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Strong Coalitional Structure in an Open Vehicle Routing Game

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Recent Advances in Game Theory and Applications

Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

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Abstract

In the chapter it is investigated a special case of one-product open vehicle routing game, in which there is a central warehouse or wholesaler, several customers, who are considered to be players. Each player is placed in a node of the transportation network and is characterized by demand and distance to the warehouse. For such a problem a coalitional transportation game (CTG) is formalized. In such a game each customer (player) should rent a track to deliver goods from the central warehouse. It is assumed that all tracks have the same capacity. The players tend to minimize their transportation costs and totally supply their demands. A player may rent a vehicle alone, or chose a coalition of players to cooperate. In cooperation the players of coalitions find the shortest path form the central depot to all the player of coalition. Transportation costs are allocated between players according to the Nash arbitration scheme. Strong equilibrium which is stable against deviations of any coalition of players is found in a CTG. A computation procedure for strong equilibrium construction is proposed. Implementation of procedure is illustrated with a numerical example.

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Acknowledgements

This work is supported by the Russian Foundation for Basic Research, projects No.16-01-00805A and 14-07-00899A and Saint-Petersburg State University, project No.9.38.245.2014

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Authors and Affiliations

  1. Center for International Logistics and Supply Chain Management of DB & RZD, Graduate School of Management, Volkhovsky Pereulok, 3, St. Petersburg, 199004, Russia

    Nikolay Zenkevich & Andrey Zyatchin

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  1. Nikolay Zenkevich
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  2. Andrey Zyatchin
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Correspondence to Andrey Zyatchin .

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Editors and Affiliations

  1. Department of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg, Russia

    Leon A. Petrosyan

  2. Institute of Applied Mathematical Research, Karelia Research Center of Russian Academy of Sciences, Petrozavodsk, Russia

    Vladimir V. Mazalov

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Zenkevich, N., Zyatchin, A. (2016). Strong Coalitional Structure in an Open Vehicle Routing Game. In: Petrosyan, L., Mazalov, V. (eds) Recent Advances in Game Theory and Applications. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-43838-2_14

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