Induced Rules for Minimum Cost Spanning Tree Problems: Towards Merge-Proofness and Coalitional Stability

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.