Induced rules for minimum cost spanning tree problems: towards merge-proofness and coalitional stability

Siwen Liu (), Peter Borm () and Henk Norde ()
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Siwen Liu: Bonn University
Peter Borm: Tilburg University
Henk Norde: Tilburg University

International Journal of Game Theory, 2025, vol. 54, issue 2, No 12, 35 pages

Abstract: Abstract This paper examines cost allocation rules for minimum cost spanning tree (MCST) problems, focusing on the properties of merge-proofness and coalitional stability. Merge-proofness ensures that no coalition of agents has the incentive to merge before participating in the cost allocation process. On the other hand, coalitional stability ensures that no coalition has the incentive to withdraw from the cost allocation process after the cost allocation proposal is made. We propose a novel class of rules called induced rules, which are derived recursively from base rules designed for two-person MCST problems. We demonstrate that induced rules exhibit both merge-proofness and coalitional stability within a restricted domain, provided that the corresponding base rules satisfy specific conditions.

Keywords: Minimum cost spanning tree problems; Cooperative games; Induced cost allocation rules; Merge-proofness; Coalitional stability (search for similar items in EconPapers)
JEL-codes: C71 D61 D79 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00182-025-00959-x

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