A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis

2017/12/22 by Parise, Francesca, Ozdaglar, Asuman · 4 citations
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1712.08277

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.

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