoretical analysis of port competition. Transportation Research Part E, 49, 92–106. Kaselimi, E. N., Notteboom, T., & Saeed, N. (2011). A game theoretical approach to the inter-relation between terminal scale and port competition. In Proceedings of international association of maritime economists (IAME) conference (pp. 1–26). Malchow, N. M., & Kanafani, A. (2004). A disaggregate analysis of port selection. Transportation Research, 40(7), 313–337. Munim, Z. H., Saeed, N., & Larsen, O. I. (2017). Tool port to landlord port: A game theory approach to analyze gains from governance model transformation. In Proceeding of international association of maritime economists conference.
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Nash, J. F. (1950). The bargaining problem. Econometrica, 18, 156–162. Nash, J. F. (1953). Two-person cooperative games. Econometrica, 21, 128–140. Park, G. K., Han, X., & Lu, D. (2010). Analysis of Port Competition using game theory. Okayama, Japan: SCIS&ISIS Okayama Convention Center. Park, N. K., & Suh, S. C. (2015). Port competition study: Cooperative game model. Journal of Contemporary Management. Polydoropoulou, A., & Litinas, N. (2007). Demand models for Greek passenger shipping. Maritime Transport: The Greek Paradigm, 21(Chapter 9), 297–322. Roger, B. M. (1991). Game theory: Analysis of conflict. pp. vii–xi. Harvard University Press. Saeed, N., & Larsen, O. I. (2010). An application of cooperative game among container terminals of one port. European Journal of Operation Research, 203(2), 393–403. Verhoeff, J. M. (1981). Seaport Competition: Government production of port services. In J. M. Verhoeff (Ed.), Transport and port economy: Between action and abstraction (pp. 181–202). Leiden: Stenfert Kroese. Vietnam Port Association. (2017). http://www.vpa.org.vn/index.jsp. Von Neuman, J., & Morgenstern, O. (1944). Theory of games and economic behavior. New York: Wiley (reprinted 1964) Zan, Y. (1999). Analysis of container port policy by the reaction of an equilibrium shipping market. Maritime Policy and Management, 26(4), 369–381. Zhang, P., Yang, L., & Wang, H. (2010). Game analysis of price competition between Hong Kong and Shenzhen container port based on Bertrand Model. In 2nd conference on environmental science and information application technology.
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Original Article
Application of game theory to analyze the competition and cooperation scenarios among container terminals in Northern Vietnam Minh Duc Nguyen a , S. June Kim b,∗ a b
Vietnam Maritime University, Viet Nam Korea Maritime & Ocean University, South Korea
a r t i c l e
i n f o
Article history: Received 10 April 2019 Received in revised form 26 August 2019 Accepted 28 August 2019 Keywords: Northern Vietnam Container terminals Game theory Handling charges
a b s t r a c t Northern Vietnam plays an important role in Vietnam’s national economy. In recent years, the sea-port industry in the area has witnessed an impressive development and fierce competition especially among local container terminals. Under the pressure of competition, local container ports are competing through attractive handling charges. The paper applies a Bertrand-Nash game model to estimate the equilibrium handling charges and equilibrium market share of each container terminal in the area. The game can be divided into non-cooperative game and cooperative game. Under the cooperative game, three different scenarios are considered. The game results will verify the implication of price competition among local container terminals and present the outcome of each coalitional scenario for further discussion. © 2019 The Authors. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction The seaport industry in Northern Vietnam has witnessed an impressive development in recent years. From 2005 to 2016, both the number of berth and total berth length doubled in figure while the area of the container yard in the whole region increased more than three times. However, the rising number of players and the slowing down of throughput growing rates hardened the competitiveness in the area. Through the period of 2000 to 2012, the supply was always higher than the demand and the gap was even greater since 2012. After 2017, the competition in the area was forecasted to be tougher than when the Lach Huyen International Container Terminal began its operation. The list of local container terminals is presented in Table 1. Under the pressure of competition, local container terminals are competing through attractive handling charges. This situation benefits only foreign shipping lines while local terminals lose profit to reinvest for improving their service quality. Therefore, it
∗ Corresponding author at: c.314, Division of Navigation Science, Korea Maritime & Ocean Univ., 727 Taejong-no, Yeongdo-gu, Busan 49112, South Korea. E-mail addresses: [email protected] (M.D. Nguyen), [email protected] (S.J. Kim). Peer review under responsibility of the Korean Association of Shipping and Logistics, Inc.
is necessary to perform analyses on the topic of handling charges and various cases of cooperation among local terminals for better mutual benefits. The purpose of the research is to fulfil the two major targets: firstly, to verify competition situation between the local container terminals and the statement that their handling charges are lower than the equivalent level and secondly, to suggest a scenario of cooperation between numbers of local container terminals which can generate the highest mutual benefit. The two targets would be reached by applying a game theoretical model to generate equivalent handling charges and profit under scenarios of cooperation and non-cooperation. Some parameters used in the model will also contribute to solve the given questions. The paper consists of five sections including Introduction section followed by Literature review to present the application of game theory in the field of port competition. The game model specification is then presented in the 3rd section under non-cooperative game and cooperative game and different scenarios. Input parameters to solve the model are the next part required before the game results can be generated. Implication and Conclusion is the last section to conclude the whole paper.
2. Literature review The first important text in game theory was “Theory of Games and Economic Behavior” published by Von Neuman and
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2 Table 1 Container terminals in Northern Vietnam. No. Terminals
Throughput 2016 (1000 TEUs)
1 Haiphong – Chua Ve 270 788 2 Haiphong – Tan Vu 3 Dinh Vu 722 4 Nam Hai 255 464 5 Nam Hai Dinh Vu 293 6 Hai An 245 7 PTSC Dinh Vu 240 8 Doan Xa 9 Green Port 280 10VIP Green Port 350 11Saigon New Port (SNP) 223 120 12Transvina 12 13Cai Lan International Container Terminal (CICT) N/A 14Quang Ninh Source: Vietnam Port Association (2017).
Morgenstern (1944). In the book, game theory was mostly considered from the perspective of mathematics. From that publication, game theory has extended further, especially under the contribution of Nash (1950, 1953). It was in the 1970s that game theory, as a way of analyzing strategic situations, began to be applied in all sorts of diverse areas including economics, politics, international relations, business, and biology (Carmichael, 2005). Game theory is described by Roger (1991) as “the study of mathematical models of conflict and cooperation intelligent rational decision makers.” Hutton (1996) describes game theory as “an intellectual framework for examining what various parties to a decision should do given their possession of inadequate information and different objectives.” In the topic of port competition, game theory has been widely recognized as an important tool. Zan (1999) used a bi-level Stackelberg game to capture the flow of foreign trade containers in order to investigate the behaviour of port users in transshipment ports. Anderson et al. (2008) developed a game theoretic best response framework for understanding how competitor ports will respond to the development of a given port and how the given port will respond. Bae Min Ju (2013), in his thesis, applied a two-stage game approach to analyze container transshipment port competition. Ishii, Lee, Texuka, and Chang (2013) developed a non-cooperative game model under stochastic demand to explain inter-port competition under demand uncertainty and derive a unique equilibrium. The competition between the port of Busan and Kobe is used as the case study. Park, Han, and Lu (2010) applied Counot Model–Quantity competition and Bertrand Model-Quantity competition to examine the response of ports under other ports’ demand and profit. In the topic of price competition among ports, game theory is also commonly applied. Han, Park, and Ahn (2012) built game models to analyze port price strategies and competition for transshipment containers between the Busan and Shanghai ports. In this research, the authors used a utility function to measure a customer’s satisfaction based on transport cost, port charges, service quality, and time. Zhang, Yang, and Wang (2010) developed a Bertrand price competition model in both the cases of cooperation and non-cooperation to study the price competition between the container ports of Hong Kong and Shenzhen. The paper analyses the solution of Nash equilibrium and raises strategies to solve the vicious competition in the price war of the two ports. Saeed and Larsen (2010) developed non-cooperative and cooperative game models to examine the equilibrium price of container terminals in one port. Park and Suh (2015) applied the model developed by Saeed and Larsen (2010) to solve the equilibrium price of container terminals in port of Busan in both non-cooperative and co-operative games.
There is no literature review on the topic of game theoretical approach to competition among container terminals in Northern Vietnam. There is also no previous research analyzing different cases of cooperation between local terminals. The paper, therefore, is the first research dealing with the cooperation among local container terminals from the perspective of handling charges. 3. The game model specification 3.1. Utility and demand for container terminal services The structure of Bertrand game is used to describe the game for container terminals in Northern Vietnam. All the container terminals are assumed to provide similar services to containers but at different charges. Customers or service users (here, shipping lines and consignors) will have to decide the container terminal which can maximize their satisfaction. In other words, container terminals will be chosen depending on the utility that they offer to users. The utility function of terminal ‘i’ (i = 1,2,3. . .12) can be presented as follows (Saeed and Larsen, 2010): Ui = ai + b(pi + OUCi)
(1)
Where: Ui is utility of terminal i ai is a derived constant which can be estimated in different ways b is price coefficient at container terminals. b can be estimated in different ways pi is handling charge of container terminal i OUCi stands for other users’ costs which are users’ additional costs beside the handling charges. The OUC can consist of the waiting cost of vessels during their stay at port, the inland transportation cost. Kaselimi, Notteboom, and Saeed (2011) describe the other users’ costs by the following formulation: OUCi = COi + f (X i/CAP i)
(2)
Where: COi is inland transportation cost which is fixed and independent to the volume of containers handled. f(Xi/CAPi) is a function of vessels’ waiting cost which commonly increases when the volume of the containers handled increases. Xi is the volume of containers handled by terminal i. CAPi stands for the capacity of terminal i. The market share of terminals is expressed by the following formulation according to Malchow and Kanafani (2004): Qi =
eU i
13
i=1
(3)
eUi
Where: Qi is the market share of terminal i The total demand of all the container terminals in Northern Vietnam can be denoted by X and expressed by the following formulation (Saeed and Larsen, 2010): X = AeLS
(4)
Where: A and are constants and 0 < < 1 LS is log sum and determined by: LS = ln
13
eU i
(5)
i=1
The demand of 1 container terminal, therefore, can be expressed by: Xi = XQi
(6)
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The profit of container terminal ‘i’ in Northern Vietnam can be defined based on the volume of containers handled as follows: ˘i = Xi(pi − ci)
(7)
Where: i is the profit of container terminal i ci is the marginal cost per TEU of container terminal i in handling cargo Before the games are modelled, it is necessary to assume some conditions to validate the model:
3
(17) can be substituted to (12) to gain: 1 + [b(Qi + 1 − Qi )](pi − ci ) = 0
(18)
Or: 1 b(Qi + 1 − Qi )
pi = Ci −
(19)
Eq. (19) is the price response function of container terminal i. 3.3. Cooperative game
- All the container terminals offer similar services but they are not exact substitutes to each other. - The total demand for the container terminal services of the whole area is fixed when the handling charge of each terminal changes. - The costs which occur in the same amount like inland transportation, berthing charge, port charge, and wharf charge, regardless of the location of the container terminals, will not be considered in the model because the utility model deals with customers’ behaviour which depends on the difference of cost of service. - When a terminal reduces its handling charge, users will choose to move their containers to this terminal. - The users’ selection will depend on only the cost while other kinds of conditions or agreements are out of scope. 3.2. Non-cooperative game Under the non-cooperative game, each container terminal will compete with others independently to maximize their own profit. Therefore, the Bertrand Nash equilibrium can be characterized by the following condition: ∂˘i =0 ∂pi
(8)
According to Eqs. (4) and (6): Xi = XQi = AeLS Qi
(9)
Subsequently: ˘i = AeLS Qi (pi − ci )
Scenario 1: The 4 container terminals of Vinalines cooperate together and the other terminals operate independently. Scenario 2: The 4 container terminals of Vinalines cooperate together and the other similar cooperation is set up between Nam Hai and Nam Dinh Vu, and between Green Port and VIP Green Port. The other terminals work independently. Scenario 3: There are 3 similar coalitions set up between terminals operated by the same operator. Those coalitions are between Chua Ve and Tan Cang Dinh Vu, Nam Hai and Nam Hai Dinh Vu, and Green Port and VIP Green Port.
(10)
Therefore, Eq. (8) becomes: ∂˘i ∂[AeLSQi(pi − ci)] = =0 ∂pi ∂pi
(11)
Eq. (11) can be differentiated to become: AeLS Qi +
Among all container terminals in Northern Vietnam, there are 6 container terminals which are owned by Vinalines with the percentage of share-holding varying from 51% to 100%. They are Chua Ve, Tan Cang Dinh Vu, Doan Xa, Dinh Vu, Quang Ninh, and Cai Lan International Container Terminal. However, the two container terminals in Quang Ninh province, including CICT and Quang Ninh, show a very low level of performance in recent years and will be eliminated. Furthermore, Chua Ve and Tan Cang Dinh Vu are the two terminals of Haiphong Port Join Stock Company (HPC). Similarly, Nam Hai and Nam Hai Dinh Vu are also operated by the same operator named Gemadept Corporation. Green Port and VIP Green Port are the two container terminals operated by Vietnam Container Shipping Join Stock Company (Viconship). Therefore, in a co-operative game, one can assume some coalitional scenarios as follows:
∂(AeLSQi) (pi − ci ) = 0 ∂pi
(12) ˘=
By handling Eq. (12) by logarithm: ln(AeLS Qi ) = ln A + LS + ln Qi
4
˘i =
i=1
(13)
By taking the derivative of Eq. (13) by pi: ∂ ln(AeLSQi) ∂ ln A + ∂ ln(LS) + ∂Ui − ∂LS ∂pi
In each case, the objective of the coalition is to maximize the total profit of all the members. This study will consider the scenario 1 first and the other cases are similar in terms of mathematical expression. In the scenario 1, the total profit of the 4 members is presented by Eq. (20) below:
(14)
∂LS ∂LS +b− ∂p ∂p
∂˘ = ∂p1
(15)
∂(AeLS Q1 ) ∂(AeLS Q2 ) (p1 − c1 ) + AeLS Q1 + (p2 − c2 ) ∂p1 ∂p1 ∂(AeLS Q4 ) ∂(AeLS Q3 ) (p3 − c3 ) + (p4 − c4 ) ∂p1 ∂p1
(21)
According to Eq. (17): (16)
∂(AeLS Q1 ) = AeLS Q1 [b(Q1 + 1 − Q1 ] ∂p1
(22)
And
(16) can be substituted to (15) to gain: ∂ ln(AeLSQi) LS Ae Qi [b(Qi + 1 − Qi )] ∂pi
(20)
In respect of the first terminal, by taking derivative of the total profit by p1:
+
And
∂LS ∂eU eU xb = ∂ ln eU = = = Qb ∂p eU eU
(pi − ci )Xi
i=1
Because ln(A) is a constant, then: ∂ ln(LS) + ∂Ui − ∂LS =
4
(17)
∂(AeLS Q2 ) (p2 − c2 ) = AeLS Q2 [b(Q1 − Q1 ](p2 − c2 ) ∂p1
(23)
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Therefore: ∂˘ = ∂p1
AeLS Q1 [b(Q1 + 1 − Q1 ](p1 − c1 ) + AeLS Q1 +AeLS Q2 [b(Q1 − Q1 ](p2 − c2 ) +AeLS Q3 [b(Q1 − Q1 ](p3 − c3 ) +AeLS Q4 [b(Q1
(24)
Qi =
− Q1 ](p4 − c4 ) = 0
(25)
+Q3 [b( − 1](p3 − c3 ) + Q4 [b( − 1](p4 − c4 ) = 0 Or: c1 − {1 + Q2 [b( − 1)](p2 − c2 ) + Q3 [b( − 1)](p3 − c3 ) +Q4 [b( − 1)](p4 − c4 )}/[b(Q1 + 1 − Q1 ]
(26)
A similar transformation is applied to the three other terminals, and the price response function of those container terminals is as follows: c2 − {1 + Q1 [b( − 1)](p1 − c1 ) + Q3 [b( − 1)](p3 − c3 ) +Q4 [b( − 1)](p4 − c4 )}/[b(Q2 + 1 − Q2 ] p3 =
c3 − {1 + Q1 [b( − 1](p1 − c1 ) + Q2 [b( − 1](p2 − c2 ) +Q4 [b( − 1)](p4 − c4 )}/[b(Q3 + 1 − Q3 ]
p4 =
13
eUi
Ui = ln Qi + ln
[b(Q1 + 1 − Q1 ](p1 − c1 ) + 1 + Q2 [b( − 1](p2 − c2 )
p2 =
eUi
i=1
Finally:
p1 =
The average utility, handling charge, and OUC of all container terminals in Northern Vietnam from 2011 to 2016 are presented in Table 2 as the input of the linear regression. In this table, Eq. (3) is solved by logarithm as follows in order to calculate the utility of each terminal:
c4 − {1 + Q1 [b( − 1)](p1 − c1 ) + Q2 [b( − 1)](p2 − c2 ) +Q3 [b( − 1)](p3 − c3 )}/[b(Q4 + 1 − Q4 ]
(27)
(28)
(29)
The other scenarios have similar price response functions. 4. Input parameters and the game results In order to set the pricing rule by the users, the Nash equilibrium for the Bertrand game will be implemented. Before that, the necessary parameters are defined. The parameters ai and b are used in the utility function as expressed in Eq. (1). Saeed and Larsen (2010) and Munim, Saeed, and Larsen (2017) define these parameters by assuming based on personal experience while Park and Suh (2015) use linear regression to estimate. All the authors consider that a change in terminal service charge will not affect the total demand profoundly but demand of individual terminals might change. Therefore, the value of is quite low and can be assumed by the value (0.01). In this research, the value of is fixed by 0.01. In order to determine the ai value, a1 = a2 = a3 = . . . = a14 = a is assumed. The values of a and b will be determined by linear regression.
⇒ ln Qi = ln
i=1
eUi
eUi
i=1
eUi
or (30)
Where ln = eU i is denoted by LS, LS = 15.24 i=1 Here, the total throughput of container terminals in Northern Vietnam is used as a proxy variable of total utility. The linear regression analysis returns the value of a as 15.79 and b as −0.078. The input to solve the game is presented in Table 3 in Appendix A. The game results of different scenarios are also presented respectively in Tables 4–7 in Appendix A. The calculated results of the non-cooperative and cooperative game reveal the following points that one can learn from the case of container terminals in Northern Vietnam. The current handling charges offered by container terminals in Northern Vietnam are at a significantly low level than the equilibrium price. This result is conformable with the fact that container terminals in the area are competing fiercely with each other and a common strategy to attract customers is offering a better price than competitors. Under this condition, only foreign shipping lines earn benefit from the price competition policy and local terminals lose profit which can be used to reinvest for better performance. This situation is harmful to the local port industry and should be changed. The value of b in the utility function (Eq. 3.1) which is determined by linear regression also reflects the elasticity of local container terminals’ utilities to handling charges. In comparison with the b value in other areas, the b value in Northern Vietnam is −0.078, the b value in Busan is −0.046 according to Park and Suh (2015), the b value in Greek Port is −0.056 according to Polydoropoulou and Litinas (2007), and the b value in port of Karachi, Pakistan is −0.05 according to Saeed and Larsen (2010). It implies that the container terminals in Northern Vietnam are more sensitive to change of handling charges than the mentioned areas. This implication is also confirmable with the current situation of handling charges in the area. The value of b in the case of container terminals in Northern Vietnam also implies that terminals’ market share can be increased significantly by reducing users’ costs. Besides the handling charge, the other user cost is also an important factor that impacts the decision of customers. Investments in improving cargo handling speed, therefore, become critical. In the case of cooperative game, Scenario 1, all the four container terminals of Vinalines show better results in profit. This increase of profit is caused by the increase of equilibrium hand-
Table 2 Input data to estimate parameters a and b. Terminals
Utility
Handling charge (USD/TEU)
OUC (USD/TEU)
Total cost (USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
12.49796 13.56904 13.37651 12.38018 12.4408 13.03943 12.57971 12.40081 12.53434 12.75747 12.30672 11.68705
35 33 33 37 33 33 36 37 33 33 33 36
3.939213 4.187564 6.62151 7.661986 7.109182 4.072414 6.201712 6.209939 5.207364 3.691217 12.90142 3.874874
38.93921 37.18756 39.62151 44.66199 40.10918 37.07241 42.20171 45.20994 38.20736 36.69122 45.90142 39.87487
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ling charges rather than expansion of throughput. The reason is because the 2 leading terminals named Tan Vu and Dinh Vu have already taken full advantage of capacity, and increase in throughput will return a significant increase in vessels’ waiting cost. The considerable increase of profit in cooperation game opens a potential coalitional strategy to given terminals. It also implies that the two terminals, Tan Vu and Dinh Vu, have a potential chance of increasing market share and profit if those terminals are invested in to expand the capacity. In addition and in the case of the cooperative game, Scenario 1, not only the four container terminals of Vinalines record better profit but also all the other container terminals in the area do the same result. It implies a positive impact of the coalitional strategies of the four terminals to the whole local market. Under all the scenarios of coalition, the profit of terminals is higher than the case where they operate independently. However, among those coalitional scenarios, the highest results of equilibrium profit can be found in Scenario 2, with Scenario 3 and the lowest equilibrium profit being found in Scenario 1. This implies that the more players join a coalition, the better the results are for all the container terminals in the area.
5
its operation in a very near future. The competition among container terminals in the area will be more difficult and, therefore, which terminals cannot keep up with the trend will be eliminated. Coalition under scenario 1 is a potential scenario that Vinalines’ terminals can apply to increase all the members’ profit. However, while the equilibrium handling charges and profit increase, the overall market share of Vinalines’ terminals slightly decreases. As a result, not only fixing appropriate level of handling charges, but other policies are also required to increase the utility of those terminals. In summary, the paper applies a Bertrand-Nash game model to estimate the equilibrium handling charges and equilibrium market share of each container terminal in the area. The game can be divided into non-cooperative game and cooperative game. Under the cooperative game, the three different scenarios are considered. The game results will verify the implication of price competition among local container terminals and present the outcome of each coalitional scenario for further discussion.
5. Implications and conclusion Conflict of interest According to the game results, there are some implications which can be suggested to related parties. The current handling charges offered by container terminals in Northern Vietnam are lower than the equilibrium handling charges in case each terminal competes independently. However, the bargaining power is currently in the hand of foreign shipping lines and all the terminals in the area need a representative organization to set the handling charges at higher level. Vietnam Port Association (VPA) and Vietnam Maritime Administration (Vinamarine) are organizations which should be in charge to issue appropriate policies. In such case, the equilibrium price in this study can be taken as reference. Various synchronized policies should be applied by terminal operators to improve terminals’ services both in the perspective of shipping lines and shippers. From the perspective of shipping lines, terminals’ competitive advantages, which should be considered, are the handling charges, vessels’ facilities and services, and cargo handling speed, among others. From the perspective of shippers, the terminals’ competitive advantages, which should be considered, are cargo value added services, distribution costs, and storage services, to name some. The general purpose is to increase the terminals’ utility which directly impacts the terminals’ market share. Lach Huyen International Container Terminal is expected to begin
The authors declare no conflicts of interest.
Uncited references Blancas Mendivil, Isbell, and Isbell (2015) and Verhoeff (1981).
Acknowledgement This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A6A3A01081098).
Appendix A.
Table 3 Input parameters for the game models. a b Total demand (TEUs)
15.79 −0.078 0.01 4,190,000
Terminals
Capacity (,000 TEUs)
Current market share
Current handling charge
Marginal cost (USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
550 1000 500 250 150 500 250 250 350 550 250 250
0.064439 0.188067 0.155131 0.057279 0.060859 0.11074 0.069928 0.058473 0.066826 0.083532 0.053222 0.02864
35 33 33 37 33 33 36 37 33 33 33 36
29 25 25 29 27 25 29 27 25 25 27 27
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6 Table 4 The results of non-cooperative game. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.06443 0.18806 0.15513 0.05727 0.06085 0.11074 0.06992 0.05847 0.06682 0.08353 0.05322 0.02864
35 33 33 37 33 33 36 37 33 33 33 36
0.0808 0.1198 0.1136 0.0619 0.0689 0.1128 0.0731 0.0698 0.0845 0.1076 0.0539 0.0533
42.83 41.27 39.39 42.55 40.65 39.37 42.71 40.66 38.89 39.28 40.43 40.42
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,014
4,716,943 7,478,392 7,066,469 3,497,309 3,940,632 6,996,437 4,210,711 3,995,031 4,946,924 6,593,619 3,016,163 2,985,802
Table 5 The results of cooperative game, Scenario 1. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.0644 0.1880 0.1551 0.0572 0.0608 0.1107 0.0699 0.0584 0.0668 0.0835 0.0532 0.0286
35 33 33 37 33 33 36 37 33 33 33 36
0.0758 0.1181 0.1119 0.0604 0.0701 0.1089 0.0752 0.0711 0.0867 0.1138 0.0543 0.0538
45.11 41.04 40.94 44.08 40.67 41.26 42.74 40.68 38.91 39.33 40.44 40.43
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,014
5,116,568 7,937,218 7,473,644 3,816,386 4,015,139 7,419,292 4,329,309 4,075,395 5,053,127 6,832,859 3,057,828 3,027,417
Table 6 The results of cooperative game, Scenario 2. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.06443 0.18806 0.15513 0.05727 0.06085 0.11074 0.06992 0.05847 0.06682 0.08353 0.05322 0.02864
35 33 33 37 33 33 36 37 33 33 33 36
0.0783 0.1243 0.1167 0.0617 0.0681 0.1065 0.0773 0.0726 0.081 0.1037 0.0551 0.0546
45.32 41.23 41.1 44.18 42.72 42.51 42.77 40.7 42.16 42.13 40.46 40.45
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,010
5,354,217 8,452,860 7,872,465 3,924,379 4,485,529 7,813,575 4,459,924 4,167,458 5,823,932 7,443,036 3,107,497 3,077,010
Table 7 The results of cooperative game, Scenario 3. Terminals
Current market share
Current handling charge (USD/TEU)
Eq. market share
Eq. handling charge (USD/TEU)
Current Profit (mil USD)
Eq. Profit (mil USD)
Chua Ve Tan Vu Dinh Vu Doan Xa Nam Hai Nam Hai Dinh Vu Hai An PTSC Green Port VIP Green Port SNP Transvina
0.06443 0.18806 0.15513 0.05727 0.06085 0.11074 0.06992 0.05847 0.06682 0.08353 0.05322 0.0286
35 33 33 37 33 33 36 37 33 33 33 36
0.0771 0.1205 0.1227 0.0631 0.067 0.1142 0.0756 0.0714 0.0795 0.1004 0.0545 0.0539
44.93 40.93 39.48 42.57 42.61 40.61 42.75 40.69 42.06 42.03 40.45 40.44
1,619,996 6,304,005 5,199,991 1,919,992 1,529,995 3,712,004 2,050,988 2,450,018 2,240,007 2,799,992 1,338,001 1,080,014
5,146,171 8,042,977 7,444,356 3,587,759 4,382,195 7,469,354 4,355,505 4,095,583 5,682,771 7,164,112 3,071,375 3,035,303
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Please cite this article in press as: M.D. Nguyen and S.J Kim. Application of game theory to analyze the competition and cooperation scenarios among container terminals in Northern Vietnam. The Asian Journal of Shipping and Logistics (2019), https://doi.org/10.1016/j.ajsl.2019.08.001