Equilibria of channel selection games in parallel multiple access channels

Perlaza, Samir M.; Lasaulce, Samson; Debbah, Mérouane

doi:10.1186/1687-1499-2013-15

Cited by 9 publications

(17 citation statements)

References 36 publications

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“…From this perspective, it is hard to cast the games presented here as potential games. If the actions of the players are restricted for instance to power allocation policies, the results on power allocation games in [9,10,11,12,13] can be seen as special cases of the results presented in this report.…”

Section: Example and Observationsmentioning

confidence: 66%

Decentralized K-User Gaussian Multiple Access Channels

Amor

Perlaza

2017

Static &Amp; Dynamic Game Theory: Foundations &Amp; Applications

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In this report, the fundamental limits of decentralized information transmission in the K-user Gaussian multiple access channel (G-MAC), with K 2, are fully characterized. Two scenarios are considered. First, a game in which only the transmitters are players is studied. In this game, the transmitters autonomously and independently tune their own transmit configurations seeking to maximize their own information transmission rates, R 1 , R 2 , . . . , R K , respectively. On the other hand, the receiver adopts a fixed receive configuration that is known a priori to the transmitters. The main result consists of the full characterization of the set of rate tuples (R 1 , R 2 , . . . , R K ) that are achievable and stable in the G-MAC when stability is considered in the sense of the η-Nash equilibrium (NE), with η 0 arbitrarily small. Second, a sequential game in which the two categories of players (the transmitters and the receiver) play in a given order is presented. For this sequential game, the main result consists of the full characterization of the set of rate tuples (R 1 , R 2 , . . . , R K ) that are stable in the sense of an η-sequential equilibrium, with η 0.

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Section: Example and Observationsmentioning

confidence: 66%

Decentralized K-User Gaussian Multiple Access Channels

Amor

Perlaza

2017

Static &Amp; Dynamic Game Theory: Foundations &Amp; Applications

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“…Only very short ESs of 4-6 elements are found for GN in both cases as expected. F=2, K=7, SNR=20dB, M=1,...,4, no pathloss, =2, M (18) are plotted in Fig. 6 illustrating our expectation of lower GN non-convergence probabilities for higher dimension networks in scenario realizations with ESs.…”

Section: Ergodic Subchains: Semi-analytic Studymentioning

confidence: 87%

“…as in [21]). Similarly to [16], [18] and other papers, for convergence analysis, each channel is assumed to change sufficiently slowly to be considered fixed during the whole transmission. Time varying channel effects are illustrated in Section V.C using the IEEE 802.11n channel model [26].…”

Section: System Model and Problem Formulationmentioning

confidence: 99%

Spectrum Sharing With Decentralized Occupation Control in Rule Regulated Networks

Kuzminskiy

Xiao

Tafazolli

2019

IEEE Trans. Cogn. Commun. Netw.

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Decentralized dynamic spectrum allocation (DSA) that exploits adaptive antenna array interference mitigation diversity at the receiver, is studied for interference-limited environments with high level of frequency reuse. The system consists of base stations (BSs) that can optimize uplink frequency allocation to their user equipments (UEs) to minimize impact of interference on the useful signal, assuming no control over resource allocation of other BSs sharing the same bands. To this end, "good neighbor" (GN) rules allow effective trade-off between the equilibrium and transient decentralized DSA behavior if the performance targets are adequate to the interference scenario. In this paper, we 1) extend the GN rules by including a spectrum occupation control that allows adaptive selection of the performance targets; 2) derive estimates of absorbing state statistics that allow formulation of applicability areas for different DSA algorithms; 3) define a semianalytic absorbing Markov chain model and study convergence probabilities and rates of DSA with occupation control including networks with possible partial breaks of the GN rules. For higher-dimension networks, we develop simplified search GN algorithms with occupation and power control and demonstrate their efficiency by means of simulations.

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“…Note that multi-channel transmission power assignment problems can be seen as joint transmission power and channel assignment problems introduced in Sect. 9 because a zero transmission power level means that the relevant channel has not been assigned [145]. Note that [144] also discussed BS selection, and further discussion can be found in [75].…”

Section: Multi-channel Systemsmentioning

confidence: 99%

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Yamamoto

2015

IEICE Trans. Commun.

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SUMMARY Potential games form a class of non-cooperative games where the convergent of unilateral improvement dynamics is guaranteed in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed. key words: potential game, game theory, radio resource management, channel assignment, transmission power control IntroductionThe broadcast nature of wireless transmissions causes cochannel interference and channel contention, which can be viewed as interactions among transceivers. Interactions among multiple decision makers can be formulated and analyzed using a branch of applied mathematics called game theory [61], [131]. Game-theoretic approaches have been applied to a wide range of wireless communication technologies, including transmission power control for code division multiple access (CDMA) cellular systems [153] and cognitive radios [132]. For a summary of game-theoretic approaches to wireless networks, we refer the interested reader to [68] [189].In this paper, we focus on potential games [126], which form a class of strategic form games with the following desirable properties:• The existence of a Nash equilibrium in potential games is guaranteed in many practical situations [126] (Theorems 1 and 2 in this paper), but is not guaranteed for general strategic form games. Example 2 in Sect. 2. We provide an overview of problems in wireless networks that can be formulated in terms of potential games. We also clarify the relations among games, and provide simpler proofs of some known results. Problem-specific learning algorithms [92], [168] are beyond the scope of this paper.The remainder of this paper is organized as follows: In Sect. 2, 3, and 4, we introduce strategic form games, potential games, and learning algorithms, respectively. We then discuss various potential games in Sects. 5 to 18, as shown in Table 1. Finally, we provide a few concluding remarks in Sect. 19.The notation used here is shown in Table 2. Unless the context indicates otherwise, sets of strategies are denoted by calligraphic uppercase letters, e.g., A i , strategies are denoted by lowercase letters, e.g., a i ∈ A i , and tuples of strategies are denoted by boldface lowercase letters, e.g., a. Note that a i is a scalar variable when A i is a set of scalars or indices, a i is a vector variable when A i is a set of vectors, and a i is a set variable when A i is a collection of sets.We use R to denote the set of real numbers, R + to denote the set of nonnegative real numbers, R ++ to denote the set of positive real numbers, and C to denote the set of complex numbers. The cardinality of set A is denoted by |A|. The power set of A is denoted by 2 A . Finally, ½condition is the indicator function, which is one when condition is true and is zero otherwise.We treat many sy...

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Equilibria of channel selection games in parallel multiple access channels

Cited by 9 publications

References 36 publications

Decentralized K-User Gaussian Multiple Access Channels

Decentralized K-User Gaussian Multiple Access Channels

Spectrum Sharing With Decentralized Occupation Control in Rule Regulated Networks

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

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