A game theoretic approach to analyzing container transshipment port competition

A GAME THEORETIC APPROACH TO ANALYZING CONTAINER TRANSSHIPMENT PORT COMPETITION BAE MIN JU NATIONAL UNIVERSITY OF SINGAPORE 2013 A GAME THEORETIC APPROACH TO ANALYZING CONTAINER TRANSSHIPMENT PORT COMPETITION BAE MIN JU (M.Eng., Korea Maritime University, South Korea) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2013 Declaration I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Bae Min Ju 22 April 2013 i        Acknowledgements First and foremost I offer my sincerest gratitude to my supervisors, Associate Professor Ek Peng Chew and Loo Hay Lee who supported me with kind guidance and great encouragement. This thesis would not have been possible without their help, support and patience. I am also grateful to all the other faculty members and staffs in the Department of Industrial and Systems Engineering, especially Ms Lai Chun Ow and Ms Celine Neo for their heartwarming support. My sincere thanks go to examiners of my thesis, Associate Professor Qiang Meng, from Department of Civil and Environmental Engineering, and Kien Ming Ng, for their thorough review, critical comments and constructive advices. I would like to acknowledge Professor Anming Zhang, from Sauder School of Business in University of British Columbia, for his kindness and invaluable comments during the preparation of the conference paper. My special thanks to fellow postgraduate students in the Department of Industrial and Systems Engineering, Liqin Chen, Yinghui Fu, Juxin Li, Qiang Wang, Qi Zhou, Aoran Mu, Yi Luo and Nugroho Artadi Pujowidianto for their kindness and cherished friendship. I am deeply indebted to my parents for their unconditional love and support in all my pursuits and my parents-in-law for their great help. Finally, I would express my deepest appreciation to my loving, supportive, encouraging and patient husband Ming Guang and my adorable daughter Shanyi. They have been the greatest source of strength and support in my work and in my life. Min Ju Bae National University of Singapore April 2013 ii     Contents Declaration . i  Acknowledgements ii  Summary . v  List of Tables . vi  List of Figures .vii  List of Symbols . x  List of Abbreviation xi  Chapter Introduction 1  1.1  1.2  1.3  1.4  Background 1  Motivation . 3  Objective 5  Overview . 6  Chapter Literature Review 8  2.1  2.2  2.3  Port Selection . 8  Port Competition . 10  2.2.1  Empirical Research 10  2.2.2  Game Theory . 11  Game Theory in Aviation Industry 13  Chapter Base Model Development 15  3.1  3.2  3.3  Overview . 15  The Model . 16  A Non-Cooperative Two-stage Game . 19  3.3.1  Stage two: Shipping Lines’ Port Call Decision 20  3.4  3.5  3.7  3.3.2  Stage one: Port Pricing Strategies . 23  Ports Collusion and Social Optimum 23  3.4.1  Ports Collusion Model . 23  3.4.2  Social Optimum Model . 24  Numerical Results . 25  Conclusions . 33  iii     Chapter Nonlinear Transshipment Demand and Multiple Nash Equilibria 35  4.1  4.2    4.3   4.4 Overview . 35  The model 35  37  Non-cooperative two-stage game . 38  Numerical Analysis 4.4.1  Shipping lines’ port call decision . 38  4.5  4.4.2  Port Pricing Strategies . 64  Conclusions . 65  Chapter Analysis on Asymmetric Shipping lines . 67  5.1  5.2  5.3  Overview . 67  The model 67  Numerical analysis 69  5.3.1  Asymmetric Shipping lines’ Port Call Decision 69  5.4  Conclusion . 79  Chapter Conclusions . 81  6.1  6.2  Conclusions of the Study . 81  Future Research . 82  Bibliography . 84  Appendix A . 89  Appendix B . 90  Appendix C . 94  Appendix D . 96  Appendix E . 98  Appendix F . 100  Appendix G . 102  Appendix H . 104  Appendix I 107  iv     Summary This thesis investigates the competition between transshipment container ports. The main purpose of this thesis is to develop the model that can capture the trends in transshipment container port competition and behaviours of key players, ports and shipping lines, in their decision making. Studying industrial events and relevant literatures led us to choose the key factors that play an important role in port competition problem. The key determinants such as port capacity, price, congestion and transshipment level are taken into account model development. Subsequently, multiple functions are created to examine the interdependency among shipping lines when determining port demand. With a linear transshipment container demand, it is able to achieve analytical properties through a two-stage game approach. Considering a nonlinear transshipment container demand in the model, it results in Multiple Nash equilibria in shipping lines’ port call decision. Asymmetric shipping lines are also studied in the model for investigating their demand driving forces. Overall, this thesis addresses the characteristics of transshipment container demand and shipping lines’ port call decision towards transshipment benefit and congestionassociated effect. Most of all, this thesis can help advance the analysis on ports’ transshipment capabilities and enable the ports to uncover and balance its demand and capacity levels so as to strategize for the long term. It can also provide better visibility on the shipping lines’ criteria when choosing a transshipment port. v     List of Tables Table 4.1 Symmetric port capacity levels……….………………………… .……………43 Table 4.2 Summary of port call strategy under various symmetric capacities……….………48 Table 4.3 Summary of port call strategy under changes in symmetric prices……….……….52 Table 4.4 Summary of port call strategy under changes in symmetric TS levels……….…53 Table 4.5 Asymmetric port capacity levels……….………………………………………….56 Table 4.6 Summary of port call strategy under asymmetric capacities……….……………58 Table 4.7 Summary of port call strategy under asymmetric prices……….…………………60 Table 4.8 Summary of port call strategy under asymmetric TS levels ……….…………63 Table 5.1 Symmetric port capacity levels for ASLs……….……………………………… .70 Table 5.2 Experimental cases for proposed pricing strategy to ASLs……….………………77 vi     List of Figures Figure 1.1 World container port traffic 1990-2011 ……….………………………………… Figure 1.2 Trends and challenges in container shipping market……….…………………… .2 Figure 2.1 Port selection criteria found in port selection literatures……….….………………9 Figure 3.1 Market structure and key variables……….………………………………………16 Figure 3.2 Effect of price differences and capacity levels on SL’s port call decision……….26 Figure 3.3 Effect of transshipment and capacity levels on SL’s port call decision……… .27 Figure 3.4 Equilibrium port prices while varying capacity differences……….…… 28 Figure 3.5 Equilibrium port prices while varying transshipment level differences……….…29 Figure 3.6 Comparison between Non-cooperative and Social optimum model….… 29 Figure 4.1 SLs’ BRCs with a Unique Nash Equilibrium…… …….……………………… 40 Figure 4.2 Multiple Nash equilibria and Stability…… … …… ………………………… 41 Figure 4.3 Multiple Nash equilibria and Robustness…… ………………….…………… 41 Figure 4.4 SLs’ BRCs when symmetric capacities at CU=100%…… … ….………… .43 Figure 4.5 Trends of SL 2’s TS benefits, congestion cost and total profit when q11 =1 …….44 Figure 4.6 SLs’ downward sloping BRCs under various levels of symmetric capacities … .45 vii     Figure 4.7 SLs’ upward sloping BRCs under various levels of symmetric capacities… 46 Figure 4.8 SLs’ BRCs under different transshipment effects… 49 Figure 4.9 Summary port call strategy under different transshipment effects… .49 Figure 4.10 Comparison base case: CU=80%, g  0.3 ,   0.3 … 50 Figure 4.11 Comparison of base case with changes in symmetric capacities and prices… .51 Figure 4.12 Comparison of base case with changes in symmetric capacities and TS levels .53 Figure 4.13 SLs’ BRCs when K1 > K2 … 57 Figure 4.14 SLs’ BRCs when 1  2 ……………………………………………………….59 Figure 4.15 SLs’ BRCs with different levels of price difference at CU=20% .60 Figure 4.16 SLs’ BRCs when g1  g2 …………………………………………………… …62 Figure 4.17 SLs’ BRCs with different levels of TS differences at CU=20%…………… …63 Figure 4.18 Unique Nash equilibrium in port pricing……………………………………… 64 Figure 5.1 ASLs’ BRCs under various levels of symmetric capacities…………………… .71 Figure 5.2 Comparison base case: CU=80%, g =0.3,  = 0.3………………………………72 Figure 5.3 Comparison of base case with changes in symmetric capacities and prices… .…73 Figure 5.4 Comparison of base case with changes in symmetric capacities and TS levels.…74 Figure 5.5 ASLs’ BRCs when K1  K ………………………………………………… …75 viii     Appendix C Same capacities and transshipment levels for both ports Proof of Proposition The first order derivate of (3.22) can be obtained K2 F1  0 6aN  f  gN  1 (A.13) Hence, the second order derivate of (3.22) is  F1 0 12 The second order derivate for port 1’ profit with respect to its price is given below.  1 F1  F1  O     1 12 1 1 (A.14) (A.13) and second order derivate of (3.22) give  1 F 2 0 1 1 (A.15) Therefore, 1 is concave in 1 . Similar result can be obtained for port 2. Proof of Proposition To prove uniqueness of port price, the contraction condition (Milgrom and Roberts, 1990) is assessed. The second order partial derivate for port is 94      1 F1  F1    1  O1  1  1 (A.16) We can get the second order derivate for port 1’s demand from (A.13) and the first order derivate for port 1’s demand with respect to port 2’s price from (3.22). F1 F  F1   0, 2 1 1 The obtained values give,  1  21 F F  2  0 1 12 1 2 Similar result is obtained for port 2. As it satisfies the contract condition, the Nash equilibrium port price, shown in (3.23), is unique. 95     Appendix D Linear Congestion Delay Cost function Proof of Proposition The first order derivate of (3.25) can be obtained g12 K1K F1  0 1 2a  g 22 K1  g12 K  (A.17) Hence, the second order derivate of (3.25) is  F1 0 12 The second order derivate for port 1’ profit with respect to its price is given (A.14). (A.17) and second order derivate of (3.29) give  1 F 2 0 1 1 (A.18) Therefore, 1 is concave in 1 . Similar result can be obtained for port 2. Proof of Proposition To solve (A.16), we can get the second order derivate for port 1’s demand from (A.17) and the first order derivate for port 1’s demand with respect to port 2’s price from (3.25). F1 g1 g K1K  F1   0, 2 2a  g 22 K1  g12 K  1 96     The obtained values justify,  1  1  12 12 2  g1K1K  g1  g  g12 K1K g1 g K1K F1 F1     1 2 a  g 22 K1  g12 K  2a  g 22 K1  g12 K  2a  g 22 K1  g12 K  The contract condition is satisfied only when 2g1  g2 . If port 2’ transshipment level is more than double of port 1’s, the Nash equilibrium port price may not be unique. Similar result is obtained for port 2. 97     Appendix E Kuhn-Tucker condition We conduct the numerical simulation based on Kuhn-Tucker condition. First, shipping lines’ profit function can be re-written in the canonical form. max  i i  1, subject to K r  Fr  r  1, ( p  c   r  Dr )  r  1, qir  0, r  1,  qir  r  1, Transform the shipping line 1’s form to Lagrangian, L1  q11 ; 1 , 2 , 3 , 4 , 5 , 6     1  K1  F1   2  K  F2  3  p  c  1  D1   4  p  c  2  D2   5 q11  6 1  q11  (A.19) The first order conditions are as follows: 1) L1  F F D F D2 F2   1  2  3 1  4  5  6  q11 q11 q11 q11 F1 q11 F2 q11 q11  0, q11 L 0 q11 2) L1 L  K1  F1  ; 1  ; 1  1  K1  F1   1 1 3) L1 L  K  F2  ; 2  ; 2  2  K  F2   2 2 4) L1 L  p  c  1  D1  ; 3  ; 3  3  p  c  1  D1   3 3 5) L1 L  p  c  2  D2  ; 4  ; 4  4  p  c    D2   4 4 98     6) L1 L  q11  ; 5  ; 5  5 q11  5 5 7) L1 L   q11  ; 6  ; 6  6 (1  q11 )  6 6 99     Appendix F Proof of Lemma Let  be a move made by shipping line from current Nash Equilibrium point (1, 0). Using Taylor series expansion, evaluate the shipping line 1’s shift,   , while shipping line remains at current Nash Equilibrium (1, 0). Taylor series expansion gives,  (1   )   1    1 and solve for   1 gives  1   (1   )  0    1  lim The profit for shipping line at Nash Equilibrium (1, 0) is: q11  ; q12  ; q21  ; q22  ; Q1  ; Q2  F11  g1q11 Q1  g1 ; F12  g q12 Q2  F21  g1q21 Q1  ; F22  g q22 Q2  g F1  F11  F21  g1 ; F2  F12  F22  g 2 F  F  g2 g2 D1  a    a 12 ; D2  a    a 22 K1 K2  K1   K2    1   p  c  1  a  g12   g1 K12  (A.20) The profit for shipping line at 1   , 0 is: q11    ; q12   ; q21  ; q22  ; Q1    ; Q2    F11  g1 1    ; F12  g 2   ; F21  ; F22  g   F1  g1 1    ; F2  g 1    100     g12 1    g 22 1    ; D  a K12 K22 D1  a 3  g12 1       1      p  c  1  a g       K    g 22 1       p  c  2  a  g 2     K   (A.21) Since it is a symmetric port case, assuming 1  2 , K1  K2 , g1  g2  1   (1   )  0    1  lim 1     3  1           g p c 1          2     lim 7   0  ag    21  1     1      1       K 2     ag    g  p  c       21   2 K 2 As assumed (1, 0) is not a Nash equilibrium,   ag1   g  p  c         2 K 2  p c  7 ag 0 K2 7ag K   p c   Finally, the threshold capacity level is found. It gives that (1, 0) is not Nash Equilibrium when the port capacity falls in above condition. 101     Appendix G Proof of Lemma Let  be a move made by shipping line from the Nash Equilibrium point (1, 1). Using Taylor series expansion, evaluate the shipping line 1’s shift,   , while shipping line remains at current Nash Equilibrium (1, 1). Taylor series expansion gives,  (1   )   1    1 Solving for   1 gives  1   (1   ) .  0    1  lim The profit for shipping line at Nash Equilibrium (1, 1) is : q11  ; q12  ; q21  ; q22  ; Q1  ; Q2  F11  g1q11 Q1  g1 ; F12  g q12 Q2  F21  g1q21 Q1  g1 ; F22  g q22 Q2  F1  g1 ; F2  F  F  8g D1  a    a 12 ; D2  a    K1  K1   K2    1   p  c  1  a  g12 K12   g1  (A.22) The profit for shipping line at 1   , 1 is: q11    ; q12   ; q21  ; q22  ; Q1    ; Q2   102     F11  g1 1      ; F12  g 2  ; F21  g1   ; F22  F1  g1       ; F2  g 2  g2 2   g 22 D a D1  a ;  K 22 K12  g12       1      p  c  1  a  g1 1        K    g 2    p  c  2  a 2  g 2  K2   (A.23) Since it is symmetric port case, assuming 1  2 , K1  K2 , g1  g2  1   (1   )  0    1  lim 1       g  p  c     1     1    1                       1    2 2   2     1    1      lim             4    0          4              ag  g  p  c       22   K   As assumed (1, 1) is not the Nash equilibrium, then we have   ag g  p  c       22    K  K2   88ag 5( p  c   ) The threshold capacity level is found. It gives that (1, 1) is not Nash Equilibrium when the port capacity falls in above condition. 103     Appendix H Proof of Theorem 1 2 Let 1 be a move made by shipping line from a Nash equilibrium point ( , ) and  be a move made by shipping line in order to respond to 1 . The purpose of this marginal analysis is to find the coefficient between shipping lines’ move on BRCs. Using Taylor series expansion, we first study the partial derivative of:  1 1   1       ,        1 ,   2   2  2  We have 1    1  1    1 ,         ,  2 2   g 1  1        g   1   1    pc a   2 K     g 1  1        g   1   1    p  c    a   2 K     g 1  1      g      1  p  c    a   2 K     g 1  1      g   1     p  c    a   2 K       1     1                      g  p  c     1  1     1   1       1   2  2    104       31 31   1  1      1   1    1  1      1   1    g      a   K  31 31     1  1    1   1  1  1    1   1  2  2    Let    1 ,  =1-1 , we have       1  2    1  1   1      1  2    1  1  1  1    1  1     1  1   1  1   2 2 1        1   2 2 1      2   1   2 2 1       2 2 1      Binomial Taylor series give:     2   1     1     2        2   1     1   2           2 2           2 2          7   1  2     7  1   2   The simplified partial derivative is obtained below,  1 1   1      1 ,        1 ,   2   2  2  7    ag    1   1     g  p  c             1        1      1      2   2       K   2  1 5      ag  2          g p c 2 2                          K    Using Taylor series expansion with respect to 1 , we get 105     7    ag    1   1   g p c                       1 1 1    K2    2   2        1 5      2  ag  2   g  p  c      21  1    21  1      21  1    21  1       K          1   1  g  p  c                    1    1    2     2      ag     1          1   1          1     2   2    K       12    g p c 2 1                21  1 1  1      1          2  5   7ag  2   21  1   1   2   21  1 1  1     K         ag   12  g  p  c       g  p  c    K          1   ag  72     1   K    2      12   21ag  ag  52 2            2 2 g p c   31  g  p  c         2    K    K     2 ag   31  1  g  p  c        K     21ag    g  p  c      K      ag  72        1 g p c           K      1 5       g  p  c           ag          K         Remains Then, we have  12  g  p  c      ag K2     1  3  21ag g p c         K2 4     R   The coefficient between moves of shipping lines is obtained:  ag  4 p  c      K  2   1  ag    p  c     21  K   106     Appendix I Searching equilibrium port price starts with port 1’s given pricing strategy. While port fixes its price at a certain value, port gives all possible prices of own and search for the price that returns maximum profit. Referring to Table A.1, port 1’s price is given as an arbitrary value while port is varying the whole range of price values. Once the best of profits is obtained, it is stored in representative variable with the information of profit and the value of price. Table A.1 An example of port price searching logic Port 1’s given price  µ1 µ2 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 Port 1’s profit -0.75 -0.75 -0.75 -0.75 -0.75 -0.75 -0.5544 -0.4786 -0.3986 -0.3133 -0.2227 -0.1273 -0.0289 0.0706 0.1688 0.2639 0.3546 0.4401 0.5203 0.5955 0.666 0.7322 0.7947 0.854 0.9107 Port ‘s profit -1.58273 -1.37454 -1.16636 -0.95818 -0.75 -0.54182 -0.40386 -0.26575 -0.15087 -0.05992 0.00673 0.0495 0.0699 0.07059 0.055 0.02666 -0.01129 -0.05634 -0.10667 -0.16101 -0.21844 -0.27839 -0.34047 -0.40447 -0.47042 Maximum profit Searching the best response price of port  107     Matlab Code for searching Nash equilibrium of port price %fix u1, vary u2% for u1=u1_lp:0.005:u1_up j=j+1; P_max=0; for u2=u2_lp:0.005:u2_up i=i+1; x0 = [0,0]; % Make a starting guess at the solution options = optimset('LargeScale','off'); options=optimset(options,'MaxFunEvals',10000000000000000000); options=optimset(options, 'MaxIter',10000000000000000000); x = fmincon(@(x)objfun(x,p,c,N,b,u1,u2,K,a,g,O,m),x0,[],[],[],[],[],[], . @(x)confuneq(x,p,c,N,b,u1,u2,K,a,g,O,m), options) [f,Q,F_11,F_12,F_21,F_22,F,D]= objfun(x,p,c,N,b,u1,u2,K,a,g,O,m); [ce, ceq] = confuneq(x,p,c,N,b,u1,u2,K,a,g,O,m); % Check the constraint values at x SL1_Profit=(p-c-u1-D(1))*F_11+(p-c-u2-D(2))*F_12; SL2_Profit=(p-c-u1-D(1))*F_21+(p-c-u2-D(2))*F_22; P_1=(u1-O(1))*F(1)-m(1)*K(1); P_2=(u2-O(2))*F(2)-m(2)*K(2); array1(i)=u1;array2(i)=u2;array3(i)=x(1);array4(i)=x(2); array5(i)=F(1);array6(i)=F(2); array7(i)=D(1);array8(i)=D(2); array9(i)=P_1;array10(i)=P_2; if (P_2 > P_max) P_max=P_2; best_r(j)=array2(i) end end end % fix u2, vary u1% k=j; l=i; for u2=u2_lp:0.005:u2_up k=k+1; P1_max=0; for u1=u1_lp:0.005:u1_up l=l+1; x0 = [0,0]; % Make a starting guess at the solution options = optimset('LargeScale','off'); 108     options=optimset(options,'MaxFunEvals',1000000000000000000000); options=optimset(options, 'MaxIter',1000000000000000000000); x = fmincon(@(x)objfun(x,p,c,N,b,u1,u2,K,a,g,O,m),x0,[],[],[],[],[],[], . @(x)confuneq(x,p,c,N,b,u1,u2,K,a,g,O,m), options) [f,Q,F_11,F_12,F_21,F_22,F,D]= objfun(x,p,c,N,b,u1,u2,K,a,g,O,m); [ce, ceq] = confuneq(x,p,c,N,b,u1,u2,K,a,g,O,m); % Check the constraint values at x SL1_Profit=(p-c-u1-D(1))*F_11+(p-c-u2-D(2))*F_12; SL2_Profit=(p-c-u1-D(1))*F_21+(p-c-u2-D(2))*F_22; P_1=(u1-O(1))*F(1)-m(1)*K(1); P_2=(u2-O(2))*F(2)-m(2)*K(2); array1(l)=u1;array2(l)=u2;array3(l)=x(1);array4(l)=x(2); array5(l)=F(1);array6(l)=F(2); array7(l)=D(1);array8(l)=D(2); array9(l)=P_1;array10(l)=P_2; if (P_1 > P1_max) P1_max=P_1; best_br(k)=array1(l); end end end % best response table% t=0; for gp=u1_lp:0.005:u1_up t=t+1; array11(t)=gp; array12(t)=best_br(k-j+t); end   109 [...]... Empirical Research Existing empirical researches have used various models to analyse actual data to draw the insights of competition between or among ports Chou et al.(2003) used SWOT analysis to analyze the competitiveness of major container ports in Asia eastern region, where the major ports are including Hong Kong, Singapore, Busan, Kaohsiung and Shanghai Yang and Yang (2005) attempted to develop an... (2010) studied intra -port competition and examined the possible combinations of coalitions among container terminals The two-stage game has been employed to analyse possible coalitions: in the first stage, three container terminals at Karachi Port decide whether to act 11     individually or to join a coalition; and in the second stage, the resulting coalition plays a non-cooperative game against non-members... port management policy He used a bi-level Stackelberg game to capture the flow of foreign trade containers Lam and Yap (2006) approached regional port competition problem with Cournot simultaneous quantity setting model Their model is used to derive the overall costs of using the terminal, and applied to competition between container terminal operators in Singapore, Port Klang and Tanjung Pelepas Anderson... relocated its major transshipment operations from the Port of Singapore (PSA) to the Port of Tanjung Pelepas (PTP) in Malaysia The impact of this relocation on the regional transshipment market structure was significant Maersk Sealand was then the largest shipping operator in Singapore Its shift to PTP resulted in a decline of approximately 11% in PSA’s overall business In 2001, PSA’s total container throughput... system to evaluate container port competition ability For this, authors combined the empirical survey method and AHP(analytical hierarchy process), and optimal path-searching algorithm An AHP analysis has been used by Yuen et al.(2012) to study port competitiveness Authors approached the problem from the users’ perspective and studied the major container ports in China and neighboring countries Adopting... 2002) A similar event took place in February 2006 between two major transshipment ports in South Korea, Busan and Gwangyang port Maersk, after merging with P&O Nedlloyd, relocated 50-60% of P&O’s transshipment operation that was originally handled in Busan port, to Gwangyang port As a result, Busan port, after 6-month later, lost about 250,000 TEU from its transshipment business with P&O Nedlloyd Two major... mainly on port competitiveness and efficiency, as represented by the cost and the container loading and discharging rates, respectively Similarly, Chou (2007) suggested port manager that if they want to become a transshipment hub port, it will be the most efficient way to attract ocean carriers by increasing the volume of import/export /transshipment containers and decreasing port charge Chang et al.(2008)... qir  1 and N qis  1  qir for r  s It has to be noted that qir is the decision variable which indicates a fraction of transshipment port calls that shipping line i makes at port r Fir is made up of two components: the gateway container and the transshipment container Since this study focuses on transshipment container demand, we assume that the gateway container demand f is constant This assumption... transportation system are likely to prefer a transshipment port that has an extensive and strong network connection Meanwhile, it has to be noted that our LTCD function generates an equal amount of transshipment volume for all shipping lines calling at same port, regardless of the number of port calls that each shipping line has made For our transshipment focus, it is assumed that the transshipment container. .. hinterland access and road congestion in order to observe their impact on ports and port competition (Zhang, 2008; Yuen et al., 2008; Wan et al., 2012; Wan and Zhang, 2013) As noticed, it is only recently that scholars and industry start to pay attention to applying game theory to competition problem in maritime industry; hence, relatively not many studies have tackled the port competition problem by game . A GAME THEORETIC APPROACH TO ANALYZING CONTAINER TRANSSHIPMENT PORT COMPETITION BAE MIN JU NATIONAL UNIVERSITY OF SINGAPORE 2013 A GAME THEORETIC APPROACH. among shipping lines when determining port demand. With a linear transshipment container demand, it is able to achieve analytical properties through a two-stage game approach. Considering a. benefit and congestion- associated effect. Most of all, this thesis can help advance the analysis on ports’ transshipment capabilities and enable the ports to uncover and balance its demand and capacity