Research Paper#Game Theory, Reinforcement Learning, Mean Field Games🔬 ResearchAnalyzed: Jan 3, 2026 15:39
Discrete-Time Mean Field Games with Probabilistic Framework
Published:Dec 30, 2025 16:10
•1 min read
•ArXiv
Analysis
This paper introduces a probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs), addressing the challenges of common noise and randomized actions. It establishes a connection between MFTGs and Mean Field Markov Games (MFMGs) and proves the existence of optimal closed-loop policies under specific conditions. The work is significant for advancing the theoretical understanding of MFTGs, particularly in scenarios with complex noise structures and randomized agent behaviors. The 'Mean Field Drift of Intentions' example provides a concrete application of the developed theory.
Key Takeaways
- •Introduces a probabilistic framework for discrete-time MFTGs.
- •Addresses common noise and randomized actions.
- •Establishes a connection between MFTGs and MFMGs.
- •Proves the existence of optimal closed-loop policies under specific conditions.
- •Provides a concrete example: Mean Field Drift of Intentions.
Reference
“The paper proves the existence of an optimal closed-loop policy for the original MFTG when the state spaces are at most countable and the action spaces are general Polish spaces.”