6 research outputs found
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 for Energy Sharing Games
With the proliferation of distributed generators and energy storage systems,
traditional passive consumers in power systems have been gradually evolving
into the so-called "prosumers", i.e., proactive consumers, which can both
produce and consume power. To encourage energy exchange among prosumers, energy
sharing is increasingly adopted, which is usually formulated as a generalized
Nash game (GNG). In this paper, a distributed approach is proposed to seek the
Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we
convert the GNG into an equivalent optimization problem. A
Krasnosel'ski{\v{i}}-Mann iteration type algorithm is thereby devised to solve
the problem and consequently find the GNE in a distributed manner. The
convergence of the proposed algorithm is proved rigorously based on the
nonexpansive operator theory. The performance of the algorithm is validated by
experiments with three prosumers, and the scalability is tested by simulations
using 123 prosumers
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