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BAn energyefficient approach to power control and receiver design in wireless data networks,[
 IEEE Trans. Commun.,
, 2005
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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 55 (8 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.
Mandayam, “Pricing for enabling forwarding in selfconfiguring ad hoc networks
 IEEE Journal on Selected Areas in Communications
, 2005
"... Abstract—The assumption that all nodes cooperate to relay packets for each other may not be realistic for commercial wireless ad hoc networks. An autonomous (selfish) node in a wireless network has two disincentives for forwarding for others: energy expenditure (real cost) and possible delays for it ..."
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Cited by 36 (2 self)
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Abstract—The assumption that all nodes cooperate to relay packets for each other may not be realistic for commercial wireless ad hoc networks. An autonomous (selfish) node in a wireless network has two disincentives for forwarding for others: energy expenditure (real cost) and possible delays for its own data (opportunity cost). We introduce a mechanism that “fosters cooperation through bribery ” in the context of forwarding in ad hoc networks. Using a microeconomic framework based on game theory, we design and analyze a pricing algorithm that encourages forwarding among autonomous nodes by reimbursing forwarding. Taking a joint networkcentric and usercentric approach, the revenue maximizing network and utility (measured in bitsperJoule) maximizing nodes interact through prices for channel use, reimbursements for forwarding, transmitter power control, as well as forwarding and destination preferences. In a threenode (twosources, oneaccesspoint) network, the network converges to an architecture that induces forwarding only when the network geometries are such that forwarding is likely to increase individual benefits (network revenue and node utilities). For other geometries, the network converges to architectures that do not favor forwarding. We then generalize to a multinode network, where it is seen that the nodes ’ willingness to forward decrease for large ratios of the average internodal distance to the smallest distance between the access point and any source node. Pricing with reimbursement generally improves the network aggregate utility (or aggregate bitsperJoule), as well as utilities and revenue compared with the corresponding pricing algorithm without reimbursement. Index Terms—Cooperation, incentive for forwarding, noncooperative game, pricing, revenue maximization, Stackelberg game, utility. I.
Liu,”NonCooperative Power Control Game and Throughput Game over Wireless Networks,”IEEE Trans
 Communications
, 2005
"... Abstract—Resource allocation is an important means to increase system performance in wireless networks. In this letter, a gametheory approach for distributed resource allocation is proposed. Observing the bilinear matrix inequality nature of resource allocation, we construct two interrelated games: ..."
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Cited by 19 (4 self)
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Abstract—Resource allocation is an important means to increase system performance in wireless networks. In this letter, a gametheory approach for distributed resource allocation is proposed. Observing the bilinear matrix inequality nature of resource allocation, we construct two interrelated games: a powercontrol game at the user level, and a throughput game at the system level, respectively, to avoid local optima. An optimal complex centralized algorithm is developed as a performance bound. The simulations show that the proposed games have nearoptimal system performance. Index Terms—Adaptive modulation, game theory, power control, rate adaptation. I.
A Stackelberg Game for Pricing Uplink Power in WideBand Cognitive Radio Networks
, 2008
"... Abstract — We study the problem of pricing uplink power in wideband cognitive radio networks under the objective of revenue maximization for the service provider and while ensuring incentive compatibility for the users. User utility is modeled as a concave function of the signaltonoise ratio (SNR ..."
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Cited by 19 (1 self)
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Abstract — We study the problem of pricing uplink power in wideband cognitive radio networks under the objective of revenue maximization for the service provider and while ensuring incentive compatibility for the users. User utility is modeled as a concave function of the signaltonoise ratio (SNR) at the base station, and the problem is formulated as a Stackelberg game. Namely, the service provider imposes differentiated prices per unit of transmitting power and the users consequently update their power levels to maximize their net utilities. We devise a pricing policy and give conditions for its optimality when all the users are to be accommodated in the network. We show that there exist infinitely many Nash equilibrium points that reward the service provider with the same revenue. The pricing policy charges more from users that have better channel conditions and more willingness to pay for the provided service. We then study properties of the optimal revenue with respect to different parameters in the network. We show that for regimes with symmetric users who share the same level of willingness to pay, the optimal revenue is concave and increasing in the number of users in the network. We analytically obtain achievable SNRs for this special case, and finally present a numerical study in support of our results. I.
Utilitybased powercontrol for a twocell CDMA data network
 IEEE Trans. Wireless Commun
, 2005
"... Abstract—Power allocation across users in two adjacent cells is studied for a codedivision multiple access (CDMA) data service. The forward link is considered and cells are modeled as onedimensional with uniformly distributed users and orthogonal signatures within each cell. Each user is assumed t ..."
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Cited by 17 (3 self)
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Abstract—Power allocation across users in two adjacent cells is studied for a codedivision multiple access (CDMA) data service. The forward link is considered and cells are modeled as onedimensional with uniformly distributed users and orthogonal signatures within each cell. Each user is assumed to have a utility function that describes the user’s received utility, or willingness to pay, for a received signaltointerferenceplusnoise ratio (SINR). The objective is to allocate the transmitted power to maximize the total utility summed over all users subject to power constraints in each cell. It is first shown that this optimization can be achieved by a pricing scheme in which each base station announces a price per unit transmitted power to the users, and each user requests power to maximize individual surplus (utility minus cost). Setting prices to maximize total revenue over both cells is also considered, and it is shown that, in general, the solution is different from the one obtained by maximizing total utility. Conditions are given for which independent optimization in each cell, which leads to a Nash equilibrium (NE), is globally optimal. It is shown that, in general, coordination between the two cells is needed to achieve the maximum utility or revenue. Index Terms—CDMA, data service, forward link, power control, pricing, resource allocation, revenue, surplus, utility. I.
A fair and efficient pricing strategy for slotted Aloha
 in MPR models, IEEE VTC
, 2006
"... Abstract — In this paper, we propose a fair pricing strategy to improve the performance of a slotted Aloha system in which users act selfishly to improve their own utility. Based on a game theoretic framework, we show that both throughput and revenue can be optimized by appropriately selecting a pri ..."
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Cited by 7 (1 self)
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Abstract — In this paper, we propose a fair pricing strategy to improve the performance of a slotted Aloha system in which users act selfishly to improve their own utility. Based on a game theoretic framework, we show that both throughput and revenue can be optimized by appropriately selecting a pricing strategy for the selfish users. Our proposed solution considers multipacket reception capabilities for the physical layer. The network enforces fairness among different users by employing a pricing policy that favors equal access probabilities. I.
Joint networkcentric and usercentric radio resource management in a multicell system
 IEEE Transactions on Communications
, 2005
"... Abstract A pricing mechanism to mediate (and allocate resources) between conflicting user and network objectives has been recently proposed Index Terms Power Control, Pricing, Utility, Radio Resource Management, Revenue Maximization I. INTRODUCTION Pricing, and more generally microeconomic princip ..."
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Cited by 3 (0 self)
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Abstract A pricing mechanism to mediate (and allocate resources) between conflicting user and network objectives has been recently proposed Index Terms Power Control, Pricing, Utility, Radio Resource Management, Revenue Maximization I. INTRODUCTION Pricing, and more generally microeconomic principles, have recently emerged as powerful tools for resource allocation in wireless networks In this paper, we extend the work in [1, 2] for a singlecell system to a multicell system. Each individual user has to adjust its transmitter power based on the base station it is assigned to. Different base station assignments will lead to different power control results. In this paper, we let the user choose the base station where the user's net utility is maximized. Therefore, the power control and base station assignment are integrated in the usercentric optimization. For the networkcentric optimization, we apply two approaches: one is global pricing where the network seeks a unit price for global revenue maximization and the other is minimax pricing where a unit price is assigned based on maximizing the revenue at the base station with the smallest local optimum unit price. The paper is organized as follows. In Section II, we define in a multicell CDMA system the user metric (utility function) and the network metric (revenue) as well as the pricing (or payment) function that mediates between the user objectives and the network objective. We present in Section III our joint usercentric and networkcentric optimization problems. Our numerical results are presented in Section IV.
A UtilityBased Approach to Power Control and Receiver Design in Wireless Data Networks
, 2005
"... Abstract — In this work, the crosslayer design problem of joint multiuser detection and power control is studied using a gametheoretic approach. The uplink of a directsequence code division multiple access (DSCDMA) data network is considered and a noncooperative game is proposed in which users ..."
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Cited by 2 (0 self)
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Abstract — In this work, the crosslayer design problem of joint multiuser detection and power control is studied using a gametheoretic approach. The uplink of a directsequence code division multiple access (DSCDMA) data network is considered and a noncooperative game is proposed in which users in the network are allowed to choose their uplink receivers as well as their transmit powers to maximize their own utilities. The utility function measures the number of reliable bits transmitted by the user per joule of energy consumed. Focusing on linear receivers, the Nash equilibrium for the proposed game is derived. It is shown that the equilibrium is one where the powers are SIRbalanced with the minimum mean square error (MMSE) detector as the receiver. In addition, this framework is used to study power control games for the matched filter, the decorrelator, and the MMSE detector; and the receivers ’ performance is compared in terms of the utilities achieved at equilibrium (in bits/Joule). The optimal cooperative solution is also discussed and compared with the noncooperative approach. Extensions of the results to the case of multiple receive antennas are also presented. In addition, an admission control scheme based on maximizing the total utility in the network is proposed. Index Terms — Power control, game theory, Nash equilibrium, utility function, multiuser detectors, crosslayer design.