Paper Info
Title
Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes
Abstract
In this paper, we propose non-model-based strategies for locally stable convergence to Nash equilibrium in quadratic noncooperative games where acquisition of information (of two different types) incurs delays. Two sets of results are introduced: (a) one, which we call cooperative scenario, where each player employs the knowledge of the functional form of his payoff and knowledge of other players' actions, but with delays; and (b) the second one, which we term the noncooperative scenario, where the players have access only to their own payoff values, again with delay. Both approaches are based on the extremum seeking perspective, which has previously been reported for real-time optimization problems by exploring sinusoidal excitation signals to estimate the Gradient (first derivative) and Hessian (second derivative) of unknown quadratic functions. In order to compensate distinct delays in the inputs of the players, we have employed predictor feedback. We apply a small-gain analysis as well as averaging theory in infinite dimensions, due to the infinite-dimensional state of the time delays, in order to obtain local convergence results for the unknown quadratic payoffs to a small neighborhood of the Nash equilibrium. We quantify the size of these residual sets and corroborate the theoretical results numerically on an example of a two-player game with delays.
Year
DOI
Venue
2021
10.1007/s10957-020-01757-z
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Keywords
DocType
Volume
Extremum seeking, Nash equilibrium, (Non)cooperative games, Time delays, Predictor feedback, Averaging in infinite dimensions
Journal
191
Issue
ISSN
Citations 
2-3
0022-3239
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Tiago Roux Oliveira18322.87
Victor Hugo Pereira Rodrigues200.68
Miroslav Krstic34987553.84
Tamer Basar43497402.11