Cost Optimization for the Transport Network of Yakutia

Authors

  • Galina I. Bubyakina Saint Petersburg State University
  • Taisia M. Plekhanova Saint Petersburg State University
  • Ekaterina V. Gromova Saint Petersburg State University

Abstract

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

Downloads

Download data is not yet available.

References

Aumann, R. J. and J. Dreze (1974). Cooperative games with coalitional structures. International Journal of Game Theory, 217–237.

Bellman, R. E. (1960). Dynamic Programming, Translation From English By Andreeva, I. M. Inostrannaya Literatura: Moscow (in Russian).

Butenko, M. S. (2015). A two-stage optimality principle on a network game with a shock of a special kind. In: 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, 573–578 (in Russian).

Ergun O. G. Kuyzu and M. W. P. Savelsbergh (2007). Shipper Collaboration. Computers & Operations Research, 34, 1551–1560.

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

Karpov, M. I. and L. A. Petrosyan (2012). Cooperative solutions in communication networks. Bulletin of St. Petersburg University, 10(4), 37–45 (in Russian).

Khmelnitskaya A. B. and E. B. Yanovskaya (2007). Owen coalitional value without additivity axiom. Mathematical Methods of Operations Research, 66(2), 255–261.

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

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

Owen, G. (1971). Game Theory, Mir: Moscow (in Russian).

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

Route map of the Republic of Sakha (Yakutia) (2009). The First Publishing polygraphic Holding: Saint Petersburg (in Russian).

Shchegryaev, A. N. and V. V. Zakharov (2014). Multi-period cooperative vehicle routing games. Contributions to Game Theory and Management, 7, 349–359.

Shapley, L. S. (1953). A value for n-person games. Contributions to the Theory of Games II ., eds Luce R.D. and Tucker A.W. – Princeton: N.J. Princeton University Press, 307–317.

Von Neumann, D. and O. Morgenstern (1944). The Theory of Games and Economic Behavior.– Princeton: Princeton University Press.

Zakharov, V. V. and A. N. Shchegryaev (2012). Stable cooperation in dynamic problems of transport routing. Mathematical Game Theory and Its Applications, 4(2), 39–56 (in Russian).

Zenkevich, N. A. and A. V. Zyatchin (2016). Strong coalitional equilibrium in transport game. Mathematical Game Theory and Its Applications, 8(1), 63–79 (in Russian).

Downloads

Published

2022-04-17

How to Cite

Bubyakina, G. I., Plekhanova, T. M., & Gromova, E. V. . (2022). Cost Optimization for the Transport Network of Yakutia. Contributions to Game Theory and Management, 10. Retrieved from https://gametheory.spbu.ru/article/view/13248

Issue

Vol. 10 (2017)

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.