99 research outputs found
On the Nash Equilibria in Decentralized Parallel Interference Channels
In this paper, the 2-dimensional decentralized parallel interference channel
(IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static
game. Each transmitter is assumed to be a fully rational entity with complete
information on the game, aiming to maximize its own individual spectral
efficiency by tuning its own power allocation (PA) vector. Two scenarios are
analysed. First, we consider that transmitters can split their transmit power
between both dimensions (PA game). Second, we consider that each transmitter is
limited to use only one dimension (channel selection CS game). In the first
scenario, the game might have either one or three NE in pure strategies (PS).
However, two or infinitely many NE in PS might also be observed with zero
probability. In the second scenario, there always exists either one or two NE
in PS. We show that in both games there always exists a non-zero probability of
observing more than one NE. More interestingly, using Monte-Carlo simulations,
we show that the highest and lowest network spectral efficiency at any of the
NE in the CS game are always higher than the ones in the PA.Comment: 6 pages, 4 figures, presented in ICCC Kyoto 201
Noisy Channel-Output Feedback Capacity of the Linear Deterministic Interference Channel
In this paper, the capacity region of the two-user linear deterministic (LD)
interference channel with noisy output feedback (IC-NOF) is fully
characterized. This result allows the identification of several asymmetric
scenarios in which imple- menting channel-output feedback in only one of the
transmitter- receiver pairs is as beneficial as implementing it in both links,
in terms of achievable individual rate and sum-rate improvements w.r.t. the
case without feedback. In other scenarios, the use of channel-output feedback
in any of the transmitter-receiver pairs benefits only one of the two pairs in
terms of achievable individual rate improvements or simply, it turns out to be
useless, i.e., the capacity regions with and without feedback turn out to be
identical even in the full absence of noise in the feedback links.Comment: 5 pages, 9 figures, see proofs in V. Quintero, S. M. Perlaza, and
J.-M. Gorce, "Noisy channel-output feedback capacity of the linear
deterministic interference channel," INRIA, Tech. Rep. 456, Jan. 2015. This
was submitted and accepted in IEEE ITW 201
Satisfaction Equilibrium: A General Framework for QoS Provisioning in Self-Configuring Networks
This paper is concerned with the concept of equilibrium and quality of
service (QoS) provisioning in self-configuring wireless networks with
non-cooperative radio devices (RD). In contrast with the Nash equilibrium (NE),
where RDs are interested in selfishly maximizing its QoS, we present a concept
of equilibrium, named satisfaction equilibrium (SE), where RDs are interested
only in guaranteing a minimum QoS. We provide the conditions for the existence
and the uniqueness of the SE. Later, in order to provide an equilibrium
selection framework for the SE, we introduce the concept of effort or cost of
satisfaction, for instance, in terms of transmit power levels, constellation
sizes, etc. Using the idea of effort, the set of efficient SE (ESE) is defined.
At the ESE, transmitters satisfy their minimum QoS incurring in the lowest
effort. We prove that contrary to the (generalized) NE, at least one ESE always
exists whenever the network is able to simultaneously support the individual
QoS requests. Finally, we provide a fully decentralized algorithm to allow
self-configuring networks to converge to one of the SE relying only on local
information.Comment: Accepted for publication in Globecom 201
Modeling Noisy Feedback in Decentralized Self-Configuring Networks
This paper introduces a generalization of the notion of Nash equilibrium (NE), namely quantal response equilibrium (QRE). In the QRE, radio devices choose their transmit/receive configuration taking into account that the estimation of their own performance contains a noise component. Here, it is shown that the notion of QRE neatly models decentralized self-configuring networks (DCSN) where feedback messages are impaired by quantization noise or decoding errors. The main contribution of the paper is twofold. First, we show that under the presence of noise in the estimation expected utility, the notion of NE no longer holds, as players cannot be considered rational. Second, we introduce a learning technique that converges to a QRE in a fully decentralized fashion. We present numerical results in the context of a channel selection problem in a parallel multiple access channel in order to illustrate our theoretical results
Learning Equilibria with Partial Information in Decentralized Wireless Networks
In this article, a survey of several important equilibrium concepts for
decentralized networks is presented. The term decentralized is used here to
refer to scenarios where decisions (e.g., choosing a power allocation policy)
are taken autonomously by devices interacting with each other (e.g., through
mutual interference). The iterative long-term interaction is characterized by
stable points of the wireless network called equilibria. The interest in these
equilibria stems from the relevance of network stability and the fact that they
can be achieved by letting radio devices to repeatedly interact over time. To
achieve these equilibria, several learning techniques, namely, the best
response dynamics, fictitious play, smoothed fictitious play, reinforcement
learning algorithms, and regret matching, are discussed in terms of information
requirements and convergence properties. Most of the notions introduced here,
for both equilibria and learning schemes, are illustrated by a simple case
study, namely, an interference channel with two transmitter-receiver pairs.Comment: 16 pages, 5 figures, 1 table. To appear in IEEE Communication
Magazine, special Issue on Game Theor
Quality-Of-Service Provisioning in Decentralized Networks: A Satisfaction Equilibrium Approach
This paper introduces a particular game formulation and its corresponding
notion of equilibrium, namely the satisfaction form (SF) and the satisfaction
equilibrium (SE). A game in SF models the case where players are uniquely
interested in the satisfaction of some individual performance constraints,
instead of individual performance optimization. Under this formulation, the
notion of equilibrium corresponds to the situation where all players can
simultaneously satisfy their individual constraints. The notion of SE, models
the problem of QoS provisioning in decentralized self-configuring networks.
Here, radio devices are satisfied if they are able to provide the requested
QoS. Within this framework, the concept of SE is formalized for both pure and
mixed strategies considering finite sets of players and actions. In both cases,
sufficient conditions for the existence and uniqueness of the SE are presented.
When multiple SE exist, we introduce the idea of effort or cost of satisfaction
and we propose a refinement of the SE, namely the efficient SE (ESE). At the
ESE, all players adopt the action which requires the lowest effort for
satisfaction. A learning method that allows radio devices to achieve a SE in
pure strategies in finite time and requiring only one-bit feedback is also
presented. Finally, a power control game in the interference channel is used to
highlight the advantages of modeling QoS problems following the notion of SE
rather than other equilibrium concepts, e.g., generalized Nash equilibrium.Comment: Article accepted for publication in IEEE Journal on Selected Topics
in Signal Processing, special issue in Game Theory in Signal Processing. 16
pages, 6 figure
Leveraging Noisy Observations in Zero-Sum Games
This paper studies an instance of zero-sum games in which one player (the
leader) commits to its opponent (the follower) to choose its actions by
sampling a given probability measure (strategy). The actions of the leader are
observed by the follower as the output of an arbitrary channel. In response to
that, the follower chooses its action based on its current information, that
is, the leader's commitment and the corresponding noisy observation of its
action. Within this context, the equilibrium of the game with noisy action
observability is shown to always exist and the necessary conditions for its
uniqueness are identified. Interestingly, the noisy observations have important
impact on the cardinality of the follower's set of best responses. Under
particular conditions, such a set of best responses is proved to be a singleton
almost surely. The proposed model captures any channel noise with a density
with respect to the Lebesgue measure. As an example, the case in which the
channel is described by a Gaussian probability measure is investigated.Comment: This paper is submitted to the 2024 IEEE International Symposium on
Information Theory (ISIT 2024
Perfect Output Feedback in the Two-User Decentralized Interference Channel
In this paper, the -Nash equilibrium (-NE) region of the two-user
Gaussian interference channel (IC) with perfect output feedback is approximated
to within bit/s/Hz and arbitrarily close to bit/s/Hz. The
relevance of the -NE region is that it provides the set of rate-pairs
that are achievable and stable in the IC when both transmitter-receiver pairs
autonomously tune their own transmit-receive configurations seeking an
-optimal individual transmission rate. Therefore, any rate tuple outside
the -NE region is not stable as there always exists one link able to
increase by at least bits/s/Hz its own transmission rate by updating its
own transmit-receive configuration. The main insights that arise from this work
are: The -NE region achieved with feedback is larger than or equal
to the -NE region without feedback. More importantly, for each rate pair
achievable at an -NE without feedback, there exists at least one rate
pair achievable at an -NE with feedback that is weakly Pareto superior.
There always exists an -NE transmit-receive configuration that
achieves a rate pair that is at most bit/s/Hz per user away from the outer
bound of the capacity region.Comment: Revised version (Aug. 2015
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