Characterizing the ELS Values with Fixed-Population Invariance Axioms

2025-11-07

AI Summary

This paper axiomatically characterizes efficient, linear, and symmetric (ELS) allocation rules for transferable-utility (TU) games with a fixed player set. Methodologically, it introduces a novel game transformation that unifies all ELS values as Shapley values of transformed games; proposes three distinct null-game consistency axioms—each uniquely identifying the Shapley, CIS, or ENSC value; and employs combinatorial and active-player consistency axioms to characterize an ELS subclass containing the least-squares value. Integrating Shapley-value transformations, linear operator theory, and axiomatic analysis, the study systematically establishes three technical pathways: composition invariance, player consistency, and null-game consistency. Contributions include: (i) the first unified representation of all ELS values as Shapley values; (ii) a complete axiomatic classification of core ELS subclasses; and (iii) sharp, distinguishing axiomatizations for the Shapley, CIS, and ENSC values—thereby substantially strengthening their theoretical foundations.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Characterizing ELS values using fixed-population invariance axioms for TU-games
• Analyzing composition axioms and active-player consistency for allocation rules
• Establishing nullified-game consistency axioms for Shapley, CIS, and ENSC values

Innovation

• ELS values as Shapley value transformations
• Composition axioms characterize least-square values
• Nullified-game consistency identifies specific values