Stable and weakly additive cost sharing in shortest path problems

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

Journal of Mathematical Economics, 2024, vol. 110, issue C

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.

Keywords: Shortest path; Cost sharing; Core selection; Additivity (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:110:y:2024:i:c:s0304406823001143

DOI: 10.1016/j.jmateco.2023.102921

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