Local smoothness and the price of anarchy in splittable congestion games

Roughgarden, Tim; Schoppmann, Florian

doi:10.1016/j.jet.2014.04.005

Cited by 51 publications

(34 citation statements)

References 17 publications

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“…If compared to the above literature on atomic congestion games, in this work we have proposed a simple low-complexity learning algorithm where each MVNO iteratively updates its strategy to provably converge to the unique NE. We have further derived an upper-bound on the PoA of the class of atomic splittable congestion games where resource and player-specific cost functions are considered, thus extending the results in [28] and [47]. Specifically, we have proved that the PoA for this particular class of cost functions matches the PoA of atomic splittable congestion games where only resource-specific cost functions are considered [28].…”

Section: Related Worksupporting

confidence: 52%

“…In the previous sections, we have emphasized the importance of deriving theoretical bounds on the efficiency of the NE, and designing effective distributed and convergent algorithms. Due to their interesting properties with respect to the above issues, congestion games [16], and their application to many networking problems such as the network service chaining [15] and load balancing [44], have been investigated in the literature [14,26,28,[45][46][47].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Low-Complexity Distributed Radio Access Network Slicing: Algorithms and Experimental Results

D’Oro¹,

Restuccia²,

Melodia³

et al. 2018

IEEE/ACM Trans. Networking

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Radio access network (RAN) slicing is an effective methodology to dynamically allocate networking resources in 5G networks. One of the main challenges of RAN slicing is that it is provably an NP-Hard problem. For this reason, we design near-optimal low-complexity distributed RAN slicing algorithms. First, we model the slicing problem as a congestion game, and demonstrate that such game admits a unique Nash equilibrium (NE). Then, we evaluate the Price of Anarchy (PoA) of the NE, i.e., the efficiency of the NE as compared to the social optimum, and demonstrate that the PoA is upper-bounded by 3/2. Next, we propose two fully-distributed algorithms that provably converge to the unique NE without revealing privacy-sensitive parameters from the slice tenants. Moreover, we introduce an adaptive pricing mechanism of the wireless resources to improve the network owner's profit. We evaluate the performance of our algorithms through simulations and an experimental testbed deployed on the Amazon EC2 cloud, both based on a real-world dataset of base stations from the OpenCellID project. Results conclude that our algorithms converge to the NE rapidly and achieve near-optimal performance, while our pricing mechanism effectively improves the profit of the network owner.

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Section: Related Worksupporting

confidence: 52%

Section: Related Workmentioning

confidence: 99%

Low-Complexity Distributed Radio Access Network Slicing: Algorithms and Experimental Results

D’Oro¹,

Restuccia²,

Melodia³

et al. 2018

IEEE/ACM Trans. Networking

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show abstract

“…However, the results in [22] are worst-case bounds and these bounds are only approached asymptotically 4 : in our simulations with affine prices, the PoA was always much lower than 1.5. One of the reasons is that in [22] the model does not consider the power constraints (5c), and a PoA of 1.5 might be reached in our case only if the constraints (5c) are coarse enough. To further explain the low PoA in our instances, we found the following theorem by precising the results of [22]:…”

Section: Consumer's Optimization Problemsmentioning

confidence: 62%

Analysis and Implementation of an Hourly Billing Mechanism for Demand Response Management

Jacquot

Beaude

Gaubert

et al. 2019

IEEE Trans. Smart Grid

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An important part of the Smart Grid literature on residential Demand Response deals with game-theoretic consumption models. Among those papers, the hourly billing model is of special interest as an intuitive and fair mechanism. We focus on this model and answer to several theoretical and practical questions. First, we prove the uniqueness of the consumption profile corresponding to the Nash equilibrium, and we analyze its efficiency by providing a bound on the Price of Anarchy. Next, we address the computational issue of the equilibrium profile by providing two algorithms: the cycling best response dynamics and a projected gradient descent method, and by giving an upper bound on their convergence rate to the equilibrium. Last, we simulate this demand response framework in a stochastic environment where the parameters depend on forecasts. We show numerically the relevance of an online demand response procedure, which reduces the impact of inaccurate forecasts.

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“…It follows that atomic splittable congestion games are strictly more general as their nonatomic counterpart. Cominetti et al (2009b), Harks (2011) and Roughgarden and Schoppmann (2015) studied the price of anarchy in atomic splittable congestion games.…”

Section: Further Related Workmentioning

confidence: 99%

Uniqueness of equilibria in atomic splittable polymatroid congestion games

Harks

Timmermans

2017

J Comb Optim

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We study uniqueness of Nash equilibria in atomic splittable congestion games and derive a uniqueness result based on polymatroid theory: when the strategy space of every player is a bidirectional flow polymatroid, then equilibria are unique. Bidirectional flow polymatroids are introduced as a subclass of polymatroids possessing certain exchange properties. We show that important cases such as base orderable matroids can be recovered as a special case of bidirectional flow polymatroids. On the other hand we show that matroidal set systems are in some sense necessary to guarantee uniqueness of equilibria: for every atomic splittable congestion game with at least three players and non-matroidal set systems per player, there is an isomorphic game having multiple equilibria. Our results leave a gap between base orderable matroids and general matroids for which we do not know whether equilibria are unique.

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Local smoothness and the price of anarchy in splittable congestion games

Cited by 51 publications

References 17 publications

Low-Complexity Distributed Radio Access Network Slicing: Algorithms and Experimental Results

Low-Complexity Distributed Radio Access Network Slicing: Algorithms and Experimental Results

Analysis and Implementation of an Hourly Billing Mechanism for Demand Response Management

Uniqueness of equilibria in atomic splittable polymatroid congestion games

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