Improved Lower Bounds on the Price of Stability of Undirected Network Design Games

Bilò, Vittorio; Caragiannis, Ioannis; Fanelli, Angelo; Monaco, Gianpiero

doi:10.1007/s00224-012-9411-6

Cited by 28 publications

(22 citation statements)

References 11 publications

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“…In similar context, other papers considered (group)strategy proof and efficient mechanisms Regarding network design games, there is a long line of works mainly focusing on fair cost allocation (Shapley cost-sharing mechanism), originated by [5]. Anshelevich et al [5] showed a tight (log k) bound on the PoS for directed networks, while for undirected networks several variants have been studied [11,12,22,24,35] but the exact value of PoS still remains an open problem. For multicast games, Li [56] proved an upper bound of O(log k/ log log k), while for broadcast games, Fiat et al [39] proved an O(log log k) upper bound which was improved to constant due to Bilò, Flammini and Moscardelli [13].…”

Section: Related Workmentioning

confidence: 99%

Designing Cost-Sharing Methods for Bayesian Games

2017

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We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE). We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable

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Section: Related Workmentioning

confidence: 99%

Designing Cost-Sharing Methods for Bayesian Games

2017

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“…In the special case of broadcast games, in which there is a single source and each other node is the sink node of a different agent, the PoS was shown to be a constant [7]. Lower bounds on the PoS in the undirected case were studied in [6], where it was shown that the PoS can be as high as 348/155, 1.862, and 20/11 in general games, single-source games, and broadcast games, respectively.…”

Section: Related Workmentioning

confidence: 99%

Do Capacity Constraints Constrain Coalitions?

Feldman

Geri

2016

ACM Trans. Econ. Comput.

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We study strong equilibria in symmetric capacitated cost-sharing connection games. In these games, a graph with designated source and sink is given, and each edge is associated with some cost. Each agent chooses strategically an -path, knowing that the cost of each edge is shared equally between all agents using it. Two settings of cost-sharing connection games have been previously studied: (i) games where coalitions can form, and (ii) games where edges are associated with capacities; both settings are inspired by real-life scenarios. In this work we combine these scenarios and analyze strong equilibria (profiles where no coalition can deviate) in capacitated games. This combination gives rise to new phenomena that do not occur in the previous settings. Our contribution is two-fold. First, we provide a topological characterization of networks that always admit a strong equilibrium. Second, we establish tight bounds on the efficiency loss that may be incurred due to strategic behavior, as quantified by the strong price of anarchy (and stability) measures. Interestingly, our results are qualitatively different than those obtained in the analysis of each scenario alone, and the combination of coalitions and capacities entails the introduction of more refined topology classes than previously studied.

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“…[5] showed a tight Θ(log k) bound for directed networks, while for undirected networks several variants have been studied [14,16,21,23,28,29,45,15] but the exact value of PoS still remains a big open problem. For multicast games, an improved upper bound of O(log k/ log log k) is known due to Li [45], while for broadcast games, a series of work [29,44] lead finally to a constant due to Bilò et al [16].…”

Section: Example 12 (Generalized Weighted Shapley)mentioning

confidence: 99%

Designing Networks with Good Equilibria under Uncertainty

Christodoulou¹,

Sgouritsa

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider the problem of designing network costsharing protocols with good equilibria under uncertainty. The underlying game is a multicast game in a rooted undirected graph with nonnegative edge costs. A set of k terminal vertices or players need to establish connectivity with the root. The social optimum is the Minimum Steiner Tree.We are interested in situations where the designer has incomplete information about the input. We propose two different models, the adversarial and the stochastic. In both models, the designer has prior knowledge of the underlying metric but the requested subset of the players is not known and is activated either in an adversarial manner (adversarial model) or is drawn from a known probability distribution (stochastic model).In the adversarial model, the goal of the designer is to choose a single, universal cost-sharing protocol that has low Price of Anarchy (PoA) for all possible requested subsets of players. The main question we address is: to what extent can prior knowledge of the underlying metric help in the design?We first demonstrate that there exist classes of graphs where knowledge of the underlying metric can dramatically improve the performance of good network cost-sharing design. For outerplanar graph metrics, we provide a universal cost-sharing protocol with constant PoA, in contrast to protocols that, by ignoring the graph metric, cannot achieve PoA better than Ω(log k). Then, in our main technical result, we show that there exist graph metrics, for which knowing the underlying metric does not help and any universal protocol has PoA of Ω(log k), which is tight. We attack this problem by developing new techniques that employ powerful tools from extremal combinatorics, and more specifically Ramsey Theory in high dimensional hypercubes.Then we switch to the stochastic model, where each player is independently activated according to some probability distribution that is known to the * Department of Computer Science, University of Liverpool, UK. Email:gchristo@liverpool.ac.uk. This work was supported by EP/M008118/1, EP/K01000X/1 and LT140046.† Department of Computer Science, University of Liverpool, UK. Email:salkmini@liverpool.ac.uk designer. We show that there exists a randomized ordered protocol that achieves constant PoA. By using standard derandomization techniques, we produce a deterministic ordered protocol that achieves constant PoA. We remark, that the first result holds also for the black-box model, where the probabilities are not known to the designer, but is allowed to draw independent (polynomially many) samples.

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Improved Lower Bounds on the Price of Stability of Undirected Network Design Games

Cited by 28 publications

References 11 publications

Designing Cost-Sharing Methods for Bayesian Games

Designing Cost-Sharing Methods for Bayesian Games

Do Capacity Constraints Constrain Coalitions?

Designing Networks with Good Equilibria under Uncertainty

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