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We propose fully-distributed algorithms for Nash equilibrium seeking inaggregative games over networks. We first consider the case where localconstraints are present and we design an algorithm combining, for each agent,(i) the projected pseudo-gradient descent and (ii) a tracking mechanism tolocally reconstruct the aggregative variable. To handle coupling constraintsarising in generalized settings, we propose another distributed algorithm basedon (i) a recently emerged augmented primal-dual scheme and (ii) two trackingmechanisms to reconstruct, for each agent, both the aggregative variable andthe coupling constraint satisfaction. Leveraging tools from singularperturbations analysis, we prove linear convergence to the Nash equilibrium forboth schemes. Finally, we run extensive numerical simulations to confirm theeffectiveness of our methods and compare them with state-of-the-art distributedequilibrium-seeking algorithms.

Tracking-based distributed equilibrium seeking for aggregative games