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Caballero-Engel meet Lasry-Lions: A uniqueness result
Fernando Alvarez1, Francesco Lippi2, Panagiotis Souganidis3
1University of Chicago and NBER, Chicago, USA.
Mathematics and Financial Economics
|October 1, 2024
Summary
This study proves equilibrium uniqueness in Mean Field Games (MFGs) with impulse control, extending previous work to non-convex adjustment costs and generalized hazard functions.
Area of Science:
- Economics
- Game Theory
- Mathematical Finance
Background:
- Mean Field Games (MFGs) model decision-makers influenced by state distributions.
- Existing models often focus on drift-control, limiting applications with non-convex costs.
Purpose of the Study:
- To establish equilibrium uniqueness in a class of MFGs with impulse control.
- To extend MFG analysis to problems with non-convex adjustment costs and generalized hazard functions.
Main Methods:
- Introduced the concept of the "Impulse Hamiltonian" for impulse control problems.
- Utilized a monotonicity assumption (strategic substitutability) to prove uniqueness.
Main Results:
- Proved the uniqueness of the equilibrium in the studied class of MFGs.
- Demonstrated that the Impulse Hamiltonian plays a key role, analogous to the classical Hamiltonian.
Conclusions:
- The framework accommodates problems with non-convex adjustment costs, expanding MFG applicability.
- The Impulse Hamiltonian is crucial for analyzing impulse control MFGs under monotonicity.
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