Wardrop Equilibria and Price of Stability for Bottleneck Games with Splittable Traffic

Мазалов, Владимир; Monien, Burkhard; Schoppmann, Florian; Tiemann, Karsten

doi:10.1007/11944874_30

Cited by 13 publications

(15 citation statements)

References 16 publications

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“…Among other results, they derived bounds on the price of anarchy. For subsequent work on the price of anarchy in bottleneck routing games with atomic and non-atomic players, we refer to the paper by Mazalov et al (2006).…”

Section: Further Related Workmentioning

confidence: 99%

Strong equilibria in games with the lexicographical improvement property

2012

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We study a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the lexicographical improvement property (LIP) and show that, in finite games, it is equivalent to the existence of a generalized strong potential function. We use this characterization to derive existence, efficiency and fairness properties of strong equilibria (SE). As our main result, we show that an important class of games that we call bottleneck congestion games has the LIP and thus the above mentioned properties. For infinite games, the LIP does neither imply the existence of a generalized strong potential nor the existence of SE. We therefore introduce the slightly more general concept of the pairwise LIP and prove that whenever the pairwise LIP is satisfied for a continuous function, then there exists a SE. As a consequence, we show that splittable bottleneck congestion games with continuous facility cost functions possess a SE.

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Section: Further Related Workmentioning

confidence: 99%

Strong equilibria in games with the lexicographical improvement property

2012

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“…For subsequent work on the price of anarchy in bottleneck routing games with atomic and non-atomic players, we refer to the paper by Mazalov et al [36].…”

Section: Related Workmentioning

confidence: 99%

“…Despite being a more realistic model for network routing, they have not received similar attention in the literature. For classes of non-atomic (with infinitesimally small players) and atomic splittable games (finite number of players with arbitrarily splittable demand) existence of PNE and bounds on the price of anarchy were considered in [12,36]. For atomic games with unsplittable demand PNE do always exist [6].…”

Section: Introductionmentioning

confidence: 99%

Computing pure Nash and strong equilibria in bottleneck congestion games

et al. 2012

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Bottleneck congestion games properly model the properties of many realworld network routing applications. They are known to possess strong equilibria-a strengthening of Nash equilibrium to resilience against coalitional deviations. In this paper, we study the computational complexity of pure Nash and strong equilibria in these games. We provide a generic centralized algorithm to compute strong equilibria, which has polynomial running time for many interesting classes of games such as, e.g., matroid or single-commodity bottleneck congestion games. In addition, we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics. Using unilateral improvement dynamics in matroid games pure Nash equilibria can be reached efficiently. In contrast, computing even a single coalitional improvement move in matroid and single-commodity games is strongly NP-hard. In addition, we establish a variety of hardness results and lower bounds regarding the duration of unilateral and coalitional improvement dynamics. They continue to hold even for convergence to approximate equilibria.

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“…Finally, several recent works [4,6,7,12,17] obtain results on the price of anarchy with the ℓ ∞ aggregation function in the conceptually similar but technically different atomic selfish routing model, where there is a finite number of players who each control a non‐negligible amount of traffic. The ℓ ∞ aggregation function was considered for the selfish routing model considered here in [11], but no price of anarchy results were given.…”

Section: Introductionmentioning

confidence: 99%

Bottleneck links, variable demand, and the tragedy of the commons

2012

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We study the price of anarchy of selfish routing with variable traffic rates and when the path cost is a non-additive function of the edge costs. Non-additive path costs are important, for example, in networking applications, where a key performance metric is the achievable throughput along a path, which is controlled by its bottleneck (most congested) edge. We prove the following results.• In multicommodity networks, the worst-case price of anarchy under the ℓ p path cost with 1 < p ≤ ∞ can be dramatically larger than under the standard ℓ 1 path cost.• In single-commodity networks, the worst-case price of anarchy under the ℓ p path cost with 1 < p < ∞ is no more than with the standard ℓ 1 path norm. (A matching lower bound follows trivially from known results.) This upper bound also applies to the ℓ ∞ path cost if and only if attention is restricted to the natural subclass of equilibria generated by distributed shortest-path routing protocols.• For a natural cost-minimization objective function, the price of anarchy with endogenous traffic rates (and under any ℓ p path cost) is no larger than that in fixed-demand networks. Intuitively, the worst-case inefficiency arising from the "tragedy of the commons" is no more severe than that from routing inefficiencies.

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Wardrop Equilibria and Price of Stability for Bottleneck Games with Splittable Traffic

Cited by 13 publications

References 16 publications

Strong equilibria in games with the lexicographical improvement property

Strong equilibria in games with the lexicographical improvement property

Computing pure Nash and strong equilibria in bottleneck congestion games

Bottleneck links, variable demand, and the tragedy of the commons

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