In this paper, the Nash equilibrium seeking issue for non-cooperative games with a coupled inequality constraint is investigated. In particular, there exists coupling between distinct decision variables of players in every cost function and the constrained inequality function. A distributed seeking algorithm with local information interaction is proposed. Specifically, a distributed observer with projection is first proposed such that the decision variables of all the other players can be estimated by every player. Next, by implementing these estimates, a seeking algorithm with projection is developed. In terms of a time-scale separation method, the stability analysis is performed. It is first shown that the distributed observer, as the fast dynamics, guarantees the estimation errors converging to an arbitrarily small neighborhood of the origin in finite time and maintaining within it afterwards. With this result, it is then shown that the seeking algorithm, as the slow dynamics, guarantees the strategy profiles converging to a neighborhood of the concerned generalized Nash equilibrium.
Distributed Nash Equilibrium Seeking for Non-Cooperative Games with a Coupled Inequality Constraint
Lect. Notes Electrical Eng.
2021-10-30
10 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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