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Schrödinger Approach to Mean Field Games
Igor Swiecicki1,2, Thierry Gobron2, Denis Ullmo1
1LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
Physical Review Letters
|April 9, 2016
Summary
This study links mean field games (MFGs) with nonlinear Schrödinger equations. This connection offers new methods for analyzing socioeconomic systems and population dynamics with coordination incentives.
Area of Science:
- Mathematical Physics
- Game Theory
- Sociology
Background:
- Mean field games (MFGs) offer a framework for modeling complex socioeconomic systems.
- Analogies exist between certain MFGs and nonlinear Schrödinger/Gross-Pitaevskii equations from physics.
Purpose of the Study:
- To explore a class of MFGs with strong analogies to nonlinear physics equations.
- To leverage techniques from physics to advance the study of MFGs.
- To analyze a population dynamics model with strong coordination incentives.
Main Methods:
- Establishing a theoretical bridge between MFGs and nonlinear Schrödinger equations.
- Transferring established results and techniques from physics to game theory.
- Detailed analysis of a population dynamics model using the MFG-physics approach.
Main Results:
- Demonstrated significant analogies between specific MFGs and nonlinear Schrödinger/Gross-Pitaevskii equations.
- Facilitated the transfer of advanced mathematical techniques from physics to MFG theory.
- Provided a novel approach for studying MFGs, particularly those involving coordination.
Conclusions:
- The established link between MFGs and nonlinear physics equations opens new avenues for research.
- This interdisciplinary approach enhances the study of socioeconomic systems and population dynamics.
- The nonlinear Schrödinger equation finds a new domain of application in game theory and social modeling.
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