729 research outputs found
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
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
Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part I: Nash Equilibria
In this two-parts paper we propose a decentralized strategy, based on a
game-theoretic formulation, to find out the optimal precoding/multiplexing
matrices for a multipoint-to-multipoint communication system composed of a set
of wideband links sharing the same physical resources, i.e., time and
bandwidth. We assume, as optimality criterion, the achievement of a Nash
equilibrium and consider two alternative optimization problems: 1) the
competitive maximization of mutual information on each link, given constraints
on the transmit power and on the spectral mask imposed by the radio spectrum
regulatory bodies; and 2) the competitive maximization of the transmission
rate, using finite order constellations, under the same constraints as above,
plus a constraint on the average error probability. In Part I of the paper, we
start by showing that the solution set of both noncooperative games is always
nonempty and contains only pure strategies. Then, we prove that the optimal
precoding/multiplexing scheme for both games leads to a channel diagonalizing
structure, so that both matrix-valued problems can be recast in a simpler
unified vector power control game, with no performance penalty. Thus, we study
this simpler game and derive sufficient conditions ensuring the uniqueness of
the Nash equilibrium. Interestingly, although derived under stronger
constraints, incorporating for example spectral mask constraints, our
uniqueness conditions have broader validity than previously known conditions.
Finally, we assess the goodness of the proposed decentralized strategy by
comparing its performance with the performance of a Pareto-optimal centralized
scheme. To reach the Nash equilibria of the game, in Part II, we propose
alternative distributed algorithms, along with their convergence conditions.Comment: Paper submitted to IEEE Transactions on Signal Processing, September
22, 2005. Revised March 14, 2007. Accepted June 5, 2007. To be published on
IEEE Transactions on Signal Processing, 2007. To appear on IEEE Transactions
on Signal Processing, 200
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