74 research outputs found
Understanding Game Theory via Wireless Power Control
In this lecture note, we introduce the basic concepts of game theory (GT), a
branch of mathematics traditionally studied and applied in the areas of
economics, political science, and biology, which has emerged in the last
fifteen years as an effective framework for communications, networking, and
signal processing (SP). The real catalyzer has been the blooming of all issues
related to distributed networks, in which the nodes can be modeled as players
in a game competing for system resources. Some relevant notions of GT are
introduced by elaborating on a simple application in the context of wireless
communications, notably the power control in an interference channel (IC) with
two transmitters and two receivers.Comment: Accepted for publication as lecture note in IEEE Signal Processing
Magazine, 13 pages, 4 figures. The results can be reproduced using the
following Matlab code: https://github.com/lucasanguinetti/ ln-game-theor
Optimal Pricing-Based Edge Computing Resource Management in Mobile Blockchain
As the core issue of blockchain, the mining requires solving a proof-of-work
puzzle, which is resource expensive to implement in mobile devices due to high
computing power needed. Thus, the development of blockchain in mobile
applications is restricted. In this paper, we consider the edge computing as
the network enabler for mobile blockchain. In particular, we study optimal
pricing-based edge computing resource management to support mobile blockchain
applications where the mining process can be offloaded to an Edge computing
Service Provider (ESP). We adopt a two-stage Stackelberg game to jointly
maximize the profit of the ESP and the individual utilities of different
miners. In Stage I, the ESP sets the price of edge computing services. In Stage
II, the miners decide on the service demand to purchase based on the observed
prices. We apply the backward induction to analyze the sub-game perfect
equilibrium in each stage for uniform and discriminatory pricing schemes.
Further, the existence and uniqueness of Stackelberg game are validated for
both pricing schemes. At last, the performance evaluation shows that the ESP
intends to set the maximum possible value as the optimal price for profit
maximization under uniform pricing. In addition, the discriminatory pricing
helps the ESP encourage higher total service demand from miners and achieve
greater profit correspondingly.Comment: 7 pages, submitted to one conference. arXiv admin note: substantial
text overlap with arXiv:1710.0156
Robust Spectrum Sharing via Worst Case Approach
This paper considers non-cooperative and fully-distributed power-allocation
for secondary-users (SUs) in spectrum-sharing environments when
normalized-interference to each secondary-user is uncertain. We model each
uncertain parameter by the sum of its nominal (estimated) value and a bounded
additive error in a convex set, and show that the allocated power always
converges to its equilibrium, called robust Nash equilibrium (RNE). In the case
of a bounded and symmetric uncertainty set, we show that the power allocation
problem for each SU is simplified, and can be solved in a distributed manner.
We derive the conditions for RNE's uniqueness and for convergence of the
distributed algorithm; and show that the total throughput (social utility) is
less than that at NE when RNE is unique. We also show that for multiple RNEs,
the the social utility may be higher at a RNE as compared to that at the
corresponding NE, and demonstrate that this is caused by SUs' orthogonal
utilization of bandwidth for increasing the social utility. Simulations confirm
our analysis
Distributed cognitive radio systems with temperature-interference constraints and overlay scheme
Cognitive radio represents a promising paradigm to further increase transmission rates in wireless networks, as well as to facilitate the deployment of self-organized networks such as femtocells. Within this framework, secondary users (SU) may exploit the channel under the premise to maintain the quality of service (QoS) on primary users (PU) above a certain level. To achieve this goal, we present a noncooperative game where SU maximize their transmission rates, and may act as well as relays of the PU in order to hold their perceived QoS above the given threshold. In the paper, we analyze the properties of the game within the theory of variational inequalities, and provide an algorithm that converges to one Nash Equilibrium of the game. Finally, we present some simulations and compare the algorithm with another method that does not consider SU acting as relays
Worst-Case Robust Distributed Power Allocation in Shared Unlicensed Spectrum
This paper considers non-cooperative and fully-distributed power-allocation
for selfish transmitter-receiver pairs in shared unlicensed spectrum when
normalized-interference to each receiver is uncertain. We model each uncertain
parameter by the sum of its nominal (estimated) value and a bounded additive
error in a convex set, and show that the allocated power always converges to
its equilibrium, called robust Nash equilibrium (RNE). In the case of a bounded
and symmetric uncertainty region, we show that the power allocation problem for
each user is simplified, and can be solved in a distributed manner. We derive
the conditions for RNE's uniqueness and for convergence of the distributed
algorithm; and show that the total throughput (social utility) is less than
that at NE when RNE is unique. We also show that for multiple RNEs, the social
utility may be higher at a RNE as compared to that at the corresponding NE, and
demonstrate that this is caused by users' orthogonal utilization of bandwidth
at RNE. Simulations confirm our analysis
Achievability of Efficient Satisfaction Equilibria in Self-Configuring Networks
International audienceIn this paper, a behavioral rule that allows radio devices to achieve an efficient satisfaction equilibrium (ESE) in fully decentralized self-configuring networks (DSCNs) is presented. The relevance of ESE in the context of DSCNs is that at such state, radio devices adopt a transmission/receive configuration such that they are able to simultaneously satisfy their individual quality-of-service (QoS) constraints. An ESE is also an efficient network configuration, i.e., individual QoS satisfaction is achieved by investing the lowest possible effort. Here, the notion of effort refers to a preference each radio device independently establishes among its own set of actions. In particular, the proposed behavioral rule requires less information than existing rules, as in the case of the classical best response dynamics and its variants. Sufficient conditions for convergence are presented in a general framework. Numerical results are provided in the context of a particular uplink power control scenario, and convergence from any initial action profile to an ESE is formally proved in this scenario. This property ensures the proposed rule to be robust to the dynamic arrival or departure of radio devices in the network
On the convergence of stochastic forward-backward-forward algorithms with variance reduction in pseudo-monotone variational inequalities
International audienceWe develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities. Our method builds on Tseng's forward-backward-forward algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed with pseudo-monotone and Lipschitz continuous operators. The main computational advantage of Tseng's algorithm is that it relies only on a single projection step, and two independent queries of a stochastic oracle. Our algorithm incorporates a variance reduction mechanism, and leads to a.s. convergence to solutions of a merely pseudo-monotone stochastic variational inequality problem. To the best of our knowledge, this is the first stochastic algorithm achieving this by using only a single projection at each iteration
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