Distributed Nash Equilibrium Seeking Research Articles

Distributed Nash Equilibrium Seeking for Multiple Coalition Games by Coalition Estimate Strategies

Distributed Nash Equilibrium Seeking for Multiple Coalition Games by Coalition Estimate Strategies

Prescribed-time fully distributed Nash equilibrium seeking of nonlinear multi-agent systems over unbalanced digraphs

This paper investigates the prescribed-time fully distributed Nash equilibrium seeking (PT-FDNES) problem for nonlinear multi-agent systems (MASs) over weight-unbalanced directed graphs (digraphs). To counterbalance unweighted communication flows caused by the unbalanced network, the temporal transformation technique is first introduced to derive a consensus-based algorithm for calculating the left eigenvector of the Laplacian matrix, based on which a prescribed-time fully distributed estimator with adaptive gains is developed to obtain the NE without requiring any global information. By utilizing this NE estimator to formulate an intermediate control law, the NE seeking problem is then effectively transformed into a local reference-tracking problem. To deal with the non-differentiability issue caused by the NE estimator and ensure the exact tracking, the dynamic gain technique and novel scaling functions are employed to derive a prescribed-time tracking controller which completely compensates for the mismatched uncertainties while reducing the computational burden. The proposed control framework enables the actions of all agents to reach the NE within a prescribed time. In addition, the obtained results are further re-designed to exhibit the robustness by introducing an improved σ-modification scheme without sacrificing the convergence performance. Numerical examples are provided to demonstrate the validity of the theoretical results.

Time-Varying Group Formation Tracking for Multiagent Systems With Competition and Cooperation via Distributed Nash Equilibrium Seeking

Time-Varying Group Formation Tracking for Multiagent Systems With Competition and Cooperation via Distributed Nash Equilibrium Seeking

Distributed Nash equilibrium seeking for multi‐agent systems with uncertainty in the cost function

Distributed Nash equilibrium seeking for multi‐agent systems with uncertainty in the cost function

Utility Decoupling for Distributed Nash Equilibrium Seeking in Weakly Acyclic Games

Utility Decoupling for Distributed Nash Equilibrium Seeking in Weakly Acyclic Games

Distributed Nash equilibrium seeking in noncooperative game with partial decision information of neighbors.

In the real world, individuals may conceal some of their real decision information to their neighbors due to competition. It is a challenge to explore the distributed Nash equilibrium when individuals play the noncooperative game with partial decision information in complex networks. In this paper, we investigate the distributed Nash equilibrium seeking problem with partial decision information of neighbors. Specifically, we construct a two-layer network model, where players in the first layer engage in game interactions and players in the second layer exchange estimations of real actions with each other. We also consider the case where the actions of some players remain unchanged due to the cost of updating or personal reluctance. By means of the Lyapunov function method and LaSalle's invariance principle, we obtain the sufficient conditions in which the consensus of individual actions and estimations can be achieved and the population actions can converge to the Nash equilibrium point. Furthermore, we investigate the case with switched topologies and derive the sufficient conditions for the convergence of individual actions to Nash equilibrium by the average dwell time method. Finally, we give numerical examples for cases of fixed and switched topologies to verify our theoretical results.

Robust distributed Nash equilibrium seeking for high-order systems with disturbances and coupling constraints

The objective of this article is to tackle the problem of distributed searching for generalized Nash equilibrium (GNE) for high-order multi-agent systems (MASs) that are subject to external disturbances and coupling constraints. To address disturbances and linear equality constraints while ensuring that high-order agents achieve the task of seeking a GNE, a novel approach has been developed that utilizes gradient descent algorithms, extended state observers, and state feedback control. By utilizing the proposed algorithm, the agents' behavior will ultimately converge to a small range around the GNE points. The proposed algorithm's effectiveness is validated through two numerical simulations.

A Collaborative Neurodynamic Optimization Approach to Distributed Nash-Equilibrium Seeking in Multicluster Games With Nonconvex Functions.

In this article, we propose a collaborative neurodynamic optimization (CNO) method for the distributed seeking of generalized Nash equilibriums (GNEs) in multicluster games with nonconvex functions. Based on an augmented Lagrangian function, we develop a projection neural network for the local search of GNEs, and its convergence to a local GNE is proven. We formulate a global optimization problem to which a global optimal solution is a high-quality local GNE, and we adopt a CNO approach consisting of multiple recurrent neural networks for scattering searches and a metaheuristic rule for reinitializing states. We elaborate on an example of a price-bidding problem in an electricity market to demonstrate the viability of the proposed approach.

Distributed Nash Equilibrium Seeking and Disturbance Rejection for High-Order Integrators Over Jointly Strongly Connected Switching Networks.

In this article, we study the problem of Nash equilibrium (NE) seeking of N -player games with high-order integrator agents over jointly strongly connected networks. The same problem was studied recently over static, undirected, and connected networks. Since a jointly strongly connected network can be directed and disconnected at every time instant, our result strictly includes the existing results as special cases. Moreover, in addition to some analytic conditions on the payoff functions, the existing results also rely on the satisfaction of an inequality involving some Lipschitz constant and the smallest nonzero eigenvalue of the Laplacian of the network graph. By adopting a different approach, our result does not rely on the satisfaction of this inequality. Furthermore, our result can also be extended to the case where the additive disturbances are imposed on the input of each agent. Our design is illustrated by two numerical examples.

A timestamp-based log-linear algorithm for solving locally-informed multi-agent finite games

In this paper, the distributed Nash equilibrium seeking problem for multi-agent finite games is considered. Considering the locally-informed communication structure, previous centralized game-theoretic learning dynamic methods are not feasible. To this end, we propose a distributed log-linear algorithm by introducing a timestamp-based communication mechanism that enables agents to acquire estimates of the true action profile from their neighborhoods. It is shown that the proposed distributed log-linear algorithm significantly outperforms the existing best response dynamics regarding both effectiveness and reliability. For illustration, a locally-informed multi-player Sudoku puzzle is introduced, where each cell is taken as a player, and each player fills numbers only based on the local information of its neighboring players. The simulation results validate the effectiveness of our algorithm in solving the locally-informed multi-player Sudoku puzzle. Our methodology provides a viable and benchmark approach to address the fully distributed locally-informed multi-agent joint decision-making problem.

Distributed Nash Equilibrium Seeking Dynamics With Discrete Communication.

In this brief, we aim to provide a distributed Nash equilibrium seeking algorithm in continuous time with discrete communications. A group of agents are considered playing a continuous-kernel noncooperative game over a network. The agents need to seek the Nash equilibrium when each player cannot get the overall action profiles in real time, rather are only able to get information from its networked neighbors. Meanwhile, a continuous-time dynamics is discussed for the players to update their variables, but the communications over the network are only assumed to allow at discrete-time instants, since continuous-time communications are prohibitive and cumbersome in practice. First, the periodic communication is considered at a fixed interval, and the solvability of Nash equilibrium seeking is shown with discrete communications. Then, an event-trigger communication scheme is proposed to further reduce the communication rounds. Nevertheless, the event-trigger communication scheme requires each player continuously monitoring its local states. To alleviate the monitoring burden, a periodic event detection mechanism is further developed. The exponential convergence of the dynamics with the three discrete communication schemes is proven. Finally, the comparative simulation studies are designed to illustrate the algorithm performance with different communication schemes and parameter settings.

Distributed Nash equilibrium seeking with stochastic event-triggered mechanism

In this paper, we study the problem of consensus-based distributed Nash equilibrium (NE) seeking in a network of players represented as a directed graph, where each player aims to minimize their own local cost functions non-cooperatively. To address bandwidth constraints and limited energy, we propose a stochastic event-triggered algorithm that triggers individual players with a probability depending on certain events, thus enhancing communication efficiency through reduced continuous communication. We prove that our developed event-triggered algorithm achieves exponential convergence to the exact NE when the underlying communication graph is strongly connected. Furthermore, we establish that our proposed event-triggered communication scheme does not exhibit Zeno behavior. Finally, through numerical simulations of a spectrum access game and comparisons with existing event-triggered methods, we demonstrate the effectiveness of our proposed algorithm.

Distributed Nash Equilibrium Seeking With Dynamics Subject to Disturbance of Unknown Frequencies Over Jointly Strongly Connected Switching Networks

In this paper, we study the problem of distributed Nash equilibrium seeking of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -player games with single integrator dynamics subject to disturbances generated by an uncertain exosystem. Similar problems have been studied for games with single integrator dynamics subject to disturbances generated by a known exosystem. In addition, this paper offers some other new features. First, the existing results only apply to static, connected, and undirected graphs while the result of this paper applies to jointly strongly connected switching graphs, which can be disconnected at every time instant. Second, the existing results are asymptotic or ultimately uniformly bounded, while our result guarantees the exponential convergence when the exosystem is known. Third, the validity of existing results relies on an inequality involving some Lipschitz constant and the smallest nonzero eigenvalue of the Laplacian of the network graph. In contrast, the result of this paper is unconditional other than satisfying the same assumptions on the cost functions as those in the literature. Our design is illustrated by an application to velocity-actuated robots in sensor networks.

Distributed Nash Equilibrium Seeking for Multicluster Aggregative Game of Euler-Lagrange Systems With Coupled Constraints.

This article considers the distributed Nash equilibrium seeking problem of a multicluster aggregative game subject to local set constraints, consensus constraints in the same cluster, and coupled linear equality and nonlinear inequality constraints among all clusters. In the considered game, each cluster is composed of a group of players formulated by uncertain Euler-Lagrange (EL) dynamics, and its objective is to minimize its own cost function, which is the sum of the local functions of all players in the cluster. The local cost function of each player depends on its own decision and an aggregate of the decisions of all the players. An adaptive continuous-time distributed strategy is developed for uncertain EL systems to reach the generalized Nash equilibrium (GNE) of multicluster aggregative game. In particular, a new auxiliary system is synthesized using a projection operator, gradient descent, and dynamic average consensus to estimate the GNE. Based on the outputs of the auxiliary system, an adaptive tracking algorithm is developed for an EL system with uncertain parameters. Using the Lyapunov stability theory, it is shown that the developed distributed strategy achieves accurate convergence to the GNE. Finally, a numerical example is presented to demonstrate the theoretical results.

Distributed Nash Equilibrium Seeking in Strongly Contractive Aggregative Population Games

Distributed Nash Equilibrium Seeking in Strongly Contractive Aggregative Population Games

Distributed Nash Equilibrium Seeking in Merely Monotone Games Using an Event- and Switching-Activated Communication Scheme

Distributed Nash Equilibrium Seeking in Merely Monotone Games Using an Event- and Switching-Activated Communication Scheme

Prescribed-Time Fully Distributed Nash Equilibrium Seeking Strategy in Networked Games

Prescribed-Time Fully Distributed Nash Equilibrium Seeking Strategy in Networked Games

Distributed Nash Equilibrium Seeking for a Class of Uncertain Nonlinear Systems subject to Bounded Disturbances

Distributed Nash Equilibrium Seeking for a Class of Uncertain Nonlinear Systems subject to Bounded Disturbances

Distributed Nash Equilibrium Seeking for Constrained Multi-Cluster Games of Second-Order Nonlinear Multi-Agent Systems

Distributed Nash Equilibrium Seeking for Constrained Multi-Cluster Games of Second-Order Nonlinear Multi-Agent Systems

Distributed Nash Equilibrium Seeking for Multi-Cluster Game of Second-Order Nonlinear Systems With Partial Information

Distributed Nash Equilibrium Seeking for Multi-Cluster Game of Second-Order Nonlinear Systems With Partial Information