155 research outputs found
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
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
Distributed averaging integral Nash equilibrium seeking on networks
Continuous-time gradient-based Nash equilibrium seeking algorithms enjoy a
passivity property under a suitable monotonicity assumption. This feature has
been exploited to design distributed algorithms that converge to Nash
equilibria and use local information only. We further exploit the passivity
property to interconnect the algorithms with distributed averaging integral
controllers that tune on-line the weights of the communication graph. The main
advantage is to guarantee convergence to a Nash equilibrium without requiring a
strong coupling condition on the algebraic connectivity of the communication
graph over which the players exchange information, nor a global high-gain
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 and Wardrop equilibria in aggregative games with coupling constraints
We consider the framework of aggregative games, in which the cost function of
each agent depends on his own strategy and on the average population strategy.
As first contribution, we investigate the relations between the concepts of
Nash and Wardrop equilibrium. By exploiting a characterization of the two
equilibria as solutions of variational inequalities, we bound their distance
with a decreasing function of the population size. As second contribution, we
propose two decentralized algorithms that converge to such equilibria and are
capable of coping with constraints coupling the strategies of different agents.
Finally, we study the applications of charging of electric vehicles and of
route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The
first three authors contributed equall
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