Probabilistic Game-Theoretic Traffic Routing

Abstract

We examine the routing problem for self-interested vehicles using stochastic decision strategies. By approximating the road latency functions and a non-linear variable transformation, we frame the problem as an aggregative game. We characterize the approximation error and we derive a new monotonicity condition for a broad category of games that encompasses the problem under consideration. Next, we propose a semidecentralized algorithm to calculate the routing as a variational generalized Nash equilibrium and demonstrate the solution's benefits with numerical simulations. We also explore a recursive receding-horizon formulation of the routing problem for potential games, showing asymptotic convergence to destinations and analysing closed-loop performance dependence on horizon length through numerical simulations.