An [imaginary time] Schrödinger approach to mean field games

Abstract

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 Schrödinger 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.

5 pages, 1 figure, should interest people working in both the physical and economical community

References in corpus (2)

• Individual vaccination as Nash equilibrium in a SIR model with application to the 2009-10 Influenza A(H1N1) epidemic in France
• 'Phase diagram' of a mean field game

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• Exactly solvable Gaussian and non-Gaussian mean-field games and collective swarms dynamics