Game Theoretic Models for Competition in Public Transit Services

Eddie Y. S. Chan, Janny M. Y. Leung

2015

Abstract

As metropolitan areas grow, the need to travel by the populace has increased the burden on the transport systems, leading to increased traffic congestion and environmental concerns. In this paper, we discuss some game-theoretic models that can be used to investigate the competitive situation when several service providers offer public transit services. The competition among the operators can be modelled by a class of games called potential games, and we discuss mathematical programmes that can be used to find the Nash equilibria for these games. By examining the equilibrium solutions, we can investigate the relative merits and tradeoffs for different structures of the transit networks, and the interplay between the services offered and the overall ridership of the system.

References

  1. Bell, M. G. H. (2000). A game theory approach to measuring the performance reliability of transport networks, Transportation Research: Part B, 34, 533-545.
  2. Castelli, L., G. Longo, R. Pesenti and W. Ukovich (2004). Two-player noncooperative games over a freight transportation network, Transportation Science, 38(2), 149-159.
  3. Chen, O. J. and M.E. Ben-Akiva (1998). Game-theoretic formulations of interaction between dynamic traffic control and dynamic traffic assignment, In Transportation Research Record: Journal of the Transportation Research Board, No. 1617, National Research Council, Washington, DC., pp. 179-188.
  4. Fernandez, E. and P. Marcotte (1992) Operators-Users Equilibrium Model in a Partially Regulated Transit System, Transportation Science, 26(2): 93-105.
  5. Fernandez L., J. E., P. Marcotte, S. Mondschein, J. Vera and A. Weintraub (1993). Solution Approaches to the Bus Operator Problem, Transportation Research, Part B, 27B(1): 1-11.
  6. Fisk, C. S. (1984). Game theory and transportation systems modelling, Transportation Research B, 18B (4/5), 301-313.
  7. James, T. (1998). A game theoretic model of road usage, Proceedings of the 3rd IMA International Conference on Mathematics in Transport and Control, 401-409.
  8. Hollander, Y. and J. N. Prashker (2006). The applicability of non-cooperative game theory in transport analysis, Transportation, 33, 481-496.
  9. Levinson, D. (2005). Micro-foundations of congestion and pricing: a game theory perspective, Transportation Research: Part A, 39, 691-704.
  10. Monderer, D. and L. S. Shapley (1996). Potential Games, Games and Economic Behaviour, 14, 124-143.
  11. Nash, J. (1950). Equilibrium points in n-person games, Proceedings of the National Academy of Sciences 36(1):48-49.
  12. Patriksson, M. and M. Labbé (eds.) (2004) Transportation Planning: State of the Art, Kluwer Academic Publishers.
  13. Pedersen, P. A. (2003). Moral Hazard in traffic games, Journal of Transport Economic Policy 37 (1), 47-68.
  14. Reyniers, D. (1992). Crowding levels and fare classes in public transport, In Griffiths, J. (ed.) Mathematics in Transport planning and Control, Oxford University Press, pp. 319-327.
  15. Rosenthal, R. W. (1973). A class of games possessing pure-strategy Nash equilibria, International Journal of Game Theory, 2, 65-67.
  16. Van Zuylen, H.J. and H. Taale (2004) . Urban network with ring roads: a two-level three player game, In: Proceedings of the 83rd Annual Meeting of the Transportation Research Board, Washington DC.
  17. von Stackelberg, H. F. (1934). Marktform und Gleichgewicht (Market and Equilibrium), Vienna.
  18. Wardrop. J. G. (1952). Some theoretical aspects of road traffic research”, Proceedings of the Institution of Civil Engineers, Part II, 1, 325-378.
Download


Paper Citation


in Harvard Style

Y. S. Chan E. and M. Y. Leung J. (2015). Game Theoretic Models for Competition in Public Transit Services . In Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-075-8, pages 133-139. DOI: 10.5220/0005218201330139


in Bibtex Style

@conference{icores15,
author={Eddie Y. S. Chan and Janny M. Y. Leung},
title={Game Theoretic Models for Competition in Public Transit Services},
booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2015},
pages={133-139},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005218201330139},
isbn={978-989-758-075-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Game Theoretic Models for Competition in Public Transit Services
SN - 978-989-758-075-8
AU - Y. S. Chan E.
AU - M. Y. Leung J.
PY - 2015
SP - 133
EP - 139
DO - 10.5220/0005218201330139