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A Unified Approach To The Myerson Value And The Position Value

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Listed:
  • Daniel Gómez

  • Enrique Gonz{’a}lez-Arangüena
  • Conrado Manuel

  • Guillermo Owen

  • Monica Del Pozo

Abstract

We reconsider the Myerson value and the position value for communication situations. In case the underlying game is a unanimity game, we show that each of these values can be computed using the inclusion--exclusion principle. Linearity of both values permits us to calculate them without needing the dividends of the induced games (graph-restricted game and link game). The expression of these dividends is only derived in the existing literature for special communication situations. Moreover, the associated inclusion--exclusion decomposability property depends on what we have called the graph allocation rule. This rule is the relative degree (relative indicator) for the position value (Myerson value). Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Daniel Gómez & Enrique Gonz{’a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(1), pages 63-76, April.
    • Handle: RePEc:kap:theord:v:56:y:2004:i:1:p:63-76
    DOI: 10.1007/s11238-004-5636-4
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
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    1. González–Arangüena, Enrique & Manuel, Conrado Miguel & del Pozo, Mónica, 2015. "Values of games with weighted graphs," European Journal of Operational Research, Elsevier, vol. 243(1), pages 248-257.
    2. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 87-110, February.
    3. Enrique González-Arangüena & Conrado Manuel & Daniel Gomez & René van den Brink, 2008. "A Value for Directed Communication Situations," Tinbergen Institute Discussion Papers 08-006/1, Tinbergen Institute.
    4. Guillermo Owen, 2013. "Current Research," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-3.
    5. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.
    6. Li, Daniel Li & Shan, Erfang, 2019. "The position value and the structures of graphs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 190-197.
    7. López, Susana & Molina, Elisenda & Saboyá, Martha & Tejada, Juan, 2024. "Node centrality based on its edges importance: The Position centrality," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 90-104.
    8. E. Gavilán & C. Manuel & D. Martín, 2026. "A position value for multigraphs," Annals of Operations Research, Springer, vol. 356(1), pages 55-84, January.

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