224 research outputs found
Crawford-Sobel meet Lloyd-Max on the grid
The main contribution of this work is twofold. First, we apply, for the first
time, a framework borrowed from economics to a problem in the smart grid
namely, the design of signaling schemes between a consumer and an electricity
aggregator when these have non-aligned objectives. The consumer's objective is
to meet its need in terms of power and send a request (a message) to the
aggregator which does not correspond, in general, to its actual need. The
aggregator, which receives this request, not only wants to satisfy it but also
wants to manage the cost induced by the residential electricity distribution
network. Second, we establish connections between the exploited framework and
the quantization problem. Although the model assumed for the payoff functions
for the consumer and aggregator is quite simple, it allows one to extract
insights of practical interest from the analysis conducted. This allows us to
establish a direct connection with quantization, and more importantly, to open
a much more general challenge for source and channel coding.Comment: ICASSP 2014, 5 page
Quantification en présence de divergence d'intérêts : application aux réseaux d'électricité intelligents
National audienceMotivated by an application to smart grid, this paper generalizes the problem of scalar quantization in the case in which an agent, the consumer, determines the quantization cells and the other agent, the electrical network operator called aggregator, determines the representatives. We know that the standard quantization consists of two fictitious agents, which can be identified as a single one, minimizing the distorsion on the cells and on the representatives. In this paper, we consider a variation of that framework where the payoff functions maximized by the two agents are distincts. Their difference is called bias and implies a new strategic approach to the problem. Using tools from game theory, this work will highlight some key differences between the "strategic quantization" and the standard quantization, namely all communication ressources are not necessarily used, the bias between the payoffs has an influence on the quantity of exchanged information and the speed of convergence of methods analogous to the Llyod-Max algorithm in the strategic caseMotivé par une application issue des « Smart Grid », les « réseaux d'électricité intelligents », cet article généralise le problème de la quantification scalaire dans le cas où un agent, un consommateur, détermine les cellules de quantification et l'autre, un opérateur de réseau appelé agrégateur, les représentants. À la différence de la quantification classique où deux agents, fictifs et que l'on peut supposer ne faire qu'un, minimisent la distorsion sur les cellules et les représentants, les utilités maximisées ici par les deux agents sont distinctes. Leur différence est mesurée par un biais et va conduire à une réinterprétation stratégique du problème de quantification. Reprenant des outils de théorie des jeux, cet article va montrer quelques différences fondamentales entre le cas de la « quantification stratégique » et celui de la quantification classique : toutes les ressources de communication ne sont pas forcément utilisées, le biais entre utilité va fortement conditionner la quantité d'information échangée et la vitesse de convergence des méthodes analogues à l'algorithme de Lloyd-Max dans le cas stratégique
On the Number of Bins in Equilibria for Signaling Games
We investigate the equilibrium behavior for the decentralized quadratic cheap
talk problem in which an encoder and a decoder, viewed as two decision makers,
have misaligned objective functions. In prior work, we have shown that the
number of bins under any equilibrium has to be at most countable, generalizing
a classical result due to Crawford and Sobel who considered sources with
density supported on . In this paper, we refine this result in the
context of exponential and Gaussian sources. For exponential sources, a
relation between the upper bound on the number of bins and the misalignment in
the objective functions is derived, the equilibrium costs are compared, and it
is shown that there also exist equilibria with infinitely many bins under
certain parametric assumptions. For Gaussian sources, it is shown that there
exist equilibria with infinitely many bins.Comment: 25 pages, single colum
Spartan Daily, January 20, 1937
Volume 25, Issue 63https://scholarworks.sjsu.edu/spartandaily/2548/thumbnail.jp
Dynamic signaling games with quadratic criteria under Nash and Stackelberg equilibria
This paper considers dynamic (multi-stage) signaling games involving an encoder and a decoder who have subjective models on the cost functions. We consider both Nash (simultaneous-move) and Stackelberg (leader-follower) equilibria of dynamic signaling games under quadratic criteria. For the multi-stage scalar cheap talk, we show that the final stage equilibrium is always quantized and under further conditions the equilibria for all time stages must be quantized. In contrast, the Stackelberg equilibria are always fully revealing. In the multi-stage signaling game where the transmission of a Gauss-Markov source over a memoryless Gaussian channel is considered, affine policies constitute an invariant subspace under best response maps for Nash equilibria; whereas the Stackelberg equilibria always admit linear policies for scalar sources but such policies may be nonlinear for multi-dimensional sources. We obtain an explicit recursion for optimal linear encoding policies for multi-dimensional sources, and derive conditions under which Stackelberg equilibria are informative. (C) 2020 Elsevier Ltd. All rights reserved
Interference Coordination via Power Domain Channel Estimation
A novel technique is proposed which enables each transmitter to acquire
global channel state information (CSI) from the sole knowledge of individual
received signal power measurements, which makes dedicated feedback or
inter-transmitter signaling channels unnecessary. To make this possible, we
resort to a completely new technique whose key idea is to exploit the transmit
power levels as symbols to embed information and the observed interference as a
communication channel the transmitters can use to exchange coordination
information. Although the used technique allows any kind of {low-rate}
information to be exchanged among the transmitters, the focus here is to
exchange local CSI. The proposed procedure also comprises a phase which allows
local CSI to be estimated. Once an estimate of global CSI is acquired by the
transmitters, it can be used to optimize any utility function which depends on
it. While algorithms which use the same type of measurements such as the
iterative water-filling algorithm (IWFA) implement the sequential best-response
dynamics (BRD) applied to individual utilities, here, thanks to the
availability of global CSI, the BRD can be applied to the sum-utility.
Extensive numerical results show that significant gains can be obtained and,
this, by requiring no additional online signaling
Signaling Games in Multiple Dimensions: Geometric Properties of Equilibrium Solutions
Signaling game problems investigate communication scenarios where encoder(s)
and decoder(s) have misaligned objectives due to the fact that they either
employ different cost functions or have inconsistent priors. This problem has
been studied in the literature for scalar sources under various setups. In this
paper, we consider multi-dimensional sources under quadratic criteria in the
presence of a bias leading to a mismatch in the criteria, where we show that
the generalization from the scalar setup is more than technical. We show that
the Nash equilibrium solutions lead to structural richness due to the subtle
geometric analysis the problem entails, with consequences in both system
design, presence of linear Nash equilibria, and an information theoretic
problem formulation. We first provide a set of geometric conditions that needs
to be satisfied in equilibrium considering any multi-dimensional source. Then,
we consider independent and identically distributed sources and characterize
necessary and sufficient conditions under which an informative linear Nash
equilibrium exists. These conditions involve the bias vector that leads to
misaligned costs. Depending on certain conditions related to the bias vector,
the existence of linear Nash equilibria requires sources with a Gaussian or a
symmetric density. Moreover, in the case of Gaussian sources, our results have
a rate-distortion theoretic implication that achievable rates and distortions
in the considered game theoretic setup can be obtained from its team theoretic
counterpart.Comment: 16 pages and 4 figure
Quadratic Signaling Games with Channel Combining Ratio
In this study, Nash and Stackelberg equilibria of single-stage and multi-stage quadratic signaling games between an encoder and a decoder are investigated. In the considered setup, the objective functions of the encoder and the decoder are misaligned, there is a noisy channel between the encoder and the decoder, the encoder has a soft power constraint, and the decoder has also noisy observation of the source to be estimated. We show that there exist only linear encoding and decoding strategies at the Stackelberg equilibrium, and derive the equilibrium strategies and costs. Regarding the Nash equilibrium, we explicitly characterize affine equilibria for the single-stage setup and show that the optimal encoder (resp. decoder) is affine for an affine decoder (resp. encoder) for the multi-stage setup. On the decoder side, between the information coming from the encoder and noisy observation of the source, our results describe what should be the combining ratio of these two channels. Regarding the encoder, we derive the conditions under which it is meaningful to transmit a message
Quadratic Signaling Games with Channel Combining Ratio
In this study, Nash and Stackelberg equilibria of single-stage and
multi-stage quadratic signaling games between an encoder and a decoder are
investigated. In the considered setup, the objective functions of the encoder
and the decoder are misaligned, there is a noisy channel between the encoder
and the decoder, the encoder has a soft power constraint, and the decoder has
also noisy observation of the source to be estimated. We show that there exist
only linear encoding and decoding strategies at the Stackelberg equilibrium,
and derive the equilibrium strategies and costs. Regarding the Nash
equilibrium, we explicitly characterize affine equilibria for the single-stage
setup and show that the optimal encoder (resp. decoder) is affine for an affine
decoder (resp. encoder) for the multi-stage setup. For the decoder side,
between the information coming from the encoder and noisy observation of the
source, our results describe what should be the combining ratio of these two
channels. Regarding the encoder, we derive the conditions under which it is
meaningful to transmit a message.Comment: 19 pages, 2 figure
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