Abstract—We consider a distributed power control scheme for wireless ad hoc networks, in which each user announces a price that reflects compensation paid by other users for their interference. We present an asynchronous distributed algorithm for updating power levels and prices. By relating this algorithm to myopic best response updates in a fictitious game, we are able to characterize convergence using supermodular game theory. Extensions of this algorithm to a multichannel network are also presented, in which users can allocate their power across multiple frequency bands. Index Terms—Distributed algorithms, game theory, power control, pricing. I.

Abstract — In this paper we develop a framework for competition of future operators likely to operate in a mixed commons/property-rights regime under the regulation of a spectrum policy server (SPS). The operators dynamically compete for customers as well as portions of available spectrum. The operators are charged by the SPS for the amount of bandwidth they use in their services. Through demand responsive pricing, the operators try to come up with convincing service offers for the customers, while trying to maximize their profits. We first consider a single-user system as an illustrative example. We formulate the competition between the operators as a noncooperative game and propose an SPS-based iterative bidding scheme that results in a Nash equilibrium of the game. Numerical results suggest that, competition increases the user’s (customer’s) acceptance probability of the offered service, while reducing the profits achieved by the operators. It is also observed that as the cost of unit bandwidth increases relative to the cost of unit infrastructure (fixed cost), the operator with superior technology (higher fixed cost) becomes more competitive. We then extend the framework to a multiuser setting where the operators are competing for a number of users at once. We propose an SPSbased bandwidth allocation scheme in which the SPS optimally allocates bandwidth portions for each user-operator session to maximize its overall expected revenue resulting from the operator payments. Comparison of the performance of this scheme to one in which the bandwidth is equally shared between the useroperator pairs reveals that such an SPS-based scheme improves the user acceptance probabilities and the bandwidth utilization in multiuser systems. I.

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The system mutual information of a multiple-input multiple-output (MIMO) system with multiple users which mutually interfere is considered. Perfect channel state information is assumed to be known to both transmitters and receivers. Asymptotic performance analysis shows that the system mutual information changes behavior as the interference becomes sufficiently strong. In particular, beamforming is the optimum signaling for all users when the interference is large. We propose several numerical approaches to decide the covariance matrices of the transmitted signals and compare their performance in terms of the system mutual information. We model the system as a noncooperative game, and perform iterative water-filling to find the Nash equilibrium distributively. A centralized global approach and a distributed iterative approach based on the gradient projection method are also proposed. Numerical results show that all proposed approaches give better performance than the standard signaling which is optimum for the case without interference. Both the global and the iterative gradient projection methods are shown to outperform the Nash equilibrium significantly.

In this work, the cross-layer design problem of joint multiuser detection and power control is studied using a game-theoretic approach that focuses on energy efficiency. The uplink of a direct-sequence code division multiple access (DS-CDMA) data network is considered and a non-cooperative 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 SIR-balanced 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 non-cooperative 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.

Abstract — CSMA/CA protocols rely on the random deferment of packet transmissions. Like most other protocols, CSMA/CA was designed with the assumption that the nodes would play by the rules. This can be dangerous, since the nodes themselves control their random deferment. Indeed, with the higher programmability of the network adapters, the temptation to tamper with the software or firmware is likely to grow; by doing so, a user could obtain a much larger share of the available bandwidth at the expense of other users. We use a game-theoretic approach to investigate the problem of the selfish behavior of nodes in CSMA/CA networks, specifically geared towards the most widely accepted protocol in this class of protocols, IEEE 802.11. We characterize two families of Nash equilibria in a single stage game, one of which always results in a network collapse. We argue that this result provides an incentive for cheaters to cooperate with each other. Explicit cooperation among nodes is clearly impractical. By applying the model of dynamic games borrowed from game theory, we derive the conditions for the stable and optimal functioning of a population of cheaters. We use this insight to develop a simple, localized and distributed protocol that successfully guides multiple selfish nodes to a Pareto-optimal Nash equilibrium. I.

We present a framework for resource control in CDMA networks carrying elastic tra#c, considering both the uplink and the downlink direction. The framework is based on microeconomics and congestion pricing, and seeks to exploit the joint control of the transmission rate and the signal quality in order to achieve e#cient utilization of network resources, in a distributed and decentralized manner. An important feature of the framework is that it incorporates both the congestion for shared resources in wireless and wired networks, and the cost of battery power at mobile hosts. We prove that for elastic tra#c, where users value only their average throughput, the user's net utility maximization problem can be decomposed into two simpler problems: one involving the selection of the optimal signal quality, and one involving the selection of the optimal transmission rate. Based on this result, the selection of signal quality can be performed as done today using outer loop power control, while rate adaptation can be integrated with rate adaptation at the transport layer.

Abstract. We study auction-based mechanisms for sharing spectrum among a group of users, subject to a constraint on the interference temperature at collocated receivers. The users access the channel using spread spectrum signaling and thus generate interference with each other. Each user receives a utility that is a function of the received signal-tointerference plus noise ratio. We propose two auction mechanisms for allocating the received power. The first is an SINR-based auction, which, when combined with logarithmic utilities, leads to a weighted max-min fair SINR allocation. The second is a power-based auction that maximizes the total utility when the bandwidth is large enough. Both auction mechanisms achieve social optimality in a large system limit where bandwidth, power and the number of users are increased in a fixed proportion. We also give sufficient conditions for global convergence of a distributed updating algorithm and discuss the convergence speed. 1

Abstract—A game-theoretic model for studying power control in multicarrier code-division multiple-access systems is proposed. Power control is modeled as a noncooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multidimensional nature of users ’ strategies and the nonquasi-concavity of the utility function make the multicarrier problem much more challenging than the single-carrier or throughput-based-utility case. It is shown that, for all linear receivers including the matched filter, the decorrelator, and the minimum-mean-square-error detector, a user’s utility is maximized when the user transmits only on its “best ” carrier. This is the carrier that requires the least amount of power to achieve a particular target signal-to-interference-plus-noise ratio at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, conditions are given that must be satisfied by the channel gains for a Nash equilibrium to exist, and the distribution of the users among the carriers at equilibrium is characterized. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in significant improvements in the total utility achieved at equilibrium compared with a single-carrier system and also to a multicarrier system in which each user maximizes its utility over each carrier independently. Index Terms—Energy efficiency, game theory, multicarrier code-division multiple-access (CDMA), multiuser detection, Nash equilibrium, power control, utility function. I.

This note shows how centralized or distributed power control algorithms in wireless communications can be viewed as S-modular games coupled policy sets (coupling is due to the fact that the set of powers of a mobile that satisfy the signal-to-interference ratio constraints depends on powers used by other mobiles). This sheds a new light on convergence properties of existing synchronous and asynchronous algorithms, and allows us to establish new convergence results of power control algorithms. Furthermore, known properties of power control algorithms allow us to extend the theory of S-modular games and obtain conditions for the uniqueness of the equilibrium and convergence of best response algorithms independently of the initial state.