Analysis of Mean-Field Games - Lecture 1

Explore the foundations of mean-field games in this comprehensive lecture from the "Advances in Applied Probability" program at ICTS Bangalore. Delve into static mean-field games, starting with motivations and context before examining abstract frameworks, Nash equilibria, and symmetric games. Learn about convergence questions, p-Wasserstein distance, and asymptotic approximations. Investigate mean-field equilibria, including uniqueness, potential games, and existence proofs. Gain insights into large-scale systems modeling and analysis through probabilistic methods, essential for understanding complex interconnected networks in technology, commerce, and beyond.

Mean-Field Games Lecture 1: Static Mean-Field Games
Motivation and Context of Mean-Field Games
Static Games
Static Games: A Motivating Example
Static Games: Abstract Framework
Nash Equilibria
Symmetric Games
Static Game: Large Symmetric Games
Convergence Questions
p-Wasserstein distance
Static Game: An Asymptotic Approximation
Proof of Convergence Theorem
Static Games: Mean-field Equilibrium
Uniqueness of Mean-Field Equilibria
Potential Games
A Converse to the Limit Theorem
Existence of Mean-Field Equilibria
Proof: A Converse to the Limit Theorem
Next Define the Random Variable