Distributed Nash Equilibrium Seeking in Strongly Contractive Aggregative Population Games
Juan Martinez-Piazuelo, Carlos Ocampo‐Martínez, Nicanor Quijano
Abstract
This paper addresses the problem of distributed Nash equilibrium (NE) seeking in strongly contractive aggregative multi-population games subject to partial-decision information. In particular, we consider the scenario where the so-called payoff providers of the multiple populations communicate through a possibly non-complete network, and we formulate some consensus-like dynamics for the payoff providers to distributedly compute their payoff signals using local information only. Moreover, by exploiting the notions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> -passivity and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> -antipassivity, we provide a unified analysis for several classes of evolutionary game dynamics. As the main contributions, we provide sufficient conditions to guarantee the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> -antipassivity of a class of continuous-time dynamical systems, and we exploit such results to design distributed NE seeking dynamics for strongly contractive aggregative population games, as well as for a class of merely contractive aggregative population games. To the best of our knowledge, this is the first paper to consider the problem of distributed NE seeking for such classes of population games and from a unifying passivity-based perspective.