A Variational Inequality Framework for Network Games

Explore a variational inequality framework for network games in this 31-minute lecture by Asu Özdağlar from the Massachusetts Institute of Technology. Delve into the connection between variational inequalities and game theory, examining properties of Game Jacobian and sufficient conditions for network games. Learn about linear quadratic games, strict monotonicity, and the relationship between conditions in symmetric networks. Discover how to apply this analysis to interventions in societal networks, gaining valuable insights into the mathematical foundations of network game theory.

Intro
Motivation
Related literature
A recap on variational inequalities
Connection to game theory
Properties of Game Jacobian
Roadmap of our Analysis
Sufficient conditions in terms of V.F(x)
The gradient of Fin network games
Example: linear quadratic games
Sufficient conditions for network games
A sufficient condition for strict monotonicity
Relation between conditions: Symmetric networks
Step 1: From network to operator properties
Step 2. From operator properties to Nash properties
From analysis to interventions
Conclusion