zbMATH — the first resource for mathematics

An equilibrium model for urban transit assignment based on game theory. (English) Zbl 1121.90029
Summary: The urban public transport system is portrayed as a special commodity market where the passenger is consumer, the transit operator is producer and the special goods is the service of the passenger’s trip. The generalized Nash equilibrium game is applied to describe how passengers adjust their route choices and trip modes. We present a market equilibrium model for urban public transport system as a series of mathematical programmings and equations, which is to describe both the competitions among different transit operators and the interactive influences among passengers. The proposed model can simultaneously predict how passengers choose their optimal routes and trip modes. An algorithm is designed to obtain the equilibrium solution. Finally, a simple numerical example is given and some conclusions are drawn.

90B10 Deterministic network models in operations research
91A40 Other game-theoretic models
Full Text: DOI
[1] Arrow, K.J.; Intriligator, M.D., Handbook of mathematical economics, vol. II, (1982), North-Holland Publishing Company New York, pp. 697-791
[2] Codenotti, B., Pemmaraju, S., Varadarajan, K., 2004. Algorithms column: The computation of market equilibrium, ACM SIGACT News, November 10. Available from: <http://www.cs.uchicago.edu/ codenott/SIGACT_NEWS_LAST.pdf>.
[3] Daniele, P.; Maugeri, A., Variational inequalities and discrete and continuum models of network equilibrium problems, Mathematical and computer modelling, 35, 689-708, (2002) · Zbl 0994.90033
[4] Gao, Z.Y.; Song, Y.F., A reserve capacity model of optimal signal control with user-equilibrium route choice, Transportation research part B, 36, 313-323, (2002)
[5] Gao, Z.Y.; Sun, H.J.; Shan, L.L., A continuous equilibrium network design model and algorithm for transit system, Transportation research part B, 38, 235-250, (2004)
[6] Gao, Z.Y.; Wu, J.J.; Sun, H.J., Solution algorithm for the bi-level discrete network design problem, Transportation research part B, 39, 479-495, (2005)
[7] Harker, P.T., Generalized Nash games and quasi-variational inequalities, European journal of operational research, 54, 1, 81-94, (1991) · Zbl 0754.90070
[8] Hawkins, R.J.; Frieden, B.R., Fisher information and equilibrium distributions in econophysics, Physics letters A, 322, 126-130, (2004) · Zbl 1118.81362
[9] Huang, T., A course of game theory and its applications (in Chinese), (2004), Capital University of Economics and Business Press Beijing
[10] Huang, G.Y.; Zhou, J., Fare competition between highway and public transport (in Chinese), Journal of southeast university (natural science edition), 34, 2, 268-273, (2004)
[11] Ichiishi, T., Game theory for economic analysis, (1983), Academic Press New York · Zbl 0522.90104
[12] Jain, K., Vazirani, V.V., Ye, Y.Y., 2005. Market equilibria for homothetic, quasi-concave utilities and economies of scale in production. Technical Paper, Management, Science and Engineering, Stanford, CA. Available from: <http://www.stanford.edu/ yyye/soda2.pdf>. · Zbl 1297.91107
[13] Li, J.; Fan, B.Q., Public transport operation scale analysis with game theory (in Chinese), Urban public transport, 2, 9-10, (2003)
[14] Lourdes, Z., A network equilibrium model for oligopolistic competition in city bus services, Transportation research part B, 32, 413-422, (1998)
[15] Nagurney, A., A multiclass, multicriteria traffic network equilibrium model, Mathematical and computer modelling, 32, 393-411, (2000) · Zbl 0965.90003
[16] Nagurney, A.; Dong, J., A multiclass, multicriteria traffic network equilibrium model with elastic demand, Transportation research part B, 36, 445-469, (2002)
[17] Ogaki, M., Aggregation under complete markets, Review of economic dynamics, 6, 977-986, (2003)
[18] Pang, J.S.; Yang, J.M., Parallel newton’s method for computing the nonlinear complementarity problems, Mathematical programming, 42, 3, 407-420, (1998)
[19] Patriksson, M.; Rockafellar, R.T., A mathematical model and descent algorithm for bilevel traffic management, Transportation science, 36, 3, 271-291, (2002) · Zbl 1134.90319
[20] Samuelson, L., Evolutionary games and equilibrium selection, (1997), The MIT Press Cambridge · Zbl 0953.91500
[21] Xiao, B.C.; Peng, J., A study of passenger transport pricing strategy for china’s civil aviation industry (in Chinese), Journal of sichuan university (social science edition), 6, 10-15, (2002)
[22] Yang, S.L.; Zhang, X., A game theoretical analysis of marketable air fare (in Chinese), Commercial research, 259, 10-13, (2002)
[23] Zhang, W.Y., Game theory and information economics (in Chinese), (1996), Shanghai People’s Press Shanghai
[24] Zhou, J.; Xu, Y., Generalized Nash managing game model for transit network (in Chinese), Journal of system engineering, 16, 4, 261-266, (2001)
[25] Zhou, J.; Lam, W.H.K.; Heydecker, B.G., The generalized Nash equilibrium model for oligopolistic transit market with elastic demand, Transportation research part B, 39, 519-544, (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.