Coalitional Bargaining via Reinforcement Learning: An Application to Collaborative Vehicle Routing

Abstract

Collaborative Vehicle Routing is where delivery companies cooperate by sharing their delivery information and performing delivery requests on behalf of each other. This achieves economies of scale and thus reduces cost, greenhouse gas emissions, and road congestion. But which company should partner with whom, and how much should each company be compensated? Traditional game theoretic solution concepts, such as the Shapley value or nucleolus, are difficult to calculate for the real-world problem of Collaborative Vehicle Routing due to the characteristic function scaling exponentially with the number of agents. This would require solving the Vehicle Routing Problem (an NP-Hard problem) an exponential number of times. We therefore propose to model this problem as a coalitional bargaining game where - crucially - agents are not given access to the characteristic function. Instead, we implicitly reason about the characteristic function, and thus eliminate the need to evaluate the VRP an exponential number of times - we only need to evaluate it once. Our contribution is that our decentralised approach is both scalable and considers the self-interested nature of companies. The agents learn using a modified Independent Proximal Policy Optimisation. Our RL agents outperform a strong heuristic bot. The agents correctly identify the optimal coalitions 79% of the time with an average optimality gap of 4.2% and reduction in run-time of 62%.