Efficiency Loss of Mixed Equilibrium Associated with Altruistic Users and Logit-based Stochastic Users in Transportation Network

  • Xiao-Jun Yu Guizhou University of Finance and Economics, Guiyang,Guizhou 550004, China
  • Chun-Hua Fang Hunan Institute of Science and Technology, xueyang, Hunan 414006, China
Keywords: efficiency loss, mixed equilibrium, variational inequality, system optimum, demand ratio,

Abstract

The efficiency loss of mixed equilibrium associated with two categories of users is investigated in this paper. The first category of users are altruistic users (AU) who have the same altruism coefficient and try to minimize their own perceived cost that assumed to be a linear combination of selfish com­ponent and altruistic component. The second category of us­ers are Logit-based stochastic users (LSU) who choose the route according to the Logit-based stochastic user equilib­rium (SUE) principle. The variational inequality (VI) model is used to formulate the mixed route choice behaviours associ­ated with AU and LSU. The efficiency loss caused by the two categories of users is analytically derived and the relations to some network parameters are discussed. The numerical tests validate our analytical results. Our result takes the re­sults in the existing literature as its special cases.

Author Biographies

Xiao-Jun Yu, Guizhou University of Finance and Economics, Guiyang,Guizhou 550004, China

a:School of Mathematics and Statistics

b: Guizhou Key Laboratory of Economic System Simulation

Chun-Hua Fang, Hunan Institute of Science and Technology, xueyang, Hunan 414006, China
School of Mathematics

References

Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria, the 16th Symposium on Theoretical Aspects of Computer Science, LNCS 1563, 1999

Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM, Vol. 49, No. 2, 2002, pp. 236-259

Correa, J. R., Schulz, A. S., Stier-Moses, N. S.: On the inefficiency of equilibria in congestion games, 11th Conference on Integer Programming and Combinatorial optimization, Berlin, Germany, 2005

Chau, C. K., Sim, K. M.: The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands, Operations Research Letter, Vol. 31, No. 5, 2003, pp. 327–334

Correa, J. R., Schulz, A. S., Stier-Moses, N. S.: Selfish routing in capacitated networks, Mathematics of Operations Research, Vol. 29, No. 4, 2004, pp. 961–976.

Guo, X. L., Yang, H., Liu, T. L.: Bounding the inefficiency of logit-based stochastic user equilibrium, European Journal of Operational Research, Vol. 201, No. 2, 2010, pp. 463-469

Liu, T. L., Chen, J., Huang, H. J.: Existence and efficiency of oligopoly equilibrium under toll and capacity competition, Transportation Research Part E, Vol. 47, No. 6, 2011, pp. 908-919

Huang, H. J., Ouyang, L. Q., Liu, T. L.: Upper bounds of efficiency loss for equilibrium behavior in traffic networks, Journal of Beijing University of Aeronautics and Astronautics, Vol. 32, No. 10, 2006, pp. 1215–1219

Roughgarden, T., Tardos, E.: Bounding the inefficiency of equilibria in non-atomic congestion games, Games and Economic Behavior, Vol. 47, No. 2, 2004, pp. 389–403

Haurie, A., Marcotte, P.: On the relationship between Nash-Cournot and Wardrop equilibria, Networks, Vol. 15, No. 3, 1985, pp. 295–308

Harker, P. T.: Multiple equilibrium behaviors on networks, Transportation Science, Vol. 22, No. 1, 1988, pp. 39–46

Yang, H., Zhang, X. N.: Existence of anonymous link tolls for system optimum on networks with mixed equilibrium behaviors, Transportation Research Part B, Vol. 42, No. 2, 2008, pp. 99-112

Liu, T. L., Ouyang, L. Q., Huang, H. J.: Mixed travel behavior in networks with ATIS and upper bound of efficiency loss, Systems Engineering – Theory & Practice, Vol. 27, No. 4, 2007, pp. 154–159

Guo, X. L., Yang., H.: User heterogeneity and bi-criteria system optimum, Transportation Research Part B, Vol. 43, No. 4, 2009, pp. 379-390

Yu, X. J., Huang, H. J.: Efficiency loss of mixed equilibrium behaviors with polynomial cost functions, Promet Traffic & Transportation, Vol. 22, No. 5, 2010, pp. 325-331

Karakostas, G., Kim, T., Viglas, A., Xia,H.: On the degradation of performance for traffic networks with oblivious users, Transportation Research Part B, Vol. 45, No. 2, 2011, pp. 364-371

Ledyard, J.: Public goods: A survey of experimental research, In J. Kagel and A. Roth, editors, Handbook of experimental economics, Princeton University Press, 1997

Levine,D. K.: Modeling altruism and spitefulness in experiments, Review of Economic Dynamics, Vol. l, No. 3, 1998, pp. 593–622

Chen, P. A., Kempe, D.: Altruism, selfishness, and spite in traffic routing., 9th ACM conference on Electronic commerce. Chicago, Illinois, USA, 2008

Huang, H. J.: Urban Transportation Network Equilibrium Analysis: Theory and Practice, Beijing, China: China Communications Press, 1994

Kinderlehrer, D., Stampacchia, G.: An introduction to variational inequalities and their applications, Academic Press, New York, 1986

Yu, X. J., Huang, H. J.: Inefficiency of the Uniform Altruism Traffic Assignment, the Second International Conference on Intelligent Computation Technology and Automation (ICICTA 09), Zhangjiajie, China, 2009

Published
2014-02-28
How to Cite
1.
Yu X-J, Fang C-H. Efficiency Loss of Mixed Equilibrium Associated with Altruistic Users and Logit-based Stochastic Users in Transportation Network. Promet - Traffic&Transportation. 2014;26(1):45-1. DOI: 10.7307/ptt.v26i1.718
Section
Articles