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A Unified Approach To The Myerson Value And The Position Value

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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).

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Authors and Affiliations

  1. Dept. de Estadística e I.O. III. E.U. de Estadística, Universidad Complutense de Madrid, Av Puerta de Hierro s/n, Spain

    Daniel Gómez, Enrique González-Arangüena, Conrado Manuel & Monica Del Pozo

  2. Department of Mathematics, Naval Postgraduate School, CA, USA

    Guillermo Owen

Authors
  1. Daniel Gómez
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  2. Enrique González-Arangüena
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  3. Conrado Manuel
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  4. Guillermo Owen
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  5. Monica Del Pozo
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Gómez, D., González-Arangüena, E., Manuel, C. et al. A Unified Approach To The Myerson Value And The Position Value. Theory and Decision 56, 63–76 (2004). https://doi.org/10.1007/s11238-004-5636-4

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  • DOI: https://doi.org/10.1007/s11238-004-5636-4

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