Geodesic
Cooperation in transportation game
Contributions to game theory and management, Tome 8 (2015), pp. 223-230.

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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 $\mu^{(i)}$, $i=1, 2,\dots,n$ respectively on the graph of routes. The stream of passengers from a stop $k$ to another stop $t$ forms the Poisson process with intensity $\lambda_{kt}$. The transport companies announce the prices for the service on each route and the passengers choose the service with minimal costs. The incoming stream $\lambda_{kt}$ is divided into $n$ Poisson flows with intensities $\lambda_{kt}^{(i)}$, $i=1, 2,\dots,n$. The problem of pricing for each player in the competition and cooperation is solved.
Keywords: Duopoly, equilibrium prices, queueing system. 
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     author = {Anna V. Melnik},
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Anna V. Melnik. Cooperation in transportation game. Contributions to game theory and management, Tome 8 (2015), pp. 223-230. http://geodesic.mathdoc.fr/item/CGTM_2015_8_a16/

[1] Hotelling H., “Stability in Competition”, Economic Journal, 39 (1929), 41–57

[2] D'Aspremont C., Gabszewicz J., Thisse J.-F., “On Hotelling's “Stability in Competition””, Econometrica, 47 (1979), 1145–1150 | MR | Zbl

[3] Altman E., Shimkin N., “Individual equilibrium and learning in processor sharing systems”, Operations Research, 46:6 (1998), 776–784 | MR | Zbl

[4] Hassin R., Haviv M., To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems, Springer, US, 2003 | MR

[5] Chen H., Wan Y., “Capacity competition of make-to-order firms”, Operations Research Letters, 33:2 (2005), 187–194 | MR | Zbl

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

[7] Luski I., “On partial equilibrium in a queueing system with two services”, The Review of Economic Studies, 43 (1976), 519–525 | Zbl

[8] Taha H. A., Operations Research: An Introduction, 9th. edition, Prentice Hall, 2011 | MR

[9] Mazalova A. V., “Duopoly in queueing system”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 4, 32–41 (in Russian)

[10] Melnik A. V., “Equilibrium in transportation game”, Mathematical Game Theory and its Applications, 6:1 (2014), 41–55 (in Russian) | Zbl