arXiv subjects

Samson Lasaulce

Publications and source records attributed to Samson Lasaulce.

At least 73 records · Page 4Linked to original sources

arXiv2015

Composite charging games in networks of electric vehicles

An important scenario for smart grids which encompass distributed electrical networks is given by the simultaneous presence of aggregators and individual consumers. In this work, an aggregator is seen as an entity (a coalition) which is able to manage jointly the energy demand of a large group of consumers or users. More precisely, the demand consists in charging an electrical vehicle (EV) battery. The way the EVs user charge their batteries matters since it strongly impacts the network, especially the distribution network costs (e.g., in terms of Joule losses or transformer ageing). Since the charging policy is chosen by the users or the aggregators, the charging problem is naturally distributed. It turns out that one of the tools suited to tackle this heterogenous scenario has been introduced only recently namely, through the notion of composite games. This paper exploits for the first time in the literature of smart grids the notion of composite game and equilibrium. By assuming a rectangular charging profile for an EV, a composite equilibrium analysis is conducted, followed by a detailed analysis of a case study which assumes three possible charging periods or time-slots. Both the provided analytical and numerical results allow one to better understand the relationship between the size (which is a measure) of the coalition and the network sum-cost. In particular, a social dilemma, a situation where everybody prefers unilaterally defecting to cooperating, while the consequence is the worst for all, is exhibited.

cs.GT↗

arXiv2015

Charging Games in Networks of Electrical Vehicles

In this paper, a static non-cooperative game formulation of the problem of distributed charging in electrical vehicle (EV) networks is proposed. This formulation allows one to model the interaction between several EV which are connected to a common residential distribution transformer. Each EV aims at choosing the time at which it starts charging its battery in order to minimize an individual cost which is mainly related to the total power delivered by the transformer, the location of the time interval over which the charging operation is performed, and the charging duration needed for the considered EV to have its battery fully recharged. As individual cost functions are assumed to be memoryless, it is possible to show that the game of interest is always an ordinal potential game. More precisely, both an atomic and nonatomic versions of the charging game are considered. In both cases, equilibrium analysis is conducted. In particular, important issues such as equilibrium uniqueness and efficiency are tackled. Interestingly, both analytical and numerical results show that the efficiency loss due to decentralization (e.g., when cost functions such as distribution network Joule losses or life of residential distribution transformers when no thermal inertia is assumed) induced by charging is small and the corresponding "efficiency", a notion close to the Price of Anarchy, tends to one when the number of EV increases.

cs.GT↗

arXiv2015

Reducing the Impact of EV Charging Operations on the Distribution Network

A key assumption made in this paper is that electric vehicle (EV) battery charging profiles are rectangular. This requires a specific and new formulation of the charging problem, involving discrete action sets for the EVs in particular. The considered cost function comprises of three components: the distribution transformer aging, the distribution energy losses, and a component inherent to the EV itself (e.g., the battery charging monetary cost). Charging start times are determined by the proposed distributed algorithm, whose analysis is conducted by using game-theoretic tools such as ordinal potential games. Convergence of the proposed algorithm is shown to be guaranteed for some important special cases. Remarkably, the performance loss w.r.t. the centralized solution is shown to be small. Simulations, based on realistic public data, allow one to gain further insights on the issues of convergence and optimality loss and provide clear messages about the tradeoff associated with the presence of the three components in the considered cost function. While simulations show that the proposed charging policy performs quite similarly to existing (continuous) charging policies such as valley-filling-type solutions when the non-EV demand forecast is perfect, they reveal an additional asset of rectangular profiles in presence of forecasting errors.

math.OC↗

arXiv2015

Game Theory for Signal Processing in Networks

In this tutorial, the basics of game theory are introduced along with an overview of its most recent and emerging applications in signal processing. One of the main features of this contribution is to gather in a single paper some fundamental game-theoretic notions and tools which, over the past few years, have become widely spread over a large number of papers. In particular, both strategic-form and coalition-form games are described in details while the key connections and differences between them are outlined. Moreover, a particular attention is also devoted to clarify the connections between strategic-form games and distributed optimization and learning algorithms. Beyond an introduction to the basic concepts and main solution approaches, several carefully designed examples are provided to allow a better understanding of how to apply the described tools.

cs.GT↗

arXiv2015

Coordination in State-Dependent Distributed Networks: The Two-Agent Case

This paper addresses a coordination problem between two agents (Agents $1$ and $2$) in the presence of a noisy communication channel which depends on an external system state $\{x_{0,t}\}$. The channel takes as inputs both agents' actions, $\{x_{1,t}\}$ and $\{x_{2,t}\}$ and produces outputs that are observed strictly causally at Agent $2$ but not at Agent $1$. The system state is available either causally or non-causally at Agent $1$ but unknown at Agent $2$. Necessary and sufficient conditions on a joint distribution $\bar{Q}(x_0,x_1,x_2)$ to be implementable asymptotically (i.e, when the number of taken actions grows large) are provided for both causal and non-causal state information at Agent $1$. Since the coordination degree between the agents' actions, $x_{1,t}$ and $x_{2,t}$, and the system state $x_{0,t}$ is measured in terms of an average payoff function, feasible payoffs are fully characterized by implementable joint distributions. In this sense, our results allow us to derive the performance of optimal power control policies on an interference channel and to assess the gain provided by non-causal knowledge of the system state at Agent $1$. The derived proofs readily yield new results also for the problem of state-amplification under a causality constraint at the decoder.

cs.IT↗

arXiv2014

Implicit Coordination in Two-Agent Team Problems; Application to Distributed Power Allocation

The central result of this paper is the analysis of an optimization problem which allows one to assess the limiting performance of a team of two agents who coordinate their actions. One agent is fully informed about the past and future realizations of a random state which affects the common payoff of the agents whereas the other agent has no knowledge about the state. The informed agent can exchange his knowledge with the other agent only through his actions. This result is applied to the problem of distributed power allocation in a two-transmitter $M-$band interference channel, $M\geq 1$, in which the transmitters (who are the agents) want to maximize the sum-rate under the single-user decoding assumption at the two receivers; in such a new setting, the random state is given by the global channel state and the sequence of power vectors used by the informed transmitter is a code which conveys information about the channel to the other transmitter.

math.OC↗

arXiv2014

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.

cs.OH↗

arXiv2014

A Cross-Layer Approach for Distributed Energy-Efficient Power Control in Interference Networks

In contrast with existing works which rely on the same type of energy-efficiency measure to design distributed power control policies, the present work takes into account the presence of a finite packet buffer at the transmitter side and the impact of transport protocols. This approach is relevant when the transmitters have a non-zero energy cost even when the radiated power is zero. A generalized energy-efficiency performance metric integrating these features is constructed under two different scenarios in terms of transport layer protocols characterized by a constant or an adaptive packet arrival rate. The derived performance metric is shown to have several attractive properties in both scenarios, which ensures convergence of the used distributed power control algorithm to a unique point. This point is the Nash equilibrium of a game for which the equilibrium analysis is conducted. Although the equilibrium analysis methodology is not new in itself, conducting it requires several non-trivial proofs, including the proof of quasi-concavity of the payoff functions. A thorough numerical analysis is provided to illustrate the effects of the proposed approach, and provides several valuable insights in terms of designing interference management policies.

cs.NI↗

arXiv2014

Coded Power Control: Performance Analysis

In this paper, we introduce the general concept of coded power control (CPC) in a particular setting of the interference channel. Roughly, the idea of CPC consists in embedding information (about a random state) into the transmit power levels themselves: in this new framework, provided the power levels of a given transmitter can be observed (through a noisy channels) by other transmitters, a sequence of power levels of the former can therefore be used to coordinate the latter. To assess the limiting performance of CPC (and therefore the potential performance brought by this new approach), we derive, as a first step towards many extensions of the present work, a general result which not only concerns power control (PC) but also any scenario involving two decision-makers (DMs) which communicate through their actions and have the following information and decision structures. We assume that the DMs want to maximize the average of an arbitrarily chosen instantaneous payoff function which depends on the DMs' actions and the state realization. DM 1 is assumed to know non-causally the state (e.g., the channel state) which affects the common payoff while the other, say DM 2, has only a strictly causal knowledge of it. DM 1 can only use its own actions (e.g., power levels) to inform DM 2 about its best action in terms of payoff. Importantly, DM 2 can only monitor the actions of DM 1 imperfectly and DM 1 does not observe DM 2. The latter assumption leads us to exploiting Shannon-theoretic tools in order to generalize an existing theorem which provides the information constraint under which the payoff is maximized. The derived result is then exploited to fully characterize the performance of good CPC policies for a given instance of the interference channel.

cs.IT↗

arXiv2013

Stochastic Differential Games and Energy-Efficient Power Control

One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The players are the transmitters who adapt their power level to the quality of their time-varying link with the receiver, their battery level, and the strategy updates of the others. The proposed model not only allows one to take into account long-term strategic interactions but also long-term energy constraints. A simple sufficient condition for the existence of a Nash equilibrium in this game is provided and shown to be verified in a typical scenario. As the uniqueness and determination of equilibria are difficult issues in general, especially when the number of players goes large, we move to two special cases: the single player case which gives us some useful insights of practical interest and allows one to make connections with the case of large number of players. The latter case is treated with a mean-field game approach for which reasonable sufficient conditions for convergence and uniqueness are provided. Remarkably, this recent approach for large system analysis shows how scalability can be dealt with in large games and only relies on the individual state information assumption.

cs.NI↗

arXiv2013

Green Power Control in Cognitive Wireless Networks

A decentralized network of cognitive and non-cognitive transmitters where each transmitter aims at maximizing his energy-efficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their non-cognitive counterparts and the former have a cost for sensing. The Stackelberg equilibrium analysis of this $2-$level hierarchical game is conducted, which allows us to better understand the effects of cognition on energy-efficiency. In particular, it is proven that the network energy-efficiency is maximized when only a given fraction of terminals are cognitive. Then, we study a sensing game where all the transmitters are assumed to take the decision whether to sense (namely to be cognitive) or not. This game is shown to be a weighted potential game and its set of equilibria is studied. Playing the sensing game in a first phase (e.g., of a time-slot) and then playing the power control game is shown to be more efficient individually for all transmitters than playing a game where a transmitter would jointly optimize whether to sense and his power level, showing the existence of a kind of Braess paradox. The derived results are illustrated by numerical results and provide some insights on how to deploy cognitive radios in heterogeneous networks in terms of sensing capabilities. Keywords: Power Control, Stackelberg Equilibrium, Energy-Efficiency.

cs.IT↗

arXiv2013

Energy-Efficient Spectrum Sharing in Relay-Assisted Cognitive Radio Systems

This work characterizes an important solution concept of a relevant spectrum game. Two energy-efficient sources communicating with their respective destination compete for an extra channel brought by a relay charging the used bandwidth through a pricing mechanism. This game is shown to possess a unique Nash bargaining solution, exploiting a time-sharing argument. This Pareto-efficient solution can be implemented by using a distributed optimization algorithm for which each transmitter uses a simple gradient-type algorithm and alternately updates its spectrum sharing policy. Typical numerical results show to what extent spectral efficiency can be improved in a system involving selfish energy-efficient sources.

cs.IT↗

arXiv2013

Mean Field Energy Games in Wireless Networks

This work tackles the problem of energy-efficient distributed power control in wireless networks with a large number of transmitters. The problem is modeled by a dynamic game. Each transmitter-receiver communication is characterized by a state given by the available energy and/or the individual channel state and whose evolution is governed by certain dynamics. Since equilibrium analysis in such a (stochastic) game is generally difficult and even impossible, the problem is approximated by exploiting the large system assumption. Under an appropriate exchangeability assumption, the corresponding mean field game is well defined and studied in detail for special cases. The main contribution of this work is to show how mean field games can be applied to the problem under investigation and provide illustrative numerical results. Our results indicate that this approach can lead to significant gains in terms of energy-efficiency at the resulting equilibrium.

cs.IT↗

arXiv2012

Resilient Source Coding

This paper provides a source coding theorem for multi-dimensional information signals when, at a given instant, the distribution associated with one arbitrary component of the signal to be compressed is not known and a side information is available at the destination. This new framework appears to be both of information-theoretical and game-theoretical interest: it provides a new type of constraints to compress an information source; it is useful for designing certain types of mediators in games and characterize utility regions for games with signals. Regarding the latter aspect, we apply the derived source coding theorem to the prisoner's dilemma and the battle of the sexes.

cs.IT↗

arXiv2012

The price of re-establishing perfect, almost perfect or public monitoring in games with arbitrary monitoring

This paper establishes a connection between the notion of observation (or monitoring) structure in game theory and the one of communication channels in Shannon theory. One of the objectives is to know under which conditions an arbitrary monitoring structure can be transformed into a more pertinent monitoring structure. To this end, a mediator is added to the game. The objective of the mediator is to choose a signalling scheme that allows the players to have perfect, almost perfect or public monitoring and all of this, at a minimum cost in terms of signalling. Graph coloring, source coding, and channel coding are exploited to deal with these issues. A wireless power control game is used to illustrate these notions but the applicability of the provided results and, more importantly, the framework of transforming monitoring structures go much beyond this example.

cs.IT↗

arXiv2012

"To sense" or "not to sense" in energy-efficient power control games

A network of cognitive transmitters is considered. Each transmitter has to decide his power control policy in order to maximize energy-efficiency of his transmission. For this, a transmitter has two actions to take. He has to decide whether to sense the power levels of the others or not (which corresponds to a finite sensing game), and to choose his transmit power level for each block (which corresponds to a compact power control game). The sensing game is shown to be a weighted potential game and its set of correlated equilibria is studied. Interestingly, it is shown that the general hybrid game where each transmitter can jointly choose the hybrid pair of actions (to sense or not to sense, transmit power level) leads to an outcome which is worse than the one obtained by playing the sensing game first, and then playing the power control game. This is an interesting Braess-type paradox to be aware of for energy-efficient power control in cognitive networks.

cs.GT↗

arXiv2012

Implicit cooperation in distributed energy-efficient networks

We consider the problem of cooperation in distributed wireless networks of selfish and free transmitters aiming at maximizing their energy-efficiency. The strategy of each transmitter consists in choosing his power control (PC) policy. Two scenarios are considered: the case where transmitters can update their power levels within time intervals less than the channel coherence time (fast PC) and the case where it is updated only once per time interval (slow PC). One of our objectives is to show how cooperation can be stimulated without assuming cooperation links between the transmitters but only by repeating the corresponding PC game and by signals from the receiver. In order to design efficient PC policies, standard and stochastic repeated games are respectively exploited to analyze the fast and slow PC problems. In the first case a cooperation plan between transmitters, that is both efficient and relies on mild information assumptions, is proposed. In the second case, the region of equilibrium utilities is derived from very recent and powerful results in game theory.

cs.GT↗

arXiv2012

Transforming Monitoring Structures with Resilient Encoders. Application to Repeated Games

An important feature of a dynamic game is its monitoring structure namely, what the players effectively see from the played actions. We consider games with arbitrary monitoring structures. One of the purposes of this paper is to know to what extent an encoder, who perfectly observes the played actions and sends a complementary public signal to the players, can establish perfect monitoring for all the players. To reach this goal, the main technical problem to be solved at the encoder is to design a source encoder which compresses the action profile in the most concise manner possible. A special feature of this encoder is that the multi-dimensional signal (namely, the action profiles) to be encoded is assumed to comprise a component whose probability distribution is not known to the encoder and the decoder has a side information (the private signals received by the players when the encoder is off). This new framework appears to be both of game-theoretical and information-theoretical interest. In particular, it is useful for designing certain types of encoders that are resilient to single deviations and provide an equilibrium utility region in the proposed setting; it provides a new type of constraints to compress an information source (i.e., a random variable). Regarding the first aspect, we apply the derived result to the repeated prisoner's dilemma.

cs.IT↗