### Citations

7193 | Convex Optimization
- BOYD, VANDENBERGHE
- 2004
(Show Context)
Citation Context ...( ∂ 2 Ui ∂P 2 i = −Bi ( ) 2 Gii Ri 1+ GiiPi Ri 1+ Gii Ri ) 2 . (1) As the second order partial derivative with respect to Pi is negative, the function Ui(Pi,P−i) is concave in Pi, hence quasi-concave =-=[10]-=-. So, all conditions of Theorem 1 hold for each FMNi. Case #2: Let player i be a MN. Similarly, the strategy set [0,Pmax] is a compact and convex set. The utility function Ui(Pi,P−i) = Biln(1+SINRi) i... |

2556 | A course in game theory
- Osborne, Rubinstein
- 1994
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Citation Context ...uence of strategies generated by best response dynamics converges to a NE, regardless of the players initial strategies. However, this does not hold in general. A nice counterexample is the following =-=[11]-=-: Let us suppose that, at round 1, Player1 believes that Player2 will choose Bach, whereas Player2 believes that Player1 will choose Stravinsky. So, Player1 will choose Bach as best response to that b... |

941 |
Parallel and Distributed Computation, Numerical Methods
- Bertsekas, Tsitsiklis
- 1989
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Citation Context ...queness of a NE is equivalent to proving the existence of a unique fixed point, which is a point that is mapped to itself by a function. We restate the following notions from distributed optimization =-=[13]-=-, which will be useful in the rest of this section. Definition 4: LetM(·) : X → X be a mapping. Letx ⋆ ∈ X be a fixed-pointM is a pseudo-contraction mapping with respect to some norm ‖·‖ if there exis... |

631 | A framework for uplink power control in cellular radio systems
- Yates
- 1995
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Citation Context ...o find a set of transmitter powers so that the SINR targets of all the links could be satisfied. Distributed iterative schemes were presented that can always find out a solution, in case there is one =-=[6]-=-. In parallel, various power control algorithms were developed that are suitable for data networks. The idea is that each user aims at maximizing its own utility function Ui(·) that penalizes the use ... |

405 |
Femtocell networks: a survey
- Chandrasekhar, Andrews, et al.
- 2008
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Citation Context ...rmed macrocells in our context, a large number of smaller and cheaper cells which are called femtocells and connect to the mobile operator network using residential DSL or cable broadband connections =-=[3]-=-. Femtocells belong to a broader class of radio access technology called small cells. Small cells are expected to be a key feature for future LTE networks, where all cells will be self-organizing [4].... |

279 |
visual networking index: Forecast and methodology
- “Cisco
- 2012
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Citation Context ...8, the yearly global mobile data traffic was 1.3 Exabytes (1 Exabyte equals 1 billion Gigabytes) [1]. The prediction was that by 2014, the data traffic per month will be 1.6 Exabytes. A study in 2011 =-=[2]-=- claims that by 2015 data traffic per month will be 6.3 Exabytes. It is also worth mentioning that more than 70% of this data traffic is generated indoors (mostly at home or at the office) [1]. Conseq... |

169 | CDMA Uplink power control as a noncooperative game
- Alpcan, Basar, et al.
- 2001
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Citation Context ... defines the price that user i has to pay for using a specific amount of power. As previously, the transmission power should not exceed FPmax. This utility function is inspired by the one proposed in =-=[7]-=-. The reasons that we choose different objective functions for each category of users are the following: Macrocell users have a higher priority to be served by the mobile operators, as they will be mo... |

103 | Constrained Power Control
- Grandhi, Zander, et al.
- 1995
(Show Context)
Citation Context ...ing the system of the KKT conditions, we get the optimal power P⋆ i : P ⋆ { } Ri i = min Pmax,γi . (2) Therefore, we arrive at the well-known Simplified Foschini-Miljanic formula with Pmax constraint =-=[12]-=-. However, the key difference is that, contrary to [12], where each node’s utility value is either 0 (when the target is not achieved) or 1 (when the target is achieved), each user gets a nonzero valu... |

48 | Methodologies for analyzing equilibria in wireless games
- Lasaulce, Altman
- 2009
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Citation Context ...minSINRi,k ·maxSINRi],0 < k < 1. B. Existence of a NE in the two-tier femtocell network game To prove that the game G has at least one NE, we use the following theorem by Debreu-Fan-Glicksberg (1952) =-=[9]-=-: Theorem 1: Let G a strategic non-cooperative game. Suppose that ∀i ∈ N = {1,2,...,N} (where N is the set of players): • The strategy set Si is a compact and convex set. • The utility Ui(s), where s ... |

19 | A stackelberg game for pricing uplink power in wide-band cognitive radio networks
- Daoud, Alpcan, et al.
- 2008
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Citation Context ...ng NE. In parallel, we shall examine which pricing policy should be adopted so as to increase the revenue of the wireless operator. Towards this direction, a Stackelberg game model such as the one in =-=[16]-=- that dealt with cognitive radio networks may be useful. Finally, open access femtocells, where FBSs can provide service to any MN that is close to them, will be studied focusing on the incentives tha... |

16 | Review of some fundamental approaches for power control in wireless networks
- Douros, Polyzos
- 2011
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Citation Context ...L TECHNIQUES Power control, i.e., selecting transmitter powers to achieve a specific target, has been extensively studied since the early 90’s. A review of some fundamental approaches can be found in =-=[5]-=-. The key feature of any power control algorithm is whether it is designed for use in a voice or data network. Power control algorithms were firstly applied in voice networks. The idea was to find a s... |

13 |
Game theory in supply chain analysis [M]. Handbook of Quantitative Supply Chain Analysis
- Cachon, Netessine
- 2004
(Show Context)
Citation Context ...gorithm 1 to a unique fixed point (i.e., a NE). As the best response dynamics scheme is a pseudo-contraction in the entire strategy space, this is the unique NE of the two-tier femtocell network game =-=[14]-=-. Let ∆T = [∆TMN 1,∆TMN 2,··· ,∆TMN N1,∆TFMN 1,∆TFMN 2,··· ,∆TFMN N2] T15 be a N-size vector. Its maximum norm ‖∆T‖∞ is defined as: ‖∆T‖∞ = max{|∆TMN 1|,|∆TMN 2|,··· ,|∆TMN N1|,|∆TFMN 1|,|∆TFMN 2|,··... |