Stochastic Nash Equilibrium Seeking for Games with General Nonlinear Payoffs

Liu, Shujun; Krstić, Miroslav

doi:10.1007/978-1-4471-4087-0_9

Cited by 1 publication

(2 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To address unknown gradients, the extremum seeking method was introduced (e.g., see References 15‐18). Following such a method, some Nash equilibrium seeking strategies have been reported (e.g., see References 13,14,19‐24 and references cited therein). The authors in References 13 and 14 employed the integrator‐type and discrete‐time extremum seeking schemes to design Nash equilibrium seeking strategies, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…The authors in References 13 and 14 employed the integrator‐type and discrete‐time extremum seeking schemes to design Nash equilibrium seeking strategies, respectively. The authors of Reference 19 provided a stochastic distributed algorithm for nonquadratic games based on the stochastic extremum seeking scheme. The authors in Reference 24 proposed an algorithm to seek the time‐varying Nash equilibrium by employing the time‐varying extremum seeking method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Consensus‐based and extremum seeking methods for distributed generalized nash equilibrium

Shao

Wang

et al. 2020

Optim Control Appl Methods

View full text Add to dashboard Cite

This article investigates the generalized Nash equilibrium (GNE) seeking for the game with equality constraints. Each player cannot directly access all the other player's actions and the gradients of all players' payoff functions are unknown. In these scenarios, an interesting question is under what distributed algorithm the GNE can be found. To address such games, we first design a two‐time‐scale distributed algorithm based on the extremum seeking method and consensus protocol. Then, by utilizing singular perturbation techniques and Lyapunov robust analysis, we show that the players' decisions can be regulated to an arbitrarily small neighborhood of the GNE. Moreover, we further consider the ideal case in which the gradients are known. In this case, the proposed strategy can be degenerated to a gradient‐based algorithm and the players' decisions exponentially converge to the GNE. Finally, two examples along with simulation results are used to illustrate the effectiveness of the proposed algorithms.

show abstract