17,232 research outputs found
Decentralized Protection Strategies against SIS Epidemics in Networks
Defining an optimal protection strategy against viruses, spam propagation or
any other kind of contamination process is an important feature for designing
new networks and architectures. In this work, we consider decentralized optimal
protection strategies when a virus is propagating over a network through a SIS
epidemic process. We assume that each node in the network can fully protect
itself from infection at a constant cost, or the node can use recovery
software, once it is infected.
We model our system using a game theoretic framework and find pure, mixed
equilibria, and the Price of Anarchy (PoA) in several network topologies.
Further, we propose both a decentralized algorithm and an iterative procedure
to compute a pure equilibrium in the general case of a multiple communities
network. Finally, we evaluate the algorithms and give numerical illustrations
of all our results.Comment: accepted for publication in IEEE Transactions on Control of Network
System
Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings
We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings. The results presented in this paper can be considered as a generalization of some known results due to Wang et al. (2010)
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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