193 research outputs found
Linear convergence in time-varying generalized Nash equilibrium problems
We study generalized games with full row rank equality constraints and we
provide a strikingly simple proof of strong monotonicity of the associated KKT
operator. This allows us to show linear convergence to a variational
equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we
propose a fully-distributed algorithm with linear convergence guarantee for
aggregative games under partial-decision information. Based on these results,
we establish stability properties for online GNE seeking in games with
time-varying cost functions and constraints. Finally, we illustrate our
findings numerically on an economic dispatch problem for peer-to-peer energy
markets
On the linear convergence of distributed Nash equilibrium seeking for multi-cluster games under partial-decision information
This paper considers the distributed strategy design for Nash equilibrium
(NE) seeking in multi-cluster games under a partial-decision information
scenario. In the considered game, there are multiple clusters and each cluster
consists of a group of agents. A cluster is viewed as a virtual noncooperative
player that aims to minimize its local payoff function and the agents in a
cluster are the actual players that cooperate within the cluster to optimize
the payoff function of the cluster through communication via a connected graph.
In our setting, agents have only partial-decision information, that is, they
only know local information and cannot have full access to opponents'
decisions. To solve the NE seeking problem of this formulated game, a
discrete-time distributed algorithm, called distributed gradient tracking
algorithm (DGT), is devised based on the inter- and intra-communication of
clusters. In the designed algorithm, each agent is equipped with strategy
variables including its own strategy and estimates of other clusters'
strategies. With the help of a weighted Fronbenius norm and a weighted
Euclidean norm, theoretical analysis is presented to rigorously show the linear
convergence of the algorithm. Finally, a numerical example is given to
illustrate the proposed algorithm
Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks
We design the first fully-distributed algorithm for generalized Nash
equilibrium seeking in aggregative games on a time-varying communication
network, under partial-decision information, i.e., the agents have no direct
access to the aggregate decision. The algorithm is derived by integrating
dynamic tracking into a projected pseudo-gradient algorithm. The convergence
analysis relies on the framework of monotone operator splitting and the
Krasnosel'skii-Mann fixed-point iteration with errors.Comment: 14 pages, 4 figure
Single-timescale distributed GNE seeking for aggregative games over networks via forward-backward operator splitting
We consider aggregative games with affine coupling constraints, where agents
have partial information on the aggregate value and can only communicate with
neighbouring agents. We propose a single-layer distributed algorithm that
reaches a variational generalized Nash equilibrium, under constant step sizes.
The algorithm works on a single timescale, i.e., does not require multiple
communication rounds between agents before updating their action. The
convergence proof leverages an invariance property of the aggregate estimates
and relies on a forward-backward splitting for two preconditioned operators and
their restricted (strong) monotonicity properties on the consensus subspace.Comment: 8 pages, 8 figures, submitted to TA
Nash Equilibrium Seeking in N-Coalition Games via a Gradient-Free Method
This paper studies an -coalition non-cooperative game problem, where the
players in the same coalition cooperatively minimize the sum of their local
cost functions under a directed communication graph, while collectively acting
as a virtual player to play a non-cooperative game with other coalitions.
Moreover, it is assumed that the players have no access to the explicit
functional form but only the function value of their local costs. To solve the
problem, a discrete-time gradient-free Nash equilibrium seeking strategy, based
on the gradient tracking method, is proposed. Specifically, a gradient
estimator is developed locally based on Gaussian smoothing to estimate the
partial gradients, and a gradient tracker is constructed locally to trace the
average sum of the partial gradients among the players within the coalition.
With a sufficiently small constant step-size, we show that all players' actions
approximately converge to the Nash equilibrium at a geometric rate under a
strongly monotone game mapping condition. Numerical simulations are conducted
to verify the effectiveness of the proposed algorithm
Gradient-Free Nash Equilibrium Seeking in N-Cluster Games with Uncoordinated Constant Step-Sizes
In this paper, we consider a problem of simultaneous global cost minimization
and Nash equilibrium seeking, which commonly exists in -cluster
non-cooperative games. Specifically, the agents in the same cluster collaborate
to minimize a global cost function, being a summation of their individual cost
functions, and jointly play a non-cooperative game with other clusters as
players. For the problem settings, we suppose that the explicit analytical
expressions of the agents' local cost functions are unknown, but the function
values can be measured. We propose a gradient-free Nash equilibrium seeking
algorithm by a synthesis of Gaussian smoothing techniques and gradient
tracking. Furthermore, instead of using the uniform coordinated step-size, we
allow the agents across different clusters to choose different constant
step-sizes. When the largest step-size is sufficiently small, we prove a linear
convergence of the agents' actions to a neighborhood of the unique Nash
equilibrium under a strongly monotone game mapping condition, with the error
gap being propotional to the largest step-size and the smoothing parameter. The
performance of the proposed algorithm is validated by numerical simulations
Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens
We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We show that our method falls into the framework of singularly perturbed systems, as it involves the interconnection between a fast subsystem – the global information reconstruction dynamics – with a slow one concerning the optimization of the local strategies. This perspective plays a key role in analyzing the scheme with a constant stepsize, and in proving its linear convergence to the Nash equilibrium in strongly monotone games with local constraints. By exploiting the flexibility of our aggregative variable definition (not necessarily the arithmetic average of the agents’ strategy), we show the efficacy of our algorithm on a realistic voltage support case study for the smart grid
Tracking-based distributed equilibrium seeking for aggregative games
We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected pseudo-gradient descent and (ii) a tracking mechanism to locally reconstruct the aggregative variable. To handle coupling constraints arising in generalized settings, we propose another distributed algorithm based on (i) a recently emerged augmented primal-dual scheme and (ii) two tracking mechanisms to reconstruct, for each agent, both the aggregative variable and the coupling constraint satisfaction. Leveraging tools from singular perturbations analysis, we prove linear convergence to the Nash equilibrium for both schemes. Finally, we run extensive numerical simulations to confirm the effectiveness of our methods and compare them with state-of-the-art distributed equilibrium-seeking algorithms
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