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On a new method of analyzing properties of efficient, symmetric and linear values of TU-games

Volume 48 / 2021

Tadeusz Radzik Applicationes Mathematicae 48 (2021), 173-208 MSC: Primary 91A12; Secondary 91A06. DOI: 10.4064/am2414-5-2021 Published online: 26 November 2021

Abstract

We present a new method allowing one to discover different extra properties of efficient, symmetric and linear values of TU-games (called ESL-values). These properties are of “monotonicity”, “acceptability” and “null player properties” type. A representation formula for such family of values, generalizing the standard formula for the Shapley value, is recalled. It is then shown that a number of different properties of ESL-values can be easily identified using this formula. Several new axiomatizations of different ESL-values are also obtained as simple consequences of the presented theorems. A table of different properties for fifteen basic ESL-values is given as an illustration of the new method.

Authors

  • Tadeusz RadzikFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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