Congestion-aware path coordination game with Markov decision process dynamics

TL;DR

This paper models a congestion-aware multi-agent path coordination problem using Markov decision process dynamics, introducing a game-theoretic approach with a novel learning algorithm for efficient Nash equilibrium computation.

Contribution

It formulates a new congestion-aware path coordination game with MDP dynamics, proves equilibrium properties, and develops a scalable learning algorithm for multi-robot warehouse scenarios.

Findings

Successfully models multi-robot path coordination with congestion considerations.

Provides a dynamic programming approach to find Nash equilibria.

Demonstrates effectiveness in a warehouse robot routing case study.

Abstract

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