Geodesic
Cost optimization for the transport network of Yakutia
Contributions to game theory and management, Tome 10 (2017), pp. 7-16.

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The paper studies game-theoretic approach to the problem of reducing costs of agricultural products transportation on the transport network roads of the Sakha (Yakutia) Republic. Also were proposed a mathematical formulation of problem of players cooperation as the problem of reducing costs for the transport network in the form of cooperative game with characteristic function, as well as a cooperative game with a coalition structure. The solution of such cooperative games, i.e. the optimal cost distribution between players was found in the form of Shapley value.
Keywords: cooperative game, characteristic function, Shapley value. 
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Galina I. Bybyakina; Taisia M. Plekhanova; Ekaterina V. Gromova. Cost optimization for the transport network of Yakutia. Contributions to game theory and management, Tome 10 (2017), pp. 7-16. http://geodesic.mathdoc.fr/item/CGTM_2017_10_a1/

[1] Aumann R. J., Dreze J., “Cooperative games with coalitional structures”, International Journal of Game Theory, 1974, 217–237 | DOI | MR | Zbl

[2] Bellman R. E., Dynamic Programming, Translation From English By Andreeva I. M., Inostrannaya Literatura, M., 1960 | MR

[3] Butenko M. S., “A two-stage optimality principle on a network game with a shock of a special kind”, Control Processes and Stability, Proceedings of the 46th International Scientific Conference of Post-Graduate Students and Students, Publishing House of St. Petersburg State University, Saint Petersburg, 2015, 573–578 (in Russian)

[4] Ergun O. G. Kuyzu, M. W. P. Savelsbergh, “Shipper Collaboration”, Computers Operations Research, 34 (2007), 1551–1560 | DOI | Zbl

[5] Evtyukov S. A., Evtyukov S. S., “Parameters affecting the coupling properties of road surfaces”, Technical and Physical and mathematical sciences, 3 (2013), 75–82 (in Russian)

[6] Karpov M. I., Petrosyan L. A., “Cooperative solutions in communication networks”, Bulletin of St. Petersburg University, 10:4 (2012), 37–45 (in Russian)

[7] Khmelnitskaya A. B., Yanovskaya E. B., “Owen coalitional value without additivity axiom”, Mathematical Methods of Operations Research, 66:2 (2007), 255–261 | DOI | MR | Zbl

[8] Krajewska M. A., Kopfer H., Laporte G., Ropke S., Zaccour G., “Horizontal cooperation among freight carriers: request allocation and profit sharing”, Journal of the Operational Research Society, 59 (2008), 1483–1491 | DOI | Zbl

[9] Mazalov V. V., Mathematical Game Theory and Its Applications, Saint Petersburg, Lan', 2010 (in Russian)

[10] Owen G., Game Theory, Mir, M., 1971 (in Russian) | Zbl

[11] Petrosyan L. A., Zenkevich N. A., Shevkoplyas E. V., Game theory, BHV, Saint Petersburg, 2017 (in Russian)

[12] Route map of the Republic of Sakha (Yakutia), The First Publishing polygraphic Holding, Saint Petersburg, 2009 (in Russian)

[13] Shchegryaev A. N., Zakharov V. V., “Multi-period cooperative vehicle routing games”, Contributions to Game Theory and Management, 7 (2014), 349–359 | MR

[14] Shapley L. S., “A value for n-person games”, Contributions to the Theory of Games II, eds. Luce R. D., Tucker A. W., N.J. Princeton University Press, Princeton, 1953, 307–317 | MR

[15] Von Neumann D., Morgenstern O., The Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944 | MR

[16] Zakharov V. V., Shchegryaev A. N., “Stable cooperation in dynamic problems of transport routing”, Mathematical Game Theory and Its Applications, 4:2 (2012), 39–56 (in Russian) | MR | Zbl

[17] Zenkevich N. A., Zyatchin A. V., “Strong coalitional equilibrium in transport game”, Mathematical Game Theory and Its Applications, 8:1 (2016), 63–79 (in Russian) | MR | Zbl