On cycle-free accessible union stable network structures

Encarnación Algaba (), René Brink () and Chris Dietz ()
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Encarnación Algaba: Matemática Aplicada II and Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Escuela Superior de Ingenieros
René Brink: VU University Amsterdam
Chris Dietz: VU University Amsterdam

4OR, 2025, vol. 23, issue 3, No 5, 329-347

Abstract: Abstract We investigate set theoretic properties that characterize the collection of connected coalitions in cycle-free undirected graphs among the accessible union stable network structures. It turns out that the only additional requirement is that every non-unitary feasible coalition can be written in a unique way as a union of non-unitary supports. As a consequence, a fairness axiom for solutions for cooperative games on cycle-free accessible union stable network structures can be defined that, together with the well-known component efficiency, characterizes the Shapley value on the class of cycle-free accessible union stable network structures. Since this fairness axiom combines ideas behind the traditional fairness axiom and balanced contributions, we refer to it as balanced fairness.

Keywords: Cooperative game; Cycle-free graph; Accessible union stable structure; Shapley value; Axiomatization; 91A12; 91A43; 05C21 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10288-025-00594-y

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