Characterizations of Proportional Division Value in TU-Games via Fixed-Population Consistency

TL;DR

This paper characterizes the proportional division value in TU-games using axioms related to scale invariance, composition, and fixed-player payoffs, providing a comprehensive axiomatic foundation.

Contribution

It introduces a new axiomatic characterization of the proportional division value based on fixed-population consistency and related axioms.

Findings

Axioms uniquely characterize the proportional division value.

Homogeneity axiom captures scale invariance.

Composition axioms ensure consistency under game decomposition.

Abstract

We study the proportional division value in TU-games, which distributes the worth of the grand coalition in proportion to each player's stand-alone worth. Focusing on fixed-population consistency, we characterize the proportional division value through three types of axioms: a homogeneity axiom, composition axioms, and a nullified-game consistency axiom. The homogeneity axiom captures scale invariance with respect to the grand coalition's worth. The composition axioms ensure that payoffs remain consistent when the game is decomposed and recomposed. The nullified-game consistency axiom requires that when some players' payoffs are fixed, the solution for the remaining players, computed in the game adjusted to account for these fixed payoffs, coincides with their original payoffs. Together with efficiency and a fairness-related axiom, these axioms characterize the proportional division value.