Axiomatic Characterizations of a Proportional Influence Measure for Sequential Projects with Imperfect Reliability

Axioms ◽

10.3390/axioms10040247 ◽

2021 ◽

Vol 10 (4) ◽

pp. 247

Author(s):

Andries van van Beek ◽

Peter Borm ◽

Marieke Quant

Keyword(s):

Finite Number ◽

Task Group ◽

Influence Measure ◽

Axiomatic Characterizations ◽

Finite Set ◽

Group A ◽

The Relationship

We define and axiomatically characterize a new proportional influence measure for sequential projects with imperfect reliability. We consider a model in which a finite set of players aims to complete a project, consisting of a finite number of tasks, which can only be carried out by certain specific players. Moreover, we assume the players to be imperfectly reliable, i.e., players are not guaranteed to carry out a task successfully. To determine which players are most important for the completion of a project, we use a proportional influence measure. This paper provides two characterizations of this influence measure. The most prominent property in the first characterization is task decomposability. This property describes the relationship between the influence measure of a project and the measures of influence one would obtain if one divides the tasks of the project over multiple independent smaller projects. Invariance under replacement is the most prominent property of the second characterization. If, in a certain task group, a specific player is replaced by a new player who was not in the original player set, this property states that this should have no effect on the allocated measure of influence of any other original player.

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Axiomatic characterizations under players nullification

Mathematical Social Sciences ◽

10.1016/j.mathsocsci.2016.01.002 ◽

2016 ◽

Vol 80 ◽

pp. 47-57 ◽

Cited By ~ 8

Author(s):

Sylvain Béal ◽

Sylvain Ferrières ◽

Eric Rémila ◽

Philippe Solal

Keyword(s):

Axiomatic Characterizations

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Effects of Players’ Nullification and Equal (Surplus) Division Values

International Game Theory Review ◽

10.1142/s0219198917500293 ◽

2018 ◽

Vol 20 (01) ◽

pp. 1750029 ◽

Cited By ~ 9

Author(s):

Takumi Kongo

Keyword(s):

The Other ◽

Equal Division ◽

Transferable Utility ◽

Tu Games ◽

Axiomatic Characterizations ◽

The Difference ◽

Monotonicity Axioms ◽

Equal Surplus Division

We provide axiomatic characterizations of the solutions of transferable utility (TU) games on the fixed player set, where at least three players exist. We introduce two axioms on players’ nullification. One axiom requires that the difference between the effect of a player’s nullification on the nullified player and on the others is relatively constant if all but one players are null players. Another axiom requires that a player’s nullification affects equally all of the other players. These two axioms characterize the set of all affine combinations of the equal surplus division and equal division values, together with the two basic axioms of efficiency and null game. By replacing the first axiom on players’ nullification with appropriate monotonicity axioms, we narrow down the solutions to the set of all convex combinations of the two values, or to each of the two values.

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