Schrödinger approach to mean field games

Igor Swiecicki 1, 2 Thierry Gobron 1 Denis Ullmo 2

Physical Review Letters, American Physical Society, 2016, 116, pp.128701

Mean Field Games (MFG) provide a theoretical frame to model socio-economic systems. In this letter, we study a particular class of MFG which shows strong analogies with the {\em non-linear Schr\"odinger and Gross-Pitaevski equations} introduced in physics to describe a variety of physical phenomena ranging from deep-water waves to interacting bosons. Using this bridge many results and techniques developed along the years in the latter context can be transferred to the former. As an illustration, we study in some details an example in which the "players" in the mean field game are under a strong incentive to coordinate themselves.

  • 1. LPTM - Laboratoire de Physique Théorique et Modélisation
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques