Strong coalitional equilibrium in a transportation game
- Authors: Zenkevich N.A.1, Zyatchin A.V.1
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Affiliations:
- Graduate School of Management, Department of Operations Management
- Issue: Vol 78, No 10 (2017)
- Pages: 1909-1919
- Section: Mathematical Game Theory and Applications
- URL: https://journals.rcsi.science/0005-1179/article/view/150710
- DOI: https://doi.org/10.1134/S0005117917100137
- ID: 150710
Cite item
Abstract
This paper introduces an extension of the vehicle routing problem by involving several decision makers in competition. Each customer is characterized by demand and distance to the warehouse. The problem is described in form of a cooperative transportation game (CTG). We consider customers as players in the game. Their strategies are the routes for a vehicle they should rent in a coalition to deliver goods subject to their demand with minimal transportation costs, under the assumption that transportation costs are allocated between the players according to the Nash arbitration scheme. For each profile in coalitional strategies, we define a coalitional structure of players and the costs of each player. A strong equilibrium is found for the cooperative transportation game. In addition, we develop a procedure to calculate the strong equilibrium. This procedure is illustrated by a numerical example.
About the authors
N. A. Zenkevich
Graduate School of Management, Department of Operations Management
Author for correspondence.
Email: zenkevich@gsom.spbu.ru
Russian Federation, St. Petersburg
A. V. Zyatchin
Graduate School of Management, Department of Operations Management
Email: zenkevich@gsom.spbu.ru
Russian Federation, St. Petersburg
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