Congestion-Aware Path Coordination Game With Markov Decision Process Dynamics

Inspired by the path coordination problem arising from robo-taxis, warehouse management, and mixed-vehicle routing, we model a group of heterogeneous players responding to stochastic demands as congestion game under Markov decision process dynamics. Players share common state-action space but have unique transition dynamics, each player’s cost is function joint probability distribution. For class player functions, formulate player-specific optimization problem, prove equivalence between Nash equilibrium solution potential minimization derive dynamic programming approaches solve equilibrium. We apply this multi-agent introduce congestion-based functions that enable complete individual tasks while avoiding with their opponents. Finally, present learning algorithm for finding has linear complexity in number players. demonstrate our on multi-robot which robots autonomously retrieve deliver packages congested paths.