| Abstract: |
| Mean Field Games is a powerful tool to describe competitive optimization processes among agents. A natural field of application is crowd dynamics where pedestrians optimize their path, while interacting with the others. Due to the backward-forward structure of the MFG equations, anticipation is included in the model, which is often a key element to reproduce pedestrian behavior. In this formalism, the interactions among the agents are usually considered exclusively inside the minimization of a functional (personal cost), in the decision-making level and not in the operational, at the agent scale. This approach often fails to describe situations where the granular effects are dominant, namely while passing through a bottleneck. To enhance the realism of the framework, we aim to incorporate these granular effects by considering explicit microscopic interactions in the Mean Field Game derivation. In this direction, we treat a toy-model by replacing Langevin dynamics for the agents with a one-dimensional Exclusion Process, which is a paradigmatic model of interacting particles, especially in transport and congestion phenomena. We will show how to derive the corresponding Mean Field Game equations and discuss the effect of these interactions on the Nash equilibrium of the game, in particular in the case of evacuations. This study can be seen as a first step towards the study of other interacting models and their potential Mean Field Games counterparts. |
|