857 research outputs found
Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control
This paper considers decentralized control and optimization methodologies for
large populations of systems, consisting of several agents with different
individual behaviors, constraints and interests, and affected by the aggregate
behavior of the overall population. For such large-scale systems, the theory of
aggregative and mean field games has been established and successfully applied
in various scientific disciplines. While the existing literature addresses the
case of unconstrained agents, we formulate deterministic mean field control
problems in the presence of heterogeneous convex constraints for the individual
agents, for instance arising from agents with linear dynamics subject to convex
state and control constraints. We propose several model-free feedback
iterations to compute in a decentralized fashion a mean field Nash equilibrium
in the limit of infinite population size. We apply our methods to the
constrained linear quadratic deterministic mean field control problem and to
the constrained mean field charging control problem for large populations of
plug-in electric vehicles.Comment: IEEE Trans. on Automatic Control (cond. accepted
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
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
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
Distributed Learning Policies for Power Allocation in Multiple Access Channels
We analyze the problem of distributed power allocation for orthogonal
multiple access channels by considering a continuous non-cooperative game whose
strategy space represents the users' distribution of transmission power over
the network's channels. When the channels are static, we find that this game
admits an exact potential function and this allows us to show that it has a
unique equilibrium almost surely. Furthermore, using the game's potential
property, we derive a modified version of the replicator dynamics of
evolutionary game theory which applies to this continuous game, and we show
that if the network's users employ a distributed learning scheme based on these
dynamics, then they converge to equilibrium exponentially quickly. On the other
hand, a major challenge occurs if the channels do not remain static but
fluctuate stochastically over time, following a stationary ergodic process. In
that case, the associated ergodic game still admits a unique equilibrium, but
the learning analysis becomes much more complicated because the replicator
dynamics are no longer deterministic. Nonetheless, by employing results from
the theory of stochastic approximation, we show that users still converge to
the game's unique equilibrium.
Our analysis hinges on a game-theoretical result which is of independent
interest: in finite player games which admit a (possibly nonlinear) convex
potential function, the replicator dynamics (suitably modified to account for
nonlinear payoffs) converge to an eps-neighborhood of an equilibrium at time of
order O(log(1/eps)).Comment: 11 pages, 8 figures. Revised manuscript structure and added more
material and figures for the case of stochastically fluctuating channels.
This version will appear in the IEEE Journal on Selected Areas in
Communication, Special Issue on Game Theory in Wireless Communication
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