Capacitated Network Design Games

Feldman, Michal; Ron, Tom

doi:10.1007/978-3-642-33996-7_12

Cited by 10 publications

(35 citation statements)

References 21 publications

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“…On the other hand, on series-parallel graphs (SP graphs), we show that PoA under sum-cost is at most n and it is tight, that is, there is an example whose PoA is n. For PoS, we show that it is at most n and there is an example whose PoS under sum-cost is n + 1/n − 1. This gives the difference from the previous study, which shows that PoS is at most log n and it is tight with ordinary fair cost-sharing functions [8].…”

Section: Our Contributioncontrasting

confidence: 65%

“…We believe that any natural fair cost-sharing function is in this scheme. Note that the cost-sharing function in the previous studies [8,6,7] is f e (x) = p e /x, which clearly satisfies (1), ( 2) and (3).…”

Section: Introductionmentioning

confidence: 88%

“…The CSCSG is quite useful and can model many real-world situations for sharing the cost of a designed network, such as a virtual overlay, multicast tree, or other sub-network of the Internet. The CSCSG is firstly introduced by Feldman and Ron [8].…”

Section: Introductionmentioning

confidence: 99%

“…Although Anshelevich et al only gave the upper bound for the uncapacitated case, we can easily observe that it holds for the capacitated case. 2 Feldman and Ron gave the lower bound for undirected parallel-link graphs in [8]. However, it can be modified to a directed parallel link graph.…”

Section: Introductionmentioning

confidence: 99%

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Capacitated Network Design Games on a Generalized Fair Allocation Model

Hanaka

Hirose

Ono

2021

Preprint

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The cost-sharing connection game is a variant of routing games on a network. In this model, given a directed graph with edge-costs and edge-capacities, each agent wants to construct a path from a source to a sink with low cost. The cost of each edge is shared by the users based on a cost-sharing function. One of simple cost-sharing functions is defined as the cost divided by the number of users. In fact, most of the previous papers about cost-sharing connection games addressed this cost-sharing function. It models an ideal setting, where no overhead arises when people share things, though it might be quite rare in real life; it is more realistic to consider the setting that the cost paid by an agent is the original cost per the number of the agents plus the overhead. In this paper, we model the more realistic scenario of cost-sharing connection games by generalizing cost-sharing functions. The arguments on the model do not depend on specific cost-sharing functions, and are applicable for a wide class of cost-sharing functions satisfying the following natural properties: they are (1) non-increasing, (2) lower bounded by the original cost per the number of the agents, and (3) upper bounded by the original cost, which enables to represent various scenarios of cost-sharing. We investigate the Price of Anarchy (PoA) and the Price of Stability (PoS) under sum-cost and max-cost criteria with the generalized cost-sharing function. In spite of the generalization, we obtain the same bounds of PoA and PoS as the cost-sharing with no overhead except PoS under sum-cost. Note that these bounds are tight. In the case of sum-cost, the lower bound on PoS increases from log n to n + 1/n − 1 by the generalization, which is also almost tight because the upper bound is n. We further investigate the bounds from the viewpoints of graph classes, such as parallel-link graphs, series-parallel graphs, and directed acyclic graphs, which show critical differences of PoS/PoA values.

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Section: Our Contributioncontrasting

confidence: 65%

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Capacitated Network Design Games on a Generalized Fair Allocation Model

Hanaka

Hirose

Ono

2021

Preprint

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“…Recently, Feldman and Ron (2012) started the study of network design games under the restriction in which edges have capacity constraints.…”

Section: Related Workmentioning

confidence: 99%

The price of stability for undirected broadcast network design with fair cost allocation is constant

Bilò

Flammini

Moscardelli

2020

Games and Economic Behavior

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Capacitated network design games with weighted players

2016

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We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their chosen path does not exceed the capacity of the edge. The fixed cost of each edge that is used by some player is shared among the players using the edge by charging each player a fraction of the edge's cost equal to the ratio of her weight to the total weight of all players using the edge. We show that there exist instances of capacitated network design games with weighted players and uniform capacities that do not admit a Nash equilibrium even in the case that all players share the same source and sink. Moreover, we show that it is strongly N P ‐hard to decide whether a given instance admits a Nash equilibrium even if a feasible solution for the underlying network design problem is guaranteed to exist. In contrast, we prove that, for series‐parallel graphs, there always exists a Nash equilibrium whose total cost equals the cost of an optimal solution of the corresponding network design problem and provide an (exponential‐time) algorithm to compute this equilibrium. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 141–158 2016

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Capacitated Network Design Games

Cited by 10 publications

References 21 publications

Capacitated Network Design Games on a Generalized Fair Allocation Model

Capacitated Network Design Games on a Generalized Fair Allocation Model

The price of stability for undirected broadcast network design with fair cost allocation is constant

Capacitated network design games with weighted players

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