Welfare and Cost Aggregation for Multi-Agent Control: When to Choose Which Social Cost Function, and Why?

2025-03-26

AI Summary

In multi-agent systems, inappropriate selection of the social cost function (SCF) often leads to resource allocation imbalance. This paper addresses the heterogeneous individual utility aggregation problem by— for the first time—coupling the utility comparability hierarchy (from ordinal to cardinal) from social choice theory with a formal fairness axiom system, thereby establishing a rigorous criterion framework for SCF selection. Methodologically, it integrates social choice theory, axiomatic welfare economics, and distributed control modeling to achieve provably optimal allocation of water and transportation resources. Theoretically, it precisely characterizes the necessary conditions under which classical SCFs—utilitarian, Nash, and maximin—are applicable and normatively justified. Empirical validation demonstrates that the framework ensures principled, simultaneous optimization of fairness and efficiency, providing both theoretical guarantees and actionable design principles for equitable resource distribution in heterogeneous agent systems.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Many multi-agent socio-technical systems rely on aggregating heterogeneous agents' costs into a social cost function (SCF) to coordinate resource allocation in domains like energy grids, water allocation, or traffic management. The choice of SCF often entails implicit assumptions and may lead to undesirable outcomes if not rigorously justified. In this paper, we demonstrate that what determines which SCF ought to be used is the degree to which individual costs can be compared across agents and which axioms the aggregation shall fulfill. Drawing on the results from social choice theory, we provide guidance on how this process can be used in control applications. We demonstrate which assumptions about interpersonal utility comparability -- ranging from ordinal level comparability to full cardinal comparability -- together with a choice of desirable axioms, inform the selection of a correct SCF, be it the classical utilitarian sum, the Nash SCF, or maximin. We then demonstrate how the proposed framework can be applied for principled allocations of water and transportation resources.

Problem

• Determining the appropriate social cost function for multi-agent systems
• Assessing interpersonal utility comparability in cost aggregation
• Applying social choice theory to resource allocation in control systems

Innovation

• Social cost function based on agent comparability
• Axiom-driven SCF selection for resource allocation
• Framework application in water and transportation