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Stability in shortest path problems

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  • Bahel, Eric
  • Gómez-Rúa, María
  • Vidal-Puga, Juan

Abstract

We study three remarkable cost sharing rules in the context of shortest path problems, where agents have demands that can only be supplied by a source in a network. The demander rule requires each demander to pay the cost of their cheapest connection to the source. The supplier rule charges to each demander the cost of the second-cheapest connection and splits the excess payment equally between her access suppliers. The alexia rule averages out the lexicographic allocations, each of which allows suppliers to extract rent in some pre-specified order. We show that all three rules are anonymous and demand-additive core selections. Moreover, with three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. Finally, convex combinations of the demander rule and the supplier rule are axiomatized using core selection, a second version of cost additivity and two additional axioms that ensure the fair compensation of intermediaries.

Suggested Citation

  • Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2020. "Stability in shortest path problems," MPRA Paper 98504, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:98504
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    References listed on IDEAS

    as
    1. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    2. Dutta, Bhaskar & Kar, Anirban, 2004. "Cost monotonicity, consistency and minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 223-248, August.
    3. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    4. Eric Bahel & Christian Trudeau, 2017. "Minimum incoming cost rules for arborescences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 287-314, August.
    5. Rosenthal, Edward C., 2013. "Shortest path games," European Journal of Operational Research, Elsevier, vol. 224(1), pages 132-140.
    6. Bergantiños, Gustavo & Vidal-Puga, Juan, 2009. "Additivity in minimum cost spanning tree problems," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 38-42, January.
    7. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
    8. Mohammad S. Roni & Sandra D. Eksioglu & Kara G. Cafferty & Jacob J. Jacobson, 2017. "A multi-objective, hub-and-spoke model to design and manage biofuel supply chains," Annals of Operations Research, Springer, vol. 249(1), pages 351-380, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Shortest path; cost sharing; core selection; additivity.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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