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A non-cooperative game theory approach to cost sharing in networks

Author

Listed:
  • M. A. Hinojosa

    (Universidad Pablo de Olavide)

  • A. Caro

    (Universidad Pablo de Olavide)

Abstract

This paper considers networks in which nodes have communication needs between them. The cost of building or maintaining an edge with a given capacity is the same across any pair of agents. It is known that feasibility is reached by any maximal-capacity spanning tree. A multi-stage non-cooperative game is considered in which, at each stage, every agent simultaneously decides either to propose building a connection to another agent or to wait for a better opportunity. The required capacity between any pair of agents can be seen as being to their benefit if and only if, in the resulting tree, there exists a path between them such that every edge provides at least this required capacity. On the other hand, the agents who decide to connect have to pay for the link by equally splitting the cost. The problem is analyzed in a context in which the preferences of the agents regarding benefits and costs are lexicographic. The concepts of capacity synthesis equilibrium (CSE) and strong capacity synthesis equilibrium (strong CSE) are introduced and a mechanism to reach some of these equilibria is presented. We also analyze CSEs and strong CSEs in relation to the Nash equilibria of the benefit capacity synthesis game.

Suggested Citation

  • M. A. Hinojosa & A. Caro, 2021. "A non-cooperative game theory approach to cost sharing in networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 219-251, October.
    • Handle: RePEc:spr:mathme:v:94:y:2021:i:2:d:10.1007_s00186-021-00754-w
    DOI: 10.1007/s00186-021-00754-w
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    References listed on IDEAS

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    1. Gustavo Bergantiños & Leticia Lorenzo, 2004. "A non-cooperative approach to the cost spanning tree problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 393-403, July.
    2. Norde, Henk, 2019. "The degree and cost adjusted folk solution for minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 113(C), pages 734-742.
    3. Hervé Moulin, 2013. "Cost Sharing In Networks: Some Open Questions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-10.
    4. Anna Bogomolnaia & Ron Holzman & Hervé Moulin, 2010. "Sharing the Cost of a Capacity Network," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 173-192, February.
    5. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    6. Bogomolnaia, Anna & Moulin, Hervé, 2010. "Sharing a minimal cost spanning tree: Beyond the Folk solution," Games and Economic Behavior, Elsevier, vol. 69(2), pages 238-248, July.
    7. Gustavo Bergantiños & Juan Vidal-Puga, 2015. "Characterization of monotonic rules in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 835-868, November.
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