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.

This simulator is designed to support research on centralised game-theoretical algorithms for maritime traffic management. It supports an arbitrary number of vessels and land masses import. Vessels are modelled as agents whose motion is governed by the kinematic equations and the land masses are polygon shape files. In the simulator, each vessel has access to the reward oracle, which evaluates the agents' strategies by taking into account the risk of collision and grounding, the level of compliance with the traffic rules and the operational efficiency. A game-theoretical model predictive control then generates optimal trajectories for every traffic participant simultaneously. Vessels are engaged in repeated competitive polymatrix games, whose equilibria solutions are a series of waypoints, meant to be broadcast as navigational decision support by the Vessel Traffic Services. We convey the agents' and functions' modelling principle implemented in NetLogo and present the overall simulator structure and scope.

PULSE is an algorithm for multi-agent centralised maritime traffic management that utilises a novel approach to solve polymatrix games through evolutionary dynamics. Polymatrix games are graph-based, succinct game representations with asymmetric two-player normal-form games defined on the edges. Based on the vessels’ (players’) estimated trajectories, the proposed algorithm outputs sequences of pure strategy profiles in the form of speed and heading setpoint pairs, one for each player. These are pure Nash equilibria or their approximations intended for broadcast by the central coordinator. In maritime traffic management, vessel traffic services can provide navigational assistance and decision support to vessels via route suggestion. Guidance games , in which the payoff entries are bound to one, arise from a custom reward framework designed to govern how players balance the trade-off between externalities and internal preferences. We evaluate two variants of payoff calculations: a traditional one, where payoff vectors are derived using ordered player selection, and a novel one based on a random asymmetric two-player game selection. Given the preset strategy competition time, the latter approach reduces the equilibria search time dependency on the number of players from exponential to polynomial, making it more suitable for real-time applications compared to previous work. The simulations of consecutive guidance games and their 2-simplex visualisations highlight the structural properties of the resulting games, though a complete classification within game theory remains an open challenge. Inspired by distributed consensus-seeking algorithms, PULSE is a game-theoretical, multi-agent simulation-based model predictive control planner.