A Variational Inequality Framework for Network Games: Existence, Uniqueness, ...
summary
Claims that a variational inequality reformulation unifies existence and uniqueness results for network games by mapping Nash conditions to properties of the game Jacobian and its gradient, decomposed into own effect, aggregate effect and the adjacency matrix. Derives spectral sufficient conditions using lambda_min, ||G||2 and ||G||∞, shows convergence of best-response when a derived P-matrix (Γ) holds, gives Lipschitz/differentiability comparative statics and outlines a graphon game extension.
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chapters (17)
- 0:00Intro
- 1:04Motivation
- 6:02Related literature
- 9:06A recap on variational inequalities
- 10:25Connection to game theory
- 12:12Properties of Game Jacobian
- 14:13Roadmap of our Analysis
- 14:56Sufficient conditions in terms of V.F(x)
- 18:27The gradient of Fin network games
- 19:58Example: linear quadratic games
- 20:18Sufficient conditions for network games
- 20:45A sufficient condition for strict monotonicity
- 22:35Relation between conditions: Symmetric networks
- 24:09Step 1: From network to operator properties
- 26:07Step 2. From operator properties to Nash properties
- 28:00From analysis to interventions
- 29:04Conclusion