Competition between two cities using cordon tolls: An exploration of response surfaces and possibilities for collusion

Transportmetrica A: Transport Science

Volumn 9, Issue 10, 2013, Pages 896-924

  Koh, A ^a   Shepherd, S P ^a   Watling, D ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

competition; Nash Equilibrium; networks; pricing; tolls

Indexed keywords

ELASTICITY OF DEMAND; EQUILIBRIUM PROBLEM WITH EQUILIBRIUM CONSTRAINT (EPEC); GRID SEARCH; HIERARCHICAL STRUCTURES; NASH EQUILIBRIA; NASH SOLUTIONS; RESPONSE SURFACE; TOLLS;

COMPETITION; COSTS; GAME THEORY; NETWORKS (CIRCUITS);

SURFACE PROPERTIES;

EID: 84886406530     PISSN: 23249935     EISSN: 23249943     Source Type: Journal    
DOI: 10.1080/18128602.2012.673033     Document Type: Article

References (39)

1. Bazaraa, M.S., Sherali, H.D., and Shetty, C.M. 2006. Nonlinear programming: theory and algorithms. Hoboken, NJ: Wiley.
2. Červinka, M. 2008, Hierarchical structures in equilibrium problems. Doctoral thesis. Charles University, Prague, Czech Republic
3. Chen, Y., and Florian, M. 1995). The nonlinear bilevel programming problem: formulations, regularity and optimality conditions. Optimization, 32 (3), 193-209.
4. De Borger, B., Dunkerly, F., and Proost, S. 2007). Strategic investment and pricing decisions in a congested transport corridor. Journal of Urban Economics, 62 (2), 294-316.
5. De Palma, A., and Lindsey, R. 2000). Private roads: competition under various ownership regimes. Annals of Regional Science, 34 (1), 13-35.
6. Department for Transport. 2005. The Transport Innovation Fund. Available at: http://webarchive.nationalarchives.gov.uk/20090104005813/http://www.dft.gov.uk/pgr/regional/tif/thetransportinnovationfund [accessed 31 March 2011]
7. Gühnemann, A., et al,. 2011). Implications of interdependencies between charging strategies of local authorities for the protection of sensitive areas in the Trans-Pennine Corridor. Utilities Policy, 19 (1), 42-52.
8. Harker, P.T. 1984). A variational inequality approach for the determination of oligopolistic market equilibrium. Mathematical Programming, 30 (1), 105-111.
9. Hu, X., and Ralph, D. 2007). Using EPECs to model bilevel games in restructured electricity markets with locational prices. Operations Research, 55 (5), 809-827.
10. Koh, A. 2008). Nash Equilibrium, collusion in games and co-evolutionary particle swarm algorithm. In: B. Filipič and J. Šilc eds. Bioinspired optimization methods and their applications. Slovenia: Institut Jožef Stefan, 19-28
11. Koh, A., and Shepherd, S.P. 2010). Tolling, collustion and equilibrium problems with equilibrium constraints. Trasporti Europei/European Transport, 44, 3-22.
12. Koh, A., Shepherd, S.P., and Sumalee, A. 2009). Second best toll and capacity optimisation in networks: solution algorithm and policy implications. Transportation, 36 (2), 147-165.
13. Lawphongpanich, S., and Hearn, D. 2004). An MPEC approach to second best toll pricing. Mathematical Programming B, 101 (1), 33-55.
14. Levinson, D. 2001). Why states toll: an empirical model of finance choice. Journal of Transport Economics and Policy, 35 (2), 223-238.
15. Luo, Z.Q., Pang, J.S., Ralph., D. 1996. Mathematical programs with equilibrium constraints. Cambridge, England: Cambridge University Press.
16. Mordukhovich, B.S. 2005). Optimization and equilibrium problems with equilibrium constraints. OMEGA International Journal of Management Science, 33 (5), 379-384.
17. Morton, K.W., and Mayers, D.F. 2005. Numerical solution of partial differential equations, an introduction. Cambridge, England: Cambridge University Press.
18. Nash, J. 1950. Equilibrium points in N-person games. Proceedings of the National Academy of Science USA, 36 (1), 48-49
19. Proost, S., and Sen, A. 2006). Urban transport pricing reform with two levels of government: a case study of Brussels. Transport Policy, 13 (2), 127-139.
20. Proost, S., Van Dender, K. 2001). Methodology and structure of the urban model. In: B. De Borger and S. Proost eds. Reforming transport pricing in the European Union- a modelling approach. Cheltenham, England: Edward Elgar, 65-92.
21. Rapoport, A. and Chammah, A., 1970. Prisoner s dlemma: a study in conflict and cooperation. Ann Arbor: University of Michigan Press
22. Saunders, J. 2005). The rise and fall of Edinburgh's congestion charging plans. Proceedings of the Institution of Civil Engineers, Transport, 158 (4), 193-201.
23. Scheel, H., and Scholtes, S. 1995). Mathematical programs with equilibrium constraints: stationarity, optimality and sensitivity. Mathematics of Operations Research, 25 (1), 1-22.
24. Shepherd, S. P. and Sumalee, A. 2004. A Genetic Algorithm based approach to optimal toll level and location problems, Networks and Spatial Economics, 4(2), 161-179
25. Shepherd, S.P., May, A.D., and Koh, A. 2008). How to design effective road pricing cordons. Proceedings of the Institution of Civil Engineers, Transport, 161 (3), 155-165.
26. Son, Y.S., and Baldick, R. 2004). Hybrid coevolutionary programming for Nash Equilibrium search in games with local optima. IEEE Transactions on Evolutionary Computation, 8 (4), 305-315.
27. Stiglitz, J. 2000. Economics of the public sector. London: WW Norton.
28. Sumalee, A., May, A.D., and Shepherd, S.P. 2005). Comparison of judgmental and optimal road pricing cordons. Transport Policy, 12 (5), 384-390.
29. Transport Select Committee. 2006. The draft Local Transport Bill and the Transport Innovation Fund: Government response to the Committee's ninth report of session 2006-07. In: 13th Special Report of the House of Commons Transport Select Committee, HC1056. Available at: http://www.publications.parliament.uk/pa/cm200607/cmselect/cmtran/1053/105302.htm [accessed 31 March 2011]
30. Ubbels, B., and Verhoef, E.T. 2008). Governmental competition in road charging and capacity choice. Regional Science and Urban Economics, 38 (2), 174-190.
31. Verhoef, E.T., Nijkamp, P., and Rietveld, P. 1996). Second-best congestion pricing: the case of an untolled alternative. Journal of Urban Economics, 40 (3), 279-302.
32. Walters, A. 1961). Theory and measurement of private & social cost of highway congestion. Econometrica, 29 (4), 676-699.
33. Wardrop, J.G. 1952). Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, Part II, 1 (1), 325-378.
34. Xiao, F., Yang, H., and Han, D. 2007). Competition and efficiency of private toll roads. Transportation Research B, 3 (41), 292-308.
35. Yang, H. and Woo, K.K. 2000. Competition and equilibria of private toll roads in a traffic network. Transportation Research Record, 1733, 15-22
36. Yang, H., Xiao, F., and Huang, H. 2009). Private road competition and equilibrium with traffic equilibrium constraints. Journal of Advanced Transportation, 43 (1), 21-45.
37. Ye, J.J., and Zhu, Q.J. 2003). Multiobjective optimization problem with variational inequality constraints. Mathematical Programming, 96 (1), 139-160.
38. Zhang, L., and Levinson, D. 2005). Road pricing on autonomous links. Transportation Research Record, 1932, 147-155.
39. Zhang, X.N., et al. 2011). Competitive, cooperative and Stackelberg congestion pricing for multiple regions in transportation networks. Transportmetrica, 7 (4), 297-320.