The price of stability in selfish scheduling games

Agussurja, Lucas; Lau, Hoong Chuin

doi:10.3233/wia-2009-0171

Cited by 6 publications

(4 citation statements)

References 20 publications

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“…The efficiency of PNE can be measured by the PoA and the PoS [23], [24]. We formally define these two ratios as follows:…”

Section: Efficiency Of the Proposed Game And Discussionmentioning

confidence: 99%

On the Base Station Association Problem in HetSNets

Mlika,

Driouch,

Ajib

et al. 2015

Preprint

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The dense deployment of small-cell base stations in HetSNets requires efficient resource allocation techniques. More precisely, the problem of associating users to SBSs must be revised and carefully studied. This problem is NP-hard and requires solving an integer optimization problem.In order to efficiently solve this problem, we model it using non-cooperative game theory. First, we design two non-cooperative games to solve the problem and show the existence of pure Nash equilibria (PNE) in both games. These equilibria are shown to be far from the social optimum.Hence, we propose a better game design in order to approach this optimum. This new game is proved to have no PNE in general. However, simulations show, for Rayleigh fading channels, that a PNE always exists for all instances of the game. In addition, we show that its prices of anarchy and stability are close to one. We propose a best response dynamics (BRD) algorithm that converges to a PNE when it exists. Because of the high information exchange of BRD, a completely distributed algorithm, based on the theory of learning, is proposed. Simulations show that this algorithm has tight-to-optimal performance and further it converges to a PNE (when existing) with high probability.

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“…The efficiency of PNE can be measured by the PoA and the PoS [23], [24]. We formally define these two ratios as follows:…”

Section: Efficiency Of the Proposed Game And Discussionmentioning

confidence: 99%

On the Base Station Association Problem in HetSNets

Mlika,

Driouch,

Ajib

et al. 2015

Preprint

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show abstract

“…We prove that O(Ω, P r, (P i ) i∈N , (s i ) i∈N ) cannot be a subset of the set of optimal schedules Σ * (Λ), which contradicts (2). We proceed by considering all subsets of Σ * (Λ).…”

Section: Theorem 2 (Impossibility Of Implementation)mentioning

confidence: 95%

“…In order to appropriately discuss the rapidly growing literature that studies coordinating mechanisms for supply chains and competitive scheduling environments we note that our definition of implementation can also be phrased in terms of the price of stability. 2 Fixing a mechanism and an evaluation/objective criterion, the price of stability is the ratio between the value of the best Nash equilibrium and the optimal value. Then, a mechanism implements optimal schedules if for each outsourcing problem the price of stability equals one.…”

Section: Introductionmentioning

confidence: 99%

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Implementation of optimal schedules in outsourcing with identical suppliers

2018

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This paper deals with decentralized decision-making situations in which firms outsource production orders to multiple identical suppliers. Each firm aims to minimize the sum of its completion times. We study whether a central authority can install a mechanism such that strategic interaction leads to a socially optimal schedule. For the case of single demand the shortest-first mechanism implements optimal schedules in Nash equilibrium. We show that for the general case there exists no anonymous mechanism that implements optimal schedules in correlated equilibrium.

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