Mean-field games with unbounded controls: a weak formulation approach to global solutions

2026-03-05

AI Summary

This work addresses the existence of equilibria in non-Markovian mean field games with unbounded control variables. By employing a weak formulation approach, it overcomes the conventional restrictions on boundedness of model parameters and time horizons, allowing the running cost to exhibit quadratic growth in the control. The authors establish a novel analytical framework for the existence and stability of quadratic-growth generalized McKean–Vlasov backward stochastic differential equations (BSDEs). Within this framework, they prove—under significantly more general conditions—the global existence of equilibrium solutions for such mean field games, thereby substantially extending the applicability of existing theoretical results.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized McKean-Vlasov BSDEs. Unlike earlier approaches, our approach does not require boundedness assumptions on the model parameters or time horizons and allows for running costs that are quadratic in the control variable.

Problem

• mean-field games
• unbounded controls
• weak formulation
• non-Markovian
• equilibrium existence

Innovation

• mean-field games
• unbounded controls
• weak formulation
• quadratic-growth BSDEs
• McKean-Vlasov