This paper proposes a new representation for the Public Help Index (briefly, PHI ). Based on winning coalitions, the PHI index was introduced by Bertini et al. in (2008). The goal of this article is to reformulate the PHI index using null player free winning coalitions. The set of these coalitions unequivocally defines a simple game. Expressing the PHI index by the winning coalitions that do not contain null players allows us in a transparent way to show the parts of the power assigned to null and non-null players in a simple game. Moreover, this new representation may imply a reduction of computational cost (in the sense of space complexity) in algorithms to compute the PHI index if at least one of the players is a null player. We also discuss some relationships among the Holler index, the PHI index, and the index (based on null player free winning coalitions) proposed by Álvarez-Mozos et al. in (2015).
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| http://dx.doi.org/10.1007/s10726-021-09769-4 | DOI Listing |
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