Characterizing the ELS Values with Fixed-Population Invariance Axioms

TL;DR

This paper characterizes efficient, linear, and symmetric (ELS) values in cooperative games, introducing invariance axioms that uniquely identify key values like Shapley, CIS, and ENSC.

Contribution

It provides a novel axiomatic framework for characterizing ELS values, including the Shapley, CIS, and ENSC, via fixed-population invariance axioms.

Findings

Every ELS value can be expressed as the Shapley value of a transformed game.

Three invariance axioms characterize subclasses of ELS values.

Nullified-game consistency axioms uniquely identify Shapley, CIS, and ENSC values.

Abstract

We study efficient, linear, and symmetric (ELS) values, a central family of allocation rules for cooperative games with transferable-utility (TU-games) that includes the Shapley value, the CIS value, and the ENSC value. We first show that every ELS value can be written as the Shapley value of a suitably transformed TU-game. We then introduce three types of invariance axioms for fixed player populations. The first type consists of composition axioms, and the second type is active-player consistency. Each of these two types yields a characterization of a subclass of the ELS values that contains the family of least-square values. Finally, the third type is nullified-game consistency: we define three such axioms, and each axiom yields a characterization of one of the Shapley, CIS, and ENSC values.