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Methodologies for analyzing equilibria in wireless games
 IEEE Signal Processing Magazine, Special issue on Game Theory for Signal Processing
, 2009
"... Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure s ..."
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Cited by 48 (25 self)
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Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide nonexhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection and efficiency.
A repeated game formulation of energyefficient decentralized power control
 IEEE TRANS. ON WIRELESS COMMUNICATIONS
, 2010
"... Decentralized multiple access channels where each transmitter wants to selfishly maximize his transmission energyefficiency are considered. Transmitters are assumed to choose freely their power control policy and interact (through multiuser interference) several times. It is shown that the correspo ..."
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Cited by 18 (7 self)
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Decentralized multiple access channels where each transmitter wants to selfishly maximize his transmission energyefficiency are considered. Transmitters are assumed to choose freely their power control policy and interact (through multiuser interference) several times. It is shown that the corresponding conflict of interest can have a predictable outcome, namely a finitely or discounted repeated game equilibrium. Remarkably, it is shown that this equilibrium is Paretoefficient under reasonable sufficient conditions and the corresponding decentralized power control policies can be implemented under realistic information assumptions: only individual channel state information and a public signal are required to implement the equilibrium strategies. Explicit equilibrium conditions are derived in terms of minimum number of game stages or maximum discount factor. Both analytical and simulation results are provided to compare the performance of the proposed power control policies with those already existing and exploiting the same information assumptions namely, those derived for the oneshot and Stackelberg games.
HOW CAN IGNORANT BUT PATIENT COGNITIVE TERMINALS LEARN THEIR STRATEGY AND UTILITY?
"... This paper aims to contribute to bridge the gap between existing theoretical results in distributed radio resource allocation policies based on equilibria in games (assuming complete information and rational players) and practical design of signal processing algorithms for selfconfiguring wireless ..."
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Cited by 7 (5 self)
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This paper aims to contribute to bridge the gap between existing theoretical results in distributed radio resource allocation policies based on equilibria in games (assuming complete information and rational players) and practical design of signal processing algorithms for selfconfiguring wireless networks. For this purpose, the framework of learning theory in games is exploited. Here, a new learning algorithm based on mild information assumptions at the transmitters is presented. This algorithm possesses attractive convergence properties not available for standard reinforcement learning algorithms and in addition, it allows each transmitter to learn both its optimal strategy and the values of its expected utility for all its actions. A detailed convergence analysis is conducted. In particular, a framework for studying heterogeneous wireless networks where transmitters do not learn at the same rate is provided. The proposed algorithm, which can be applied to any wireless network verifying the information assumptions stated, is applied to the case of multiple access channels in order to provide some numerical results. 1.
Dynamic power allocation games in parallel multiple access channels
 in ValueTools ’11: ACM Proceedings of the 5th International Conference on Performance Evaluation Methodologies and Tools
, 2011
"... Abstract. We analyze the distributed power allocation problem in parallel multiple access channels (MAC) by studying an associated noncooperative game which admits an exact potential function. Even though games of this type have been the subject of considerable study in the literature [1–4], we fin ..."
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Cited by 7 (6 self)
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Abstract. We analyze the distributed power allocation problem in parallel multiple access channels (MAC) by studying an associated noncooperative game which admits an exact potential function. Even though games of this type have been the subject of considerable study in the literature [1–4], we find that the sufficient conditions which ensure uniqueness of Nash equilibrium points typically do not hold in this context. Nonetheless, we show that the parallel MAC game admits a unique equilibrium almost surely, thus establishing an important class of counterexamples where these sufficient conditions are not necessary. Furthermore, if the network’s users employ a distributed learning scheme based on the replicator dynamics, we show that they converge to equilibrium from almost any initial condition, even though users only have local information at their disposal. 1.
A Bayesian GameTheoretic Approach for Distributed Resource Allocation in Fading Multiple Access Channels
"... A Bayesian gametheoretic model is developed to design and analyze the resource allocation problem in Kuser fading multiple access channels (MAC), where users are assumed to selfishly maximize their average achievable rates with incomplete information about the fading channel gains. In such a game ..."
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Cited by 6 (4 self)
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A Bayesian gametheoretic model is developed to design and analyze the resource allocation problem in Kuser fading multiple access channels (MAC), where users are assumed to selfishly maximize their average achievable rates with incomplete information about the fading channel gains. In such a gametheoretic study, the central question is whether a Bayesian equilibrium exists, and if so, whether the network operates efficiently at the equilibrium point. We prove that there exists exactly one Bayesian equilibrium in our game. Furthermore, we study the network sumrate maximization problem by assuming that users coordinate to the symmetric strategy profile. This result also serves as an upper bound for the Bayesian equilibrium. Finally, simulation results are provided to show the network efficiency at the unique Bayesian equilibrium, and compare it with other strategies.
Cooperative resource allocation games under spectral mask and total power constraints
 IEEE Trans. Signal Process
, 2010
"... Abstract—Resource allocation problems in multiuser systems, modeled as Nash bargaining (NB) cooperative games, are investigated under different constraints. Using the joint time division multiplexing and frequency division multiplexing (TDM/FDM) scheme as a manner of cooperation in the NB resource ..."
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Cited by 4 (3 self)
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Abstract—Resource allocation problems in multiuser systems, modeled as Nash bargaining (NB) cooperative games, are investigated under different constraints. Using the joint time division multiplexing and frequency division multiplexing (TDM/FDM) scheme as a manner of cooperation in the NB resource allocation game with only spectrum mask constraints (SMCs), it is shown that the efficiency of the corresponding solution depends on both the interferencetosignal and interferencetonoise ratios of the users. Sufficient conditions under which the joint TDM/FDM based NB solution outperforms a noncooperative Nash equilibrium solution are derived and shown to be mild. A semidistributed algorithm is proposed for finding the NB solution of the corresponding game with SMCs only. The NB based resource allocation game with both SMCs and total power constraints (TPCs) is shown to be a nonconvex optimization problem of high complexity. For such a game, a classification of twouser systems into bandwidth and powerdominant systems is proposed based on the concept of Paretooptimality. This classification gives insights to the resource allocation problem by showing that the benefits of both users are guaranteed to increase simultaneously only when the dominant resource in the system increases. Using this classification, efficient suboptimal algorithms of low complexity are derived based on the idea of optimally allocating the dominant resource and suboptimally allocating the other resource. Simulation results demonstrate the efficiency of the proposed cooperative NB resource allocation strategies. Index Terms—Cooperative games, multiuser systems, Nash bargaining, Paretooptimality, spectral mask constraints, total power constraints. I.
Game Theoretic Approaches to Spectrum Sharing in Decentralized SelfConfiguring Networks
, 2012
"... ..."
KPlayer Bayesian Waterfilling Game for Fading Multiple Access Channels
 3RD IEEE INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTISENSOR ADAPTIVE PROCESSING, NETHERLANDS
, 2009
"... We present a Bayesian gametheoretic approach for the distributed resource allocation problem in the context of Kuser fading multiple access channels (MAC). We assume that users have incomplete information about the channel state information (CSI), i.e., each user knows his own channel state, but d ..."
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Cited by 2 (1 self)
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We present a Bayesian gametheoretic approach for the distributed resource allocation problem in the context of Kuser fading multiple access channels (MAC). We assume that users have incomplete information about the channel state information (CSI), i.e., each user knows his own channel state, but does not know the states of other users. All users (transmitters) are considered to be rational, selfish, and each one carries the objective of maximizing its own achievable data rate. In such a gametheoretic study, the central question is whether a Bayesian equilibrium (BE) exists. Based on the assumption of two channel states, we prove that there exists exactly one BE in this game.
Green Power Control in Cognitive Wireless Networks
, 2013
"... Abstract—A decentralized network of cognitive and noncognitive transmitters where each transmitter aims at maximizing his energyefficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their noncognitive counterparts and the former have a cost for s ..."
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Abstract—A decentralized network of cognitive and noncognitive transmitters where each transmitter aims at maximizing his energyefficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their noncognitive 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 energyefficiency. In particular, it is proven that the network energyefficiency 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 timeslot) 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. Index Terms—Power Control, Stackelberg Equilibrium, EnergyEfficiency.