Speaker: Ludovic Tangpi, Associate Professor, Princeton University's ORFE department

 

Title: Particle system approximation of Nash equilibria in symmetric monotone games

 

Abstract:

We develop a probabilistic framework to approximate Nash equilibria in symmetric $N$-player games in the large population regime, via the analysis of associated mean field games (MFGs). The approximation is achieved through the analysis of a McKean–Vlasov type Langevin dynamics and their associated particle systems, with convergence to the MFG solution established in the limit of vanishing temperature parameter. Relying on displacement monotonicity or Lasry–Lions monotonicity of the cost function, we prove contractivity of the McKean–Vlasov process and uniform-in-time propagation of chaos for the particle system. Our results contribute to the general theory of interacting diffusions by showing that monotonicity can ensure convergence without requiring small interaction assumptions or functional inequalities. Based on joint works with N. Touzi and V. Hoffmann.