Cooperation in Transportation Game

Authors

  • Anna V. Melnik Saint Petersburg State University

Abstract

We consider a game-theoretic model of competition and cooperation of transport companies on a graph. First, a non-cooperative n-person game which is related to the queueing system M= M= n is considered. There are n competing transport companies which serve the stream of passengers with exponential distribution of time with parameters µ ( i), i = 1,2,..., n respectively on the graph of routes. The stream of passengers from a stop k to another stop t forms the Poisson process with intensity λ kt . The transport companies announce the prices for the service on each route and the passengers choose the service with minimal costs. The incoming stream λ kt is divided into n Poisson flows with intensities λ ( i) kt , i = 1,2,..., n. The problem of pricing for each player in the competition and cooperation is solved.

Keywords:

Duopoly, equilibrium prices, queueing system

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References

Hotelling, H. (1929). Stability in Competition. Economic Journal, 39, 41–57.

D’Aspremont, C., Gabszewicz, J., Thisse, J.-F. (1979). On Hotelling’s Stability in Competition. Econometrica, 47, 1145–1150.

Altman, E. and N. Shimkin (1998). Individual equilibrium and learning in processor sharing systems. Operations Research, 46(6), 776–784.

Hassin, R. and M. Haviv (2003). To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Springer, US.

Chen, H. and Y. Wan (2005). Capacity competition of make-to-order firms. Operations Research Letters, 33(2), 187–194.

Levhari, D. and I. Luski (1978). Duopoly pricing and waiting lines. European Economic Review, 11, 17–35.

Luski, I. (1976). On partial equilibrium in a queueing system with two services. The Review of Economic Studies, 43, 519–525.

Taha, H. A. (2011). Operations Research: An Introduction, ; 9th. Edition, Prentice Hall.

Mazalova, A. V. (2013). Duopoly in queueing system. In: Vestnik St. Petersburg University, 10(4), 32–41 (in Russian).

Melnik, A. V. (2014). Equilibrium in transportation game. Mathematical Game Theory and its Applications, 6(1), 41–55 (in Russian).

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Published

2022-05-24

How to Cite

V. Melnik, A. (2022). Cooperation in Transportation Game. Contributions to Game Theory and Management, 8. Retrieved from https://gametheory.spbu.ru/article/view/13460

Issue

Vol. 8 (2015)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.