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Stable and weakly additive cost sharing in shortest path problems

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

Abstract

In a shortest path problem, agents seek to ship their respective demands; and the cost on a given arc is linear in the flow. Previous works have proposed cost allocations falling in the core of the associated cooperative game. The present work combines core selection with weak versions of the additivity axiom, which allows to characterize a new family of rules. The demander rule charges each demander the cost of their shortest path, and the supplier rule charges the cost of the second-cheapest path while splitting the excess payment equally between access suppliers. With three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. 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. 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 fairness properties.

Suggested Citation

  • Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2024. "Stable and weakly additive cost sharing in shortest path problems," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    • Handle: RePEc:eee:mateco:v:110:y:2024:i:c:s0304406823001143
    DOI: 10.1016/j.jmateco.2023.102921
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    References listed on IDEAS

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    Cited by:

    1. Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2024. "Merge-proofness and cost solidarity in shortest path games," MPRA Paper 120606, University Library of Munich, Germany.

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