Compound Poisson Limits in Weighted Bernoulli Congestion Games: Theory Meets Experiments

Congestion games provide a key framework for modeling traffic in transporta- tion networks. Cominetti et al. (2023) studied Bernoulli congestion games with homogeneous players and showed that Nash equilibria converge to Poisson ran- dom variables linked to the Wardrop equilibrium of the nonatomic game. In this work, we extend this model to weighted Bernoulli congestion games, allowing heterogeneous player weights. We have proven that arc loads and flows at equi- librium converge to compound Poisson random variables, thereby strengthening the bridge between atomic and nonatomic models. We provided numerical ex- periments that further demonstrate that even with a small number of players, the equilibrium closely approximates the limiting behavior, highlighting the model’s ability to capture the natural stochasticity of traffic flows.