Karma Mechanisms for Decentralised, Cooperative Multi Agent Path Finding

Multi-Agent Path Finding (MAPF) is a fundamental coordination problem in large-scale robotic and cyber-physical systems, where multiple agents must compute conflict-free trajectories with limited computational and communication resources. While centralised optimal solvers provide guarantees on solution optimality, their exponential computational complexity limits scalability to large-scale systems and real-time applicability. Existing decentralised heuristics are faster, but result in suboptimal outcomes and high cost disparities. This paper proposes a decentralised coordination framework for cooperative MAPF based on Karma mechanisms - artificial, non-tradeable credits that account for agents' past cooperative behaviour and regulate future conflict resolution decisions. The approach formulates conflict resolution as a bilateral negotiation process that enables agents to resolve conflicts through pairwise replanning while promoting long-term fairness under limited communication and without global priority structures. The mechanism is evaluated in a lifelong robotic warehouse multi-agent pickup-and-delivery scenario with kinematic orientation constraints. The results highlight that the Karma mechanism balances replanning effort across agents, reducing disparity in service times without sacrificing overall efficiency. Code: https://github.com/DerKevinRiehl/karma_dmapf