288 research outputs found
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 for Stochastic Generalized Nash Equilibrium Problems
This work examines a stochastic formulation of the generalized Nash
equilibrium problem (GNEP) where agents are subject to randomness in the
environment of unknown statistical distribution. We focus on fully-distributed
online learning by agents and employ penalized individual cost functions to
deal with coupled constraints. Three stochastic gradient strategies are
developed with constant step-sizes. We allow the agents to use heterogeneous
step-sizes and show that the penalty solution is able to approach the Nash
equilibrium in a stable manner within , for small step-size
value and sufficiently large penalty parameters. The operation
of the algorithm is illustrated by considering the network Cournot competition
problem
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
Real and Complex Monotone Communication Games
Noncooperative game-theoretic tools have been increasingly used to study many
important resource allocation problems in communications, networking, smart
grids, and portfolio optimization. In this paper, we consider a general class
of convex Nash Equilibrium Problems (NEPs), where each player aims to solve an
arbitrary smooth convex optimization problem. Differently from most of current
works, we do not assume any specific structure for the players' problems, and
we allow the optimization variables of the players to be matrices in the
complex domain. Our main contribution is the design of a novel class of
distributed (asynchronous) best-response- algorithms suitable for solving the
proposed NEPs, even in the presence of multiple solutions. The new methods,
whose convergence analysis is based on Variational Inequality (VI) techniques,
can select, among all the equilibria of a game, those that optimize a given
performance criterion, at the cost of limited signaling among the players. This
is a major departure from existing best-response algorithms, whose convergence
conditions imply the uniqueness of the NE. Some of our results hinge on the use
of VI problems directly in the complex domain; the study of these new kind of
VIs also represents a noteworthy innovative contribution. We then apply the
developed methods to solve some new generalizations of SISO and MIMO games in
cognitive radios and femtocell systems, showing a considerable performance
improvement over classical pure noncooperative schemes.Comment: to appear on IEEE Transactions in Information Theor
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