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Cooperative strong equilibrium in vehicle routing game

  • Mathematical game Theory and Applications
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Abstract

In this paper, a game-theoretic approach is considered for the vehicle routing problem with many distributors. Each customer is characterized by demand and wholesale price. Within such a statement, some customers are possibly not visited by a distributor in the optimal solution. This problem is called the vehicle routing game (VRG) in coordinated strategies. A procedure for determining a strong equilibrium in the VRG is proposed which is stable against coalitional deviations. According to the procedure, the optimization problem is solved iteratively for each distributor. The set of unvisited customers is reduced at each step. The existence of two classes of strong equilibria is proved. The concept of a cooperative strong equilibrium is presented. All results are illustrated by numerical examples.

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Authors and Affiliations

  1. Graduate School of Management, Department of Operations Management, St. Petersburg State University, St. Petersburg, Russia

    N. A. Zenkevich & A. V. Zyatchin

  2. Deutsche Bahn and Russian Railways Center for International Logistics and Supply Chain Management, St. Petersburg, Russia

    A. V. Zyatchin

Authors
  1. N. A. Zenkevich
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  2. A. V. Zyatchin
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Correspondence to N. A. Zenkevich.

Additional information

Original Russian Text © N.A. Zenkevich, A.V. Zyatchin, 2013, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2013, No. 3, pp. 3–26.

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Zenkevich, N.A., Zyatchin, A.V. Cooperative strong equilibrium in vehicle routing game. Autom Remote Control 77, 1867–1881 (2016). https://doi.org/10.1134/S0005117916100131

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  • DOI: https://doi.org/10.1134/S0005117916100131

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