# A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis Source: [A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis]() Collection index: [llms.txt]() Data updated: 2026-06-05T05:01:30.457Z Authors: Francesca Parise, Asuman Ozdaglar Published: 2017-12-22T01:59:39.000Z ## Abstract We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with multidimensional and possibly constrained strategy sets. We delineate the relations between these conditions and characterize classes of networks that satisfy each of these conditions. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Nash Equilibrium Uniqueness on Linear quadratic network games Single activity, β=0](): Nash Equilibrium Uniqueness; Linear quadratic network games Single activity, β=0; Sufficient Condition (Complements, δ \> 0): not recorded. - [Nash Equilibrium Uniqueness on Linear quadratic network games Multiple activities, β≠0](): Nash Equilibrium Uniqueness; Linear quadratic network games Multiple activities, β≠0; Sufficient Condition (Complements, δ \> 0): not recorded. ## Original sources and implementation [Original paper]() [PDF]()