Centralised Decision Support in Maritime Vessel Traffic Services: A Polymatrix Game Solution

Given the increasing complexity of maritime traffic, particularly with the growing integration of autonomous vessels alongside conventional vessels, the need for enhanced coordination and decision support systems has become critical to ensure safety and efficiency. This article presents a concept for a centralised decision support system for local maritime traffic and can be used in centres for remote operations or vessel traffic services. By formalising a non-zero-sum asymmetric polymatrix game, we achieve collision and grounding avoidance of non-cooperative agents. Time-varying and state-dependent payoff matrices are constructed using a reward framework that combines metrics for compliance with maritime traffic rules, global collision risk, grounding risk, and an operational efficiency metric for speed and route optimisation. A pure Nash equilibrium is reached in a polymatrix game, a fully connected graph of traffic participants on vertices with bimatrix games on the edges. Strategy probability distributions in infinite populations located on the graph’s vertices are updated with the replicator revision protocol. The equilibrium constitutes a control message consisting of advised speed and heading commands broadcast to all traffic participants. To validate the proposed idea, we have developed a scalable multi-agent system simulator and present results from a collision avoidance scenario with three vessels and 49 strategies available to each. Engaged vessels achieved safe and efficient passage, guided by the advised speed and heading changes.