Hamilton's Rule for Enabling Altruism in Multi-Agent Systems

2025/05/14 by Butler, Brooks A., Magnus Egerstedt, Egerstedt, Magnus
Decision Sciences · Physics and Astronomy · Social Sciences · #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #FOS: Electrical engineering #Game Theory and Applications #Multiagent Systems (cs.MA) #Opinion Dynamics and Social Influence #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2505.09841

openalex publication_date 2025/05/14 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

This paper explores the application of Hamilton's rule to altruistic decision-making in multi-agent systems. Inspired by biological altruism, we introduce a framework that evaluates when individual agents should incur costs to benefit their neighbors. By adapting Hamilton's rule, we define agent ``fitness" in terms of task productivity rather than genetic survival. We formalize altruistic decision-making through a graph-based model of multi-agent interactions and propose a solution using collaborative control Lyapunov functions. The approach ensures that altruistic behaviors contribute to the collective goal-reaching efficiency of the system. We illustrate this framework on a multi-agent way-point navigation problem, where we show through simulation how agent importance levels influence altruistic decision-making, leading to improved coordination in navigation tasks.

Citations

• Resilience to Non-Compliance in Coupled Cooperating Systems
• Collaborative Safe Formation Control for Coupled Multi-Agent Systems
• Collaborative Safety-Critical Control for Dynamically Coupled Networked Systems
• Social Coordination and Altruism in Autonomous Driving
• High-order Barrier Functions: Robustness, Safety and Performance-Critical Control
• Robot Risk-Awareness by Formal Risk Reasoning and Planning
• Designing Fully Distributed Consensus Protocols for Linear Multi-Agent Systems With Directed Graphs

Related

• Beyond classical Hamilton's Rule. State distribution asymmetry and the dynamics of altruism
• Learning Altruistic Behaviours in Reinforcement Learning without External Rewards
• Resolving social dilemmas with minimal reward transfer
• Resource Allocation with Multi-Team Collaboration Based on Hamilton's Rule
• Altruism Design in Networked Public Goods Games