How to best aggregate agent costs for multi-agent control?
Welfare and Cost Aggregation for Multi-Agent Control: When to Choose Which Social Cost Function, and Why?
This paper explores how to aggregate individual costs into a single social cost function (SCF) for multi-agent control systems, such as resource allocation (water, energy) and traffic management. The choice of aggregation method (e.g., sum, max, Nash product) depends on how comparable individual costs are (e.g., can they be directly compared, or are they only meaningful relative to each other within an agent?). This comparability level then dictates which mathematical operations on the SCF are valid.
For LLM-based multi-agent systems, this research highlights the importance of carefully considering the nature of agent “costs” or utilities when designing a system-level objective. The framework can guide the selection of aggregation mechanisms based on whether LLM outputs can be meaningfully compared and inform what operations (e.g., averaging, ranking) are justifiable on the combined LLM outputs. This impacts fairness and efficiency considerations within multi-agent LLM applications.