Re-routing game: The inadequacy of mean-field approach in modeling the herd behavior in path switching

Coordination of vehicle routes is a feasible way to ease traffic congestion issues amid a fixed road infrastructure. Nevertheless, even when optimal route configurations are provided to individual drivers, it is hard to achieve due to the fact that greedy drivers may switch to other routes to lower individual costs. Recent research uses a mean-field cavity approach from spin glass studies to analyze the impact of path switching in optimized transportation networks. However, this method only provides a mean-field approximation, which does not account for the collective herd behavior in path switching due to uncoordinated individual decisions. In this study, we propose an exhaustive cavity approach to investigate the impact of uncoordinated path switching in a re-routing game and reveal that greedy drivers’ decisions can be highly correlated, leading to the failure of mean-field approaches. Our theoretical results fit well with simulations, and our developed framework can be generalized to analyze other games with multiple players and rounds. Our results shed light on the impact of herd behavior among uncoordinated human drivers in suppressing congestion through path coordination.