An egalitarian approach for sharing the cost of a spanning tree

A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source. Hence the question is how to fairly allocate the total cost among these agents. Our approach, reinterpreting the spanning tree cost allocation as a claims problem defines a simple way to allocate the optimal cost with two main criteria: (1) each individual only pays attention to a few connection costs (the total cost of the optimal network and the cost of connecting himself to the source); and (2) an egalitarian criteria is used to share costs. Then, using claims rules, we define an egalitarian solution so that the total cost is allocated as equally as possible. We show that this solutions could propose allocations outside the core, a counter-intuitive fact whenever cooperation is necessary. Then we propose a modification to get a core selection, obtaining in this case an alternative interpretation of the Folk solution.Financial support from the Spanish Ministry of Economy and Competitiveness under projects ECO2016-75410-P (AEI/FEDER UE) and ECO2016-77200-P (AEI/FEDER UE), and from Universitat Rovira i Virgili and Generalitat de Catalunya under projects 2018PRF-URV-B2-53 and 2017SGR770, is gratefully acknowledged. Financial support from the Generalitat Valenciana (BEST/2019 grants) to visit the UNSW is gratefully acknowledged