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On cycle-free accessible union stable network structures

Author

Listed:
  • 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)

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.

Suggested Citation

  • Encarnación Algaba & René Brink & Chris Dietz, 2025. "On cycle-free accessible union stable network structures," 4OR, Springer, vol. 23(3), pages 329-347, September.
    • Handle: RePEc:spr:aqjoor:v:23:y:2025:i:3:d:10.1007_s10288-025-00594-y
    DOI: 10.1007/s10288-025-00594-y
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