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Strong Equilibria In The Vehicle Routing Game

Author

Listed:
  • NIKOLAY ZENKEVICH

    (Department of Operations Management, Graduate School of Management, St. Petersburg University, Volkhovsky Per. 3, St. Petersburg 199004, Russia)

  • ANDREY ZYATCHIN

    (Center for International Logistics and Supply Chain Management, DB & RZD, Graduate School of Management, St. Petersburg University, Russia;
    Department of Operations Management, Graduate School of Management, St. Petersburg University, Volkhovsky Per. 3, St. Petersburg 199004, Russia)

Abstract

This paper introduces an extension of the vehicle routing problem by including several distributors in competition. Each customer is characterized by demand and a wholesale price. Under this scenario a solution may have unserviced customers and elementary routes with no customer visits. The problem is described as a vehicle routing game (VRG) with coordinated strategies. We provide a computable procedure to calculate a strong equilibrium (SE) in the VRG that is stable against deviations from any coalition. Following this procedure, we solve iteratively optimization subproblems for a single distributor, reducing the set of unserviced customers at each iteration. We prove that strong equilibria of one type exist for a VRG, and we provide conditions for another type to exist. We also introduce a semi-cooperative SE that helps reduce a set of strong equilibria in the VRG. Our methodology is suited for parallel computing, and could be efficiently applied to routing vehicles with a few compartments. It also calculates a numerical example for a three person VRG with six cars and twelve customers.

Suggested Citation

  • Nikolay Zenkevich & Andrey Zyatchin, 2014. "Strong Equilibria In The Vehicle Routing Game," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-13.
    • Handle: RePEc:wsi:igtrxx:v:16:y:2014:i:04:n:s0219198914500133
    DOI: 10.1142/S0219198914500133
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    More about this item

    Keywords

    Game theory; combinatorial optimization; graph theory; networks; vehicle routing problem; 91A06; 91A43; 05C57;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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