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2946. Parallel axiomatizations of generalized weighted-egalitarian Shapley values

Invited abstract in session TD-36: Game Theory, Solutions and Structures VIII, stream Game Theory, Solutions and Structures.

Tuesday, 14:30-16:00
Room: 32 (building: 306)

Authors (first author is the speaker)

1. Hyungkyu Cheon
Industrial and Management Engineering, POSTECH
2. Dong Gu Choi
POSTECH

Abstract

Joosten (1996) attempted to reconcile marginalism and egalitarianism by proposing the egalitarian Shapley values, which is a convex combination of the Shapley value and the equal division values. Abe and Nakada (2019) generalized the equal division values of egalitarian Shapley values to propose weighted-egalitarian Shapley values. Recently, Cheon and Choi (2024) introduced a new solution by generalizing the Shapley values to the weighted Shapley values within this weighted-egalitarian Shapley values framework.
In this study, we further advance the generalization of TU-values. This research delineates the axiomatic properties of solutions resulting from the convex combination of four classes of TU-values. These classes include convex combinations of the weighted division values with weighted Shapley values, positively weighted Shapley values, random order values, and the Harsanyi set. This research has been influenced by the parallel axiomatization of Besner (2020). Besner (2020) axiomatized weighted, positively weighted, and multiweighted Shapley values, random order values, and the Harsanyi set, presenting the axiomatization of all individual classes as a single theorem for all classes. In our study as well, within the main theorem, the axiomatization of adjacent two classes differs by only one axiom, and the process of generalization of classes of solutions and weakening of corresponding axioms progresses in the same direction.

Keywords

Status: accepted

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