548 research outputs found
A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games
We address the generalized aggregative equilibrium seeking problem for
noncooperative agents playing average aggregative games with affine coupling
constraints. First, we use operator theory to characterize the generalized
aggregative equilibria of the game as the zeros of a monotone set-valued
operator. Then, we massage the Douglas-Rachford splitting to solve the monotone
inclusion problem and derive a single layer, semi-decentralized algorithm whose
global convergence is guaranteed under mild assumptions. The potential of the
proposed Douglas-Rachford algorithm is shown on a simplified resource
allocation game, where we observe faster convergence with respect to
forward-backward algorithms.Comment: arXiv admin note: text overlap with arXiv:1803.1044
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
Towards time-varying proximal dynamics in Multi-Agent Network Games
Distributed decision making in multi-agent networks has recently attracted
significant research attention thanks to its wide applicability, e.g. in the
management and optimization of computer networks, power systems, robotic teams,
sensor networks and consumer markets. Distributed decision-making problems can
be modeled as inter-dependent optimization problems, i.e., multi-agent
game-equilibrium seeking problems, where noncooperative agents seek an
equilibrium by communicating over a network. To achieve a network equilibrium,
the agents may decide to update their decision variables via proximal dynamics,
driven by the decision variables of the neighboring agents. In this paper, we
provide an operator-theoretic characterization of convergence with a
time-invariant communication network. For the time-varying case, we consider
adjacency matrices that may switch subject to a dwell time. We illustrate our
investigations using a distributed robotic exploration example.Comment: 6 pages, 3 figure
Distributed strategy-updating rules for aggregative games of multi-integrator systems with coupled constraints
In this paper, we explore aggregative games over networks of multi-integrator
agents with coupled constraints. To reach the general Nash equilibrium of an
aggregative game, a distributed strategy-updating rule is proposed by a
combination of the coordination of Lagrange multipliers and the estimation of
the aggregator. Each player has only access to partial-decision information and
communicates with his neighbors in a weight-balanced digraph which
characterizes players' preferences as to the values of information received
from neighbors. We first consider networks of double-integrator agents and then
focus on multi-integrator agents. The effectiveness of the proposed
strategy-updating rules is demonstrated by analyzing the convergence of
corresponding dynamical systems via the Lyapunov stability theory, singular
perturbation theory and passive theory. Numerical examples are given to
illustrate our results.Comment: 9 pages, 4 figure
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