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We provide a distributed algorithm to learn a Nash equilibrium in a class ofnon-cooperative games with strongly monotone mappings and unconstrained actionsets. Each player has access to her own smooth local cost function and cancommunicate to her neighbors in some undirected graph. We consider adistributed communication-based gradient algorithm. For this procedure, weprove geometric convergence to a Nash equilibrium. In contrast to our previousworks [15], [16], where the proposed algorithms required two parameters to beset up and the analysis was based on a so called augmented game mapping, theprocedure in this work corresponds to a standard distributed gradient play and,thus, only one constant step size parameter needs to be chosen appropriately toguarantee fast convergence to a game solution. Moreover, we provide a rigorouscomparison between the convergence rate of the proposed distributed gradientplay and the rate of the GRANE algorithm presented in [15]. It allows us todemonstrate that the distributed gradient play outperforms the GRANE in termsof convergence speed.

Geometric Convergence of Distributed Gradient Play in Games with Unconstrained Action Sets