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Sample average approximation method for stochastic complementarity problems with applications to supply chain supernetworks
Existence of anonymous link tolls for decentralizing an oligopolistic game and the efficiency analysis
1. | School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, China |
2. | Department of Mathematics, Hong Kong Baptist University, Hong Kong |
References:
[1] |
R. P. Agdeppa, N. Yamashita and M. Fukushima, An implicit programming approach for the road pricing problem with nonadditive route costs,, Journal of Industrial and Management Optimization, 4 (2008), 183.
|
[2] |
M. S. Bazarra, H. D. Sherali and C. M. Shetty, "Nonlinear Programming: Theory and Algorithms,", John Wiley and Sons, (1993). Google Scholar |
[3] |
P. Bergendorff, D. W. Hearn and M. V. Ramana, Congestion toll pricing of traffic networks,, in, (1997), 51.
|
[4] |
C. K. Chau and K. M. Sim, The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands,, Operations Research Letters, 31 (2003), 327.
doi: 10.1016/S0167-6377(03)00030-0. |
[5] |
R. Cole, Y. Dodis and T. Roughgarden, Pricing network edges for heterogeneous selfish users,, in, (2003), 521.
|
[6] |
R. Cole, Y. Dodis and T. Roughgarden, How much can tolls help selfish routing,, in, (2003), 98.
doi: 10.1145/779928.779941. |
[7] |
R. Cominetti, J. R. Correa and N. E. Stier-Moses, The impact of oligopolistic competition in networks,, Operation Research, 57 (2009), 1421.
doi: 10.1287/opre.1080.0653. |
[8] |
J. Correa, A. Schulz and N. Stier Moses, Selfish routing in capacitated networks,, Mathematics of Operations Research, 29 (2004), 961.
doi: 10.1287/moor.1040.0098. |
[9] |
J. Correa, A. Schulz and N. Stier Moses, Computational complexity, fairness, and the price of anarchy of the maximum latency problem,, in, (2004), 59.
doi: 10.1007/978-3-540-25960-2_5. |
[10] |
A. Czumaj and B. Vöcking, Tight bounds for worst-case equilibria,, in, (2002), 413.
|
[11] |
S. C. Dafermos and F. T. Sparrow, Optimal resource allocation and toll patterns in user-optimized transport network,, Journal of Transport Economics and Policy, 5 (1971), 198. Google Scholar |
[12] |
S. C. Dafermos, An extended traffic assignment modal with applications to two-way traffic,, Transportation Science, 5 (1971), 366.
doi: 10.1287/trsc.5.4.366. |
[13] |
S. C. Dafermos, The traffic assignment problem for multiclass-user transportation network,, Transportation Science, 6 (1972), 73.
doi: 10.1287/trsc.6.1.73. |
[14] |
S. Dafermos, Toll pattern for multiclass-user transportation network,, Transportation Science, 7 (1973), 211.
doi: 10.1287/trsc.7.3.211. |
[15] |
S. Devarajan, A note on network equilibrium and non-cooperative games,, Transportaion Research B, 15 (1981), 421.
doi: 10.1016/0191-2615(81)90026-6. |
[16] |
R. B. Dial, Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin case,, Transportation Research B, 33 (1999), 189.
doi: 10.1016/S0191-2615(98)00026-5. |
[17] |
R. B. Dial, Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case,, Transportation Research B, 34 (2000), 645.
doi: 10.1016/S0191-2615(99)00046-6. |
[18] |
S. D. Flam and Charles Horvath, Network games; adaptations to Nash-Cournot equilibrium,, Annals of Operations Research, 64 (1996), 179.
doi: 10.1007/BF02187645. |
[19] |
L. Fleischer, K. Jain and M. Mahdain, Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games,, in, (2004).
doi: 10.1109/FOCS.2004.69. |
[20] |
D. R. Han, J. Sun and M. Ang, New bounds for the price of anarchy under nonlinear and asymmetric costs,, Optimization, (). Google Scholar |
[21] |
D. R. Han, H. K. Lo, J. Sun and H. Yang, The toll effect on price of anarchy when costs are nonlinear and asymmetric,, European Journal of Operational Research, 186 (2008), 300.
doi: 10.1016/j.ejor.2007.01.027. |
[22] |
D. R. Han, H. Yang and X. M. Yuan, The efficiency analysis for oligopolistic games when cost functions are nonseparable,, International Journal of Mathematical Modelling and Numerical Optimisation, 1 (2010), 237.
doi: 10.1504/IJMMNO.2010.031751. |
[23] |
P. T. Harker, Multiple equlibrium behaviors on Networks,, Transportation Science, 22 (1988), 39.
doi: 10.1287/trsc.22.1.39. |
[24] |
A. Haurie and P. Marcotte, On the relationship between Nash-Cournot and Wardrop equlibria,, Networks, 15 (1985), 295.
doi: 10.1002/net.3230150303. |
[25] |
D. W. Hearn and M. B. Yildirim, A toll pricing framework for traffic assignment problem with elastic demand,, in, (2002), 135.
|
[26] |
G. Karakostas and S. G. Kolliopoulos, The efficiency of optimal taxes,, in, (2004), 3.
|
[27] |
G. Karakostas and S. Kolliopoulos, Edge pricing of multicommodity networks for heterogeneous users,, in, (2004), 268.
doi: 10.1109/FOCS.2004.26. |
[28] |
E. Koutsoupias and C. H. Papadimitriou, Worst-case equilibria,, in, 1563 (1999), 404.
doi: 10.1007/3-540-49116-3_38. |
[29] |
G. S. Liu and J. Z. Zhang, Decision making of transportation plan, a bilevel transportation problem approach,, Journal of Industrial and Management Optimization, 1 (2005), 305.
|
[30] |
S. Mehrotra and J. Sun, An interior point algorithm for solving smooth convex programs based on Newton's method,, in, 114 (1991), 265.
|
[31] |
M. Netter, Equilibrium and marginal-cost pricing on a road network with several traffic flow types,, in, (1971), 155. Google Scholar |
[32] |
M. Patriksson, "The Traffic Assignment Problem--Models and Methods,", VSP BV, (). Google Scholar |
[33] |
G. Perakis, The "price of anarchy" under nonlinear and asymmetric costs,, Mathematics of Operations Research, 32 (2007), 614.
doi: 10.1287/moor.1070.0258. |
[34] |
R. W. Rosenthal, The network equilibrium problem in integers,, Networks, 3 (1973), 53.
doi: 10.1002/net.3230030104. |
[35] |
T. Roughgarden and E. Tardos, How bad is selfish routing,, Journal of the ACM, 49 (2002), 236.
doi: 10.1145/506147.506153. |
[36] |
T. Roughgarden, "Selfish Routing and the Price of Anarchy,", MIT Press, (2005). Google Scholar |
[37] |
Y. Sheffi, "Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods,", Prentice-Hall, (1985). Google Scholar |
[38] |
M. Shubik, "Game Theory in the Social Sciences: Concepts and Solutions,", Cambridge, (1985). Google Scholar |
[39] |
J. Sun, A convergence analysis for a convex version of Dikin's algorithm,, Annals of Operations Research, 62 (1996), 357.
doi: 10.1007/BF02206823. |
[40] |
C. Swamy, The effectiveness of Stackelberg strategies and tolls for network congestion games,, in, (2007), 1133.
|
[41] |
J. G. Wardrop, Some theoretical aspects of road traffic research,, in, (1952), 325. Google Scholar |
[42] |
H. Yang and H. J. Huang, Principle of marginal-cost pricing: How does it work in a general network?,, Transportation Research A, 32 (1998), 45.
doi: 10.1016/S0965-8564(97)00018-9. |
[43] |
H. Yang and H. J. Huang, The multi-class, multi-criteria traffic network equilibrium and system optimum problem,, Transportation Research B, 38 (2004), 1.
doi: 10.1016/S0191-2615(02)00074-7. |
[44] |
H. Yang and H. J. Huang, "Mathematical and Economic Theory of Road Pricing,", Elsevier, (2005). Google Scholar |
[45] |
H. Yang and X. N. Zhang, Existence of anonymous link tolls for system optimum on networks with mixed equilibrium behaviors,, Transportation Research B, 42 (2008), 99.
doi: 10.1016/j.trb.2007.07.001. |
[46] |
X. N. Zhang, H. Yang and H. J. Huang, Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum,, European Journal of Operational Research, 189 (2008), 146.
doi: 10.1016/j.ejor.2007.05.004. |
show all references
References:
[1] |
R. P. Agdeppa, N. Yamashita and M. Fukushima, An implicit programming approach for the road pricing problem with nonadditive route costs,, Journal of Industrial and Management Optimization, 4 (2008), 183.
|
[2] |
M. S. Bazarra, H. D. Sherali and C. M. Shetty, "Nonlinear Programming: Theory and Algorithms,", John Wiley and Sons, (1993). Google Scholar |
[3] |
P. Bergendorff, D. W. Hearn and M. V. Ramana, Congestion toll pricing of traffic networks,, in, (1997), 51.
|
[4] |
C. K. Chau and K. M. Sim, The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands,, Operations Research Letters, 31 (2003), 327.
doi: 10.1016/S0167-6377(03)00030-0. |
[5] |
R. Cole, Y. Dodis and T. Roughgarden, Pricing network edges for heterogeneous selfish users,, in, (2003), 521.
|
[6] |
R. Cole, Y. Dodis and T. Roughgarden, How much can tolls help selfish routing,, in, (2003), 98.
doi: 10.1145/779928.779941. |
[7] |
R. Cominetti, J. R. Correa and N. E. Stier-Moses, The impact of oligopolistic competition in networks,, Operation Research, 57 (2009), 1421.
doi: 10.1287/opre.1080.0653. |
[8] |
J. Correa, A. Schulz and N. Stier Moses, Selfish routing in capacitated networks,, Mathematics of Operations Research, 29 (2004), 961.
doi: 10.1287/moor.1040.0098. |
[9] |
J. Correa, A. Schulz and N. Stier Moses, Computational complexity, fairness, and the price of anarchy of the maximum latency problem,, in, (2004), 59.
doi: 10.1007/978-3-540-25960-2_5. |
[10] |
A. Czumaj and B. Vöcking, Tight bounds for worst-case equilibria,, in, (2002), 413.
|
[11] |
S. C. Dafermos and F. T. Sparrow, Optimal resource allocation and toll patterns in user-optimized transport network,, Journal of Transport Economics and Policy, 5 (1971), 198. Google Scholar |
[12] |
S. C. Dafermos, An extended traffic assignment modal with applications to two-way traffic,, Transportation Science, 5 (1971), 366.
doi: 10.1287/trsc.5.4.366. |
[13] |
S. C. Dafermos, The traffic assignment problem for multiclass-user transportation network,, Transportation Science, 6 (1972), 73.
doi: 10.1287/trsc.6.1.73. |
[14] |
S. Dafermos, Toll pattern for multiclass-user transportation network,, Transportation Science, 7 (1973), 211.
doi: 10.1287/trsc.7.3.211. |
[15] |
S. Devarajan, A note on network equilibrium and non-cooperative games,, Transportaion Research B, 15 (1981), 421.
doi: 10.1016/0191-2615(81)90026-6. |
[16] |
R. B. Dial, Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin case,, Transportation Research B, 33 (1999), 189.
doi: 10.1016/S0191-2615(98)00026-5. |
[17] |
R. B. Dial, Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case,, Transportation Research B, 34 (2000), 645.
doi: 10.1016/S0191-2615(99)00046-6. |
[18] |
S. D. Flam and Charles Horvath, Network games; adaptations to Nash-Cournot equilibrium,, Annals of Operations Research, 64 (1996), 179.
doi: 10.1007/BF02187645. |
[19] |
L. Fleischer, K. Jain and M. Mahdain, Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games,, in, (2004).
doi: 10.1109/FOCS.2004.69. |
[20] |
D. R. Han, J. Sun and M. Ang, New bounds for the price of anarchy under nonlinear and asymmetric costs,, Optimization, (). Google Scholar |
[21] |
D. R. Han, H. K. Lo, J. Sun and H. Yang, The toll effect on price of anarchy when costs are nonlinear and asymmetric,, European Journal of Operational Research, 186 (2008), 300.
doi: 10.1016/j.ejor.2007.01.027. |
[22] |
D. R. Han, H. Yang and X. M. Yuan, The efficiency analysis for oligopolistic games when cost functions are nonseparable,, International Journal of Mathematical Modelling and Numerical Optimisation, 1 (2010), 237.
doi: 10.1504/IJMMNO.2010.031751. |
[23] |
P. T. Harker, Multiple equlibrium behaviors on Networks,, Transportation Science, 22 (1988), 39.
doi: 10.1287/trsc.22.1.39. |
[24] |
A. Haurie and P. Marcotte, On the relationship between Nash-Cournot and Wardrop equlibria,, Networks, 15 (1985), 295.
doi: 10.1002/net.3230150303. |
[25] |
D. W. Hearn and M. B. Yildirim, A toll pricing framework for traffic assignment problem with elastic demand,, in, (2002), 135.
|
[26] |
G. Karakostas and S. G. Kolliopoulos, The efficiency of optimal taxes,, in, (2004), 3.
|
[27] |
G. Karakostas and S. Kolliopoulos, Edge pricing of multicommodity networks for heterogeneous users,, in, (2004), 268.
doi: 10.1109/FOCS.2004.26. |
[28] |
E. Koutsoupias and C. H. Papadimitriou, Worst-case equilibria,, in, 1563 (1999), 404.
doi: 10.1007/3-540-49116-3_38. |
[29] |
G. S. Liu and J. Z. Zhang, Decision making of transportation plan, a bilevel transportation problem approach,, Journal of Industrial and Management Optimization, 1 (2005), 305.
|
[30] |
S. Mehrotra and J. Sun, An interior point algorithm for solving smooth convex programs based on Newton's method,, in, 114 (1991), 265.
|
[31] |
M. Netter, Equilibrium and marginal-cost pricing on a road network with several traffic flow types,, in, (1971), 155. Google Scholar |
[32] |
M. Patriksson, "The Traffic Assignment Problem--Models and Methods,", VSP BV, (). Google Scholar |
[33] |
G. Perakis, The "price of anarchy" under nonlinear and asymmetric costs,, Mathematics of Operations Research, 32 (2007), 614.
doi: 10.1287/moor.1070.0258. |
[34] |
R. W. Rosenthal, The network equilibrium problem in integers,, Networks, 3 (1973), 53.
doi: 10.1002/net.3230030104. |
[35] |
T. Roughgarden and E. Tardos, How bad is selfish routing,, Journal of the ACM, 49 (2002), 236.
doi: 10.1145/506147.506153. |
[36] |
T. Roughgarden, "Selfish Routing and the Price of Anarchy,", MIT Press, (2005). Google Scholar |
[37] |
Y. Sheffi, "Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods,", Prentice-Hall, (1985). Google Scholar |
[38] |
M. Shubik, "Game Theory in the Social Sciences: Concepts and Solutions,", Cambridge, (1985). Google Scholar |
[39] |
J. Sun, A convergence analysis for a convex version of Dikin's algorithm,, Annals of Operations Research, 62 (1996), 357.
doi: 10.1007/BF02206823. |
[40] |
C. Swamy, The effectiveness of Stackelberg strategies and tolls for network congestion games,, in, (2007), 1133.
|
[41] |
J. G. Wardrop, Some theoretical aspects of road traffic research,, in, (1952), 325. Google Scholar |
[42] |
H. Yang and H. J. Huang, Principle of marginal-cost pricing: How does it work in a general network?,, Transportation Research A, 32 (1998), 45.
doi: 10.1016/S0965-8564(97)00018-9. |
[43] |
H. Yang and H. J. Huang, The multi-class, multi-criteria traffic network equilibrium and system optimum problem,, Transportation Research B, 38 (2004), 1.
doi: 10.1016/S0191-2615(02)00074-7. |
[44] |
H. Yang and H. J. Huang, "Mathematical and Economic Theory of Road Pricing,", Elsevier, (2005). Google Scholar |
[45] |
H. Yang and X. N. Zhang, Existence of anonymous link tolls for system optimum on networks with mixed equilibrium behaviors,, Transportation Research B, 42 (2008), 99.
doi: 10.1016/j.trb.2007.07.001. |
[46] |
X. N. Zhang, H. Yang and H. J. Huang, Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum,, European Journal of Operational Research, 189 (2008), 146.
doi: 10.1016/j.ejor.2007.05.004. |
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