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Competitive pricing for spectrum sharing in cognitive radio networks: Dynamic game, inefficiency of nash equilibrium, and collusion
 IEEE JSAC
"... Abstract—We address the problem of spectrum pricing in a cognitive radio network where multiple primary service providers compete with each other to offer spectrum access opportunities to the secondary users. By using an equilibrium pricing scheme, each of the primary service providers aims to maxim ..."
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Abstract—We address the problem of spectrum pricing in a cognitive radio network where multiple primary service providers compete with each other to offer spectrum access opportunities to the secondary users. By using an equilibrium pricing scheme, each of the primary service providers aims to maximize its profit under quality of service (QoS) constraint for primary users. We formulate this situation as an oligopoly market consisting of a few firms and a consumer. The QoS degradation of the primary services is considered as the cost in offering spectrum access to the secondary users. For the secondary users, we adopt a utility function to obtain the demand function. With a Bertrand game model, we analyze the impacts of several system parameters such as spectrum substitutability and channel quality on the Nash equilibrium (i.e., equilibrium pricing adopted by the primary services). We present distributed algorithms to obtain the solution for this dynamic game. The stability of the proposed dynamic game algorithms in terms of convergence to the Nash equilibrium is studied. However, the Nash equilibrium is not efficient in the sense that the total profit of the primary service providers is not maximized. An optimal solution to gain the highest total profit can be obtained. A collusion can be established among the primary services so that they gain higher profit than that for the Nash equilibrium. However, since one or more of the primary service providers may deviate from the optimal solution, a punishment mechanism may be applied to the deviating primary service provider. A repeated game among primary service providers is formulated to show that the collusion can be maintained if all of the primary service providers are aware of this punishment mechanism, and therefore, properly weight their profits to be obtained in the future. Index Terms—Spectrum sharing, cognitive radio, pricing scheme, game theory, Nash equilibrium, distributed adaptation, collusion. I.
Energyefficient resource allocation in wireless networks: An overview of gametheoretic approaches
 IEEE Signal Process. Magazine
, 2007
"... A gametheoretic model is proposed to study the crosslayer problem of joint power and rate control with quality of service (QoS) constraints in multipleaccess networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own ..."
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Cited by 25 (6 self)
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A gametheoretic model is proposed to study the crosslayer problem of joint power and rate control with quality of service (QoS) constraints in multipleaccess networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility while satisfying its QoS requirements. The user’s QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queuing delays. The utility function considered here measures energy efficiency and is particularly suitable for wireless networks with energy constraints. The Nash equilibrium solution for the proposed noncooperative game is derived and a closedform expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a “size ” for the user which is an indication of the amount of network resources consumed by the user. Using this competitive multiuser framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are studied. In addition, analytical expressions are given for users ’ delay profiles and the delay performance of the users at Nash equilibrium is quantified.
Coalition games with cooperative transmission: A cure for the curse of boundary nodes in selfish packetforwarding wireless networks
 IEEE Trans. Comm
, 2009
"... Abstract — In wireless packetforwarding networks with selfish nodes, applications of a repeated game can induce the nodes to forward each others ’ packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the ..."
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Cited by 20 (6 self)
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Abstract — In wireless packetforwarding networks with selfish nodes, applications of a repeated game can induce the nodes to forward each others ’ packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the other nodes do not depend on them. This problem is sometimes known as the curse of the boundary nodes. To overcome this problem, an approach based on coalition games is proposed, in which the boundary nodes can use cooperative transmission to help the backbone nodes in the middle of the network. In return, the backbone nodes are willing to forward the boundary nodes’ packets. The stability of the coalitions is studied using the concept of a core. Then two types of fairness, namely, the minmax fairness using nucleolus and the average fairness using the Shapley function are investigated. Finally, a protocol is designed using both repeated games and coalition games. Simulation results show how boundary nodes and backbone nodes form coalitions together according to different fairness criteria. The proposed protocol can improve the network connectivity by about 50%, compared with pure repeated game schemes. I.
Power Allocation Games for MIMO Multiple Access Channels with Coordination
, 2009
"... A game theoretic approach is used to derive the optimal decentralized power allocation (PA) in fast fading multiple access channels where the transmitters and receiver are equipped with multiple antennas. The players (the mobile terminals) are free to choose their PA in order to maximize their indiv ..."
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Cited by 15 (11 self)
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A game theoretic approach is used to derive the optimal decentralized power allocation (PA) in fast fading multiple access channels where the transmitters and receiver are equipped with multiple antennas. The players (the mobile terminals) are free to choose their PA in order to maximize their individual transmission rates (in particular they can ignore some specified centralized policies). A simple coordination mechanism between users is introduced. The nature and influence of this mechanism is studied in detail. The coordination signal indicates to the users the order in which the receiver applies successive interference cancellation and the frequency at which this order is used. Two different games are investigated: the users can either adapt their temporal PA to their decoding rank at the receiver or optimize their spatial PA between their transmit antennas. For both games a thorough analysis of the existence, uniqueness and sumrate efficiency of the network Nash equilibrium is conducted. Analytical and simulation results are provided to assess the gap between the decentralized network performance and its equivalent virtual multiple input multiple output system, which is shown to be zero in some cases and relatively small in general.
Introducing Hierarchy in Energy Games
, 2009
"... In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energyefficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energyefficiency ..."
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Cited by 14 (9 self)
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In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energyefficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energyefficiency. Specifically, we introduce hierarchy in two different ways: 1. Assuming singleuser decoding at the receiver, we investigate a Stackelberg formulation of the game where one user is the leader whereas the other users are assumed to be able to react to the leader’s decisions; 2. Assuming neither leader nor followers among the users, we introduce hierarchy by assuming successive interference cancellation at the receiver. It is shown that introducing a certain degree of hierarchy in noncooperative power control games not only improves the individual energy efficiency of all the users but can also be a way of insuring the existence of a nonsaturated equilibrium and reaching a desired tradeoff between the global network performance at the equilibrium and the requested amount of signaling. In this respect, the way of measuring the global performance of an energyefficient network is shown to be a critical issue.
Discrete power control: Cooperative and noncooperative optimization
 in INFOCOM
, 2007
"... Abstract — We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a ..."
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Cited by 13 (2 self)
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Abstract — We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. We consider two frameworks concerning the state information of the channels of other mobiles: (i) the case of full state information and (ii) the case of local state information. In each of the two frameworks, we consider both cooperative as well as noncooperative power control. We manage to characterize the structure of equilibria policies and, more generally, of bestresponse policies in the noncooperative case. We present an algorithm to compute equilibria policies in the case of two noncooperative players. Finally, we study the case where a malicious mobile, which also has average power constraints, tries to jam the communication of the other mobile. Our results are illustrated and validated through various numerical examples. I.
NonAtomic Games for MultiUser Systems
"... In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel ..."
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Cited by 11 (5 self)
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In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the matched filter, the MMSE filter and the optimum filter. The goal of this paper is to extend previous work, and to derive simple expressions for the noncooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of nonatomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows.
Distributed energy efficient spectrum access in cognitive radio wireless ad hoc networks," CebCom
 Director of Advanced Telecommunications Institute, Stevens Institute of Technology (19841998); Member, Technology Staff in COMSAT (currently Lockheed Martin) Laboratories (198184) and Network Analysis Corporation (CONTEL) (197981); Research Associate i
, 2005
"... Abstract—In this paper, energy efficient spectrum access is considered for a wireless cognitive radio ad hoc network, where each node is equipped with cognitive radio, has limited energy, and the network is an OFDMA system operating on time slots. In each slot, the users with new traffic demand will ..."
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Cited by 8 (0 self)
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Abstract—In this paper, energy efficient spectrum access is considered for a wireless cognitive radio ad hoc network, where each node is equipped with cognitive radio, has limited energy, and the network is an OFDMA system operating on time slots. In each slot, the users with new traffic demand will sense the spectrum and locate the available subcarrier set. Given the data rate requirement and maximal power limit, a constrained optimization problem is formulated for each individual user to minimize the energy consumption per bit over all selected subcarriers, while avoid introducing harmful interference to the existing users. Because of the multidimensional and nonconvex nature of the problem, a fully distributed subcarrier selection and power allocation algorithm is proposed by combining an unconstrained optimization method with a constrained partitioning procedure. Due to the noncooperative behavior among new users, they will execute distributed power control to manage the cochannel interference when needed. Simulation results demonstrate that the proposed scheme performs tightly to the global optimal solution. In addition, the comparison between the proposed energy efficient allocation scheme and the well established rate or power efficient allocation algorithms is carried out to demonstrate the advantage of the proposed scheme in terms of network lifetime. Index Terms—Resource allocation, cognitive radio, ad hoc network, OFDMA. I.
Dynamic Discrete Power Control in Cellular Networks
"... We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to ..."
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Cited by 6 (3 self)
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We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. We consider two frameworks concerning the state information of the channels of other mobiles: (i) the case of full state information and (ii) the case of local state information. In each of the two frameworks, we consider both cooperative as well as noncooperative power control. We manage to characterize the structure of equilibria policies and, more generally, of bestresponse policies in the noncooperative case. We present an algorithm to compute equilibria policies in the case of two noncooperative players. Finally, we study the case where a malicious mobile, which also has average power constraints, tries to jam the communication of another mobile. Our results are illustrated and validated through various numerical examples. I
Wardrop Equilibrium for CDMA Systems
"... Abstract — In this contribution, the performance of an uplink CDMA system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while per ..."
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Cited by 5 (1 self)
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Abstract — In this contribution, the performance of an uplink CDMA system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). We consider the realistic case of frequency selective channels. This scenario illustrates the case of decentralized schemes and aims at reducing the downlink signaling overhead. Various receivers are considered, namely the Matched filter, the MMSE filter and the optimum filter. The goal of this paper is to derive simple expressions for the noncooperative Nash equilibrium as the number of mobiles becomes large. To that end we combine two asymptotic methodologies. The first is asymptotic random matrix theory which allows us to obtain explicit expressions for the impact of all other mobiles on any given tagged mobile. The second is the theory of nonatomic games along with the Wardrop equilibrium concept which allows us to compute good approximations of the Nash equilibrium as the number of mobiles grow. 1 I.