Title: Stochastic games and MFGs for fuel follower problems: NE and PO

Abstract: In this talk we aim to understand how MFG and especially the aggregation in MFG formulation changes the nature of the solution for stochastic games, in a singular control setting. We start by investigating the classical fuel follower problems for N-player games as well as the MFG. In this singular control framework, the NE points are easier than the PO to analyze. The latter is derived through an auxillary multi-dimensional control problem which provides interesting insight for the nature of PO. The analysis of the Nash Equilibria (NE) and Pareto Optimality (PO) are linked with the Skorokhod problem with non-smooth boundary and unbounded domains. We then show connections and differences of N players games and MFGs in terms of both NE and PO.