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## Auction-based spectrum sharing (2004)

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### Other Repositories/Bibliography

Venue: | WiOpt '04 |

Citations: | 119 - 18 self |

### Citations

7717 |
Matrix Analysis
- Horn, Johnson
- 1990
(Show Context)
Citation Context ...r transposition should be clear from the context.sfurther assume that K is irreducible, which is true unless some users are completely isolated from each other. 11 . From the Perron-Frobenius theorem =-=[23], the -=-eigenvalue of K with maximum modulus is real, positive, simple, and the corresponding eigenvector is positive componentwise. Denote this eigenvalue as ρK. If ρK < 1, then limn→∞ K n = 0, and (I ... |

2398 |
Microeconomic Theory
- Mas-Colell, Whinston, et al.
- 1995
(Show Context)
Citation Context ... all other users scaled by the bandwidth. We consider auction mechanisms to allocate the received power as a function of bids the users submit. We model the resulting problem as a noncooperative game =-=[2], -=-and characterize the Nash equilibria and related properties for two different auction mechanisms. Our approach is similar to a share auction (see [3–7] and the references therein), or divisible auct... |

1944 |
Rate control in communication networks: shadow prices, proportional fairness and stability
- Kelly, Maulloo, et al.
- 1998
(Show Context)
Citation Context ...p i = ∗ i n0 + (P − p∗ i θi = , (5) )/B πs and user i pays C (γ ∗ i ) = πs γ ∗ i = θi. It follows that both the SINR allocation and payments are weighted max-min fair with the weights =-={θi} 1≤i≤M . In [16]-=-, Kelly et al. showed that logarithmic utility functions lead to a weighted proportional fair rate allocation in a network rate control problem. Their problem is convex and uncoupled across users sinc... |

476 | A simple distributed autonomous power control algorithm and its convergence
- Foschini
- 1993
(Show Context)
Citation Context ...the unique NE in a stable system. Therefore incremental or random asynchronous updates do not improve convergence. The update (15) is mathematically similar to the power control algorithm proposed in =-=[20]-=- (see also [21], [22]) for a cellular network, where users adjust their powers (without any power constraints) to meet some preset target SINRs. In those papers, the matrix K depends only on the chann... |

471 | Fundamental design issues for the future Internet
- Shenker
- 1995
(Show Context)
Citation Context ...ntinuously differentiable in γi. 2 This approximates the weighted rate of user i in the high SINR regime.sUtilities that satisfy this assumption are commonly used to model “elastic” data applicat=-=ions [16]. For each i , -=-the received SINR is given by γi = n0 + 1 B pihii � � j�=i pjhji �, (1) where pi is user i’s transmission power, hij is the channel gain from user i’s transmitter to user j’s receiver, ... |

337 | Efficient power control via pricing in wireless data networks
- Saraydar, Mandayam, et al.
- 2002
(Show Context)
Citation Context ...l system utility [10]. This has been referred to as the price of anarchy (e.g., [6]). In order to achieve a more desirable system operating point, we allow the manager to announce a unit price (e.g., =-=[11, 12]-=-) either for received SINR or received power. SINR pricing with logarithmic utilities leads to a weighted max-min fair SINR allocation. Power pricing maximizes the total utility for a large enough ban... |

176 | CDMA uplink power control as a noncooperative game,” - Alpcan, Basar, et al. - 2002 |

169 | Stride scheduling: Deterministic proportional- share resource management
- Waldspurger, Weihl
- 1995
(Show Context)
Citation Context ... assume a weighted proportional allocation rule in which a user’s power allocation is proportional to his bid. This type of allocation rule has been studied in a wide range of applications (e.g., se=-=e [8, 9]-=-), including network resource allocation (e.g., [6, 7]). Given this allocation, the users participate in a game with the objective of maximizing their own benefit. It is well known that the Nash Equil... |

166 |
Auctions of Divisible Goods: On the Rationale for the Treasury Experiment.
- Back, Zender
- 1993
(Show Context)
Citation Context ...i≤M is weighted max-min fair with weights {wi} 1≤i≤M if no xi can be increased without decreasing some xj such that xj/wj ≤ xi/wi. The SINR allocation at the NE is γ ∗ p i = ∗ i n0 + (P �=-=�� p∗ i θi = , (5) )/B πs and u-=-ser i pays C (γ ∗ i ) = πs γ ∗ i = θi. It follows that both the SINR allocation and payments are weighted max-min fair with the weights {θi} 1≤i≤M . In [16], Kelly et al. showed that loga... |

120 | Channel Access Algorithms with Active Link Protection for Wireless
- Bambos, Chen, et al.
- 2000
(Show Context)
Citation Context ...n a stable system. Therefore incremental or random asynchronous updates do not improve convergence. The update (15) is mathematically similar to the power control algorithm proposed in [20] (see also =-=[21]-=-, [22]) for a cellular network, where users adjust their powers (without any power constraints) to meet some preset target SINRs. In those papers, the matrix K depends only on the channel gains and th... |

89 |
Inefficiency of Nash Equilibria
- Dubey
- 1986
(Show Context)
Citation Context ... Equilibrium (NE) of ⋆ This work was supported by the Northwestern-Motorola Center for Communications, and by NSF CAREER award CCR-0238382.sa game typically does not maximize the total system utilit=-=y [10]-=-. This has been referred to as the price of anarchy (e.g., [6]). In order to achieve a more desirable system operating point, we allow the manager to announce a unit price (e.g., [11, 12]) either for ... |

43 |
The chairman assignment problem.
- Tijdeman
- 1980
(Show Context)
Citation Context ... assume a weighted proportional allocation rule in which a user’s power allocation is proportional to his bid. This type of allocation rule has been studied in a wide range of applications (e.g., se=-=e [8, 9]-=-), including network resource allocation (e.g., [6, 7]). Given this allocation, the users participate in a game with the objective of maximizing their own benefit. It is well known that the Nash Equil... |

38 | Nash equilibrium and decentralized negotiation in auctioning divisible resources”, Group Decision and Negotiation
- Maheswaran, Basar
- 2003
(Show Context)
Citation Context ...utility depends on his SINR level, which in turn depends on the power assigned to other users, making the users’ demand curves dependent on each other. Instead, we adopt a signaling system similar t=-=o [6, 7], -=-where users submit one dimensional bids for the resource. We assume a weighted proportional allocation rule in which a user’s power allocation is proportional to his bid. This type of allocation rul... |

32 | Network resource allocation and a congestion game
- Johari, Tsitsiklis
- 2004
(Show Context)
Citation Context ...utility depends on his SINR level, which in turn depends on the power assigned to other users, making the users’ demand curves dependent on each other. Instead, we adopt a signaling system similar t=-=o [6, 7], -=-where users submit one dimensional bids for the resource. We assume a weighted proportional allocation rule in which a user’s power allocation is proportional to his bid. This type of allocation rul... |

31 | Auctioning divisible goods, - Wang, Zender - 2002 |

23 | Distributed power control for time varying wireless networks: Optimality and convergence,” in
- Holliday, Bambos, et al.
- 2003
(Show Context)
Citation Context ...able system. Therefore incremental or random asynchronous updates do not improve convergence. The update (15) is mathematically similar to the power control algorithm proposed in [20] (see also [21], =-=[22]-=-) for a cellular network, where users adjust their powers (without any power constraints) to meet some preset target SINRs. In those papers, the matrix K depends only on the channel gains and the targ... |

15 |
Auctioning divisible goods. Economic Theory
- Wang, Zender
- 2002
(Show Context)
Citation Context ... given in the appendix; as shown there, user i ′ s best response bid is bi = kib−i. The bidding and power profiles at the NE are: b ∗ i = ki 1+ki 1 − � β and p M kl l=1 1+kl ∗ i = ki P fo=-=r 1 ≤ i ≤ M. (4) -=-1 + kisIn order to have a unique Nash Equilibrium, the manager has to announce a positive reserve bid (β > 0). Otherwise, there either exists no NE or an infinite number of NEs. However, since the us... |

15 |
A New Framework for Power Control
- Famolari, Mandayam, et al.
- 1999
(Show Context)
Citation Context ...l system utility [10]. This has been referred to as the price of anarchy (e.g., [6]). In order to achieve a more desirable system operating point, we allow the manager to announce a unit price (e.g., =-=[11, 12]-=-) either for received SINR or received power. SINR pricing with logarithmic utilities leads to a weighted max-min fair SINR allocation. Power pricing maximizes the total utility for a large enough ban... |

14 | Distributed algorithms for nash equilibria of flow control games,”
- Alpcan, Basar
- 2003
(Show Context)
Citation Context ...assume that each user updates the bid using a myopic algorithm, pi i.e., he submits the best response bid assuming all the other bids are fixed: b (n+1) i This is similar to the PUA algorithm used in =-=[17]. -=-= kib (n) −i Proposition 5. In an SINR-based auction with logarithmic utilities, the myopic bid updating algorithm in (9) globally and geometrically converges to the unique NE in a stable system if ... |

14 |
On Congestion Pricing in a Wireless Network
- Heikkinen
- 2002
(Show Context)
Citation Context ...e enough system with co-located receivers if the total power and bandwidth are increased in fixed proportion to the number of users. Related work on uplink power control for CDMA has appeared in [12]�=-=��[15]. -=-A key difference here is that there is a constraint on the total received power at all times 1 . Because of this, a user’s interference depends on his own power allocation, which can make the proble... |

9 | Utility based power control in cellular radio systems - Xiao, Schroff, et al. - 2001 |

3 |
Auction design for the allocation of emission permits, 2001 working paper
- Sunnevag
(Show Context)
Citation Context ... order to converge globally to the Nash Equilibrium (NE). This makes the auction mechanisms easily implementable and scalable with the population size. Our approach is similar to a share auction (see =-=[3]��-=-�[7] and the references therein), or divisible auction, where a perfectly divisible good is split among bidders whose payments depend solely on the bids. A common form of bids in a share auction is fo... |

2 |
On Congestion Pricing in a Wireless Network, Wireless Networks 8
- Heikkinen
- 2002
(Show Context)
Citation Context ...E is η = E[θ](n0+P/B) π s P/M η → 1, the price π s converges to the right-hand side of (8), which is proportional to the system load M/P. This coincides with the congestion pricing scheme propo=-=sed in [15]-=-, where the equilibrium price reflects the congestion degree of the system. At the NE of the limiting system, all users receive the same fixed noise plus interference level (n0 + P/B). This is because... |

2 |
Putting Auction Thoery to Work
- Milgrom
- 2004
(Show Context)
Citation Context ...d β, and uses a corresponding reserve power that interferes with the other users. In contrast with the situation where the manager submits a reserve bid to extract more revenue from the other bidders=-= [17]-=-, here the main purpose of the reserve bid is to guarantee a unique desirable outcome of the auction. We will show that the interference generated by the manager can be made arbitrarily small. Althoug... |

1 |
Auction design for the allocation of emission permits. working paper
- Sunnevag
- 2001
(Show Context)
Citation Context ...Auction In this case Ci (γi) = π s γi = π s pi/ � n0 + power, as well as the interference he receives. Define � P −pi B , so that each user’s payment depends on the received ki = θi (P + =-=Bn0) B (πs . (3) P −-=- θin0) Theorem 1. In an SINR-based auction with logarithmic utility, 1. For β > 0, a unique Nash Equilibrium exists if ki > 0 for all i and �M ki i=1 < 1, otherwise no Nash 1+ki Equilibrium exists... |