Selfish unsplittable flows

Fotakis, Dimitris; Kontogiannis, Spyros; Spirakis, Paul G.

doi:10.1016/j.tcs.2005.09.024

Cited by 171 publications

(181 citation statements)

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“…We say that is consistent if every game in possesses a PNE. Using this terminology, the results of Fotakis et al [16,17], Harks et al [22], and Panagopoulou and Spirakis [30] yield that is consistent if contains either affine functions or certain exponential functions. A natural open question is to decide whether there are further consistent functions, that is, functions guaranteeing the existence of a PNE.…”

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confidence: 93%

“…Harks et al [22] generalized this existence result to nonuniform exponential cost functions of the form c f x = a f e x + b f for some a f b f ∈ , where a f and b f may depend on the facility f , while must be equal for all facilities. It is worth noting that the positive results of Fotakis et al [16,17], Harks et al [22], and Panagopoulou and Spirakis [30] are particularly important as they establish existence of PNE for the respective sets of cost functions independent of the underlying game structure, that is, independent of the underlying strategy set, demand vector, and number of players, respectively. In this paper, we further explore the equilibrium existence problem in weighted congestion games.…”

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confidence: 95%

“…In contrast to unweighted congestion games, weighted congestion games do not always admit a PNE. Fotakis et al [16] and Libman and Orda [24] each constructed a single-commodity network instance with two players having demands one and two, respectively, and showed that these games do not have a PNE. Their instances use different nondecreasing cost values per edge that are defined at the three possible loads, 1 2 3.…”

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confidence: 99%

“…Interestingly, Anshelevich et al [5] showed that for cost functions of the form c f x =c f /x c f ∈ ≥0 , every two-player game possesses a PNE. For games with affine cost functions, Fotakis et al [16,17] proved that every weighted congestion game possesses a PNE. Later, Panagopoulou and Spirakis [30] proved that PNE always exist for instances with uniform exponential cost functions c f x = e x .…”

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confidence: 99%

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On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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We study the existence of pure Nash equilibria in weighted congestion games. Let denote a set of cost functions. We say that is consistent if every weighted congestion game with cost functions in possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consistency of continuous cost functions. We prove that a set of continuous functions is consistent for two-player games if and only if contains only monotonic functions and for all nonconstant functions c 1 c 2 ∈ , there are constants a b ∈ such that c 1 x = a c 2 x + b for all x ∈ ≥0 . For games with at least three players, we prove that is consistent if and only if exactly one of the following cases holds: (a) contains only affine functions; (b) contains only exponential functions such that c x = a c e x + b c for some a c b c ∈ , where a c and b c may depend on c, while must be equal for every c ∈ . The latter characterization is even valid for three-player games. Finally, we derive several characterizations of consistency of cost functions for games with restricted strategy spaces, such as weighted network congestion games or weighted congestion games with singleton strategies.

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confidence: 93%

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On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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“…There is one common resource, every player can request an arbitrary part of this resource and the payoff of every player depends on the moves of all players. Note that this game bears some similarity with congestion games [23] but it does not fit into the class of congestion games or weighted congestion games (See for example [23,16,15,9]). In the one-shot game the cost cannot be a timeout since there is only one round.…”

Section: Window-games With Non-aimd Flowsmentioning

confidence: 99%

Window-Games between TCP Flows

Efraimidis

Tsavlidis

2008

Algorithmic Game Theory

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Abstract. We consider network congestion problems between TCP flows and define a new game, the Window-game, which models the problem of network congestion caused by the competing flows. Analytical and experimental results show the relevance of the Window-game to the real TCP game and provide interesting insight on Nash equilibria of the respective network games. Furthermore, we propose a new algorithmic queue mechanism, called Prince, which at congestion makes a scapegoat of the most greedy flow. Preliminary evidence shows that Prince achieves efficient Nash equilibria while requiring only limited computational resources.

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Algorithmic Game Theory and Applications

Nayak

2007

Handbook of Applied Algorithms

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Most of the existing and foreseen complex networks, such as the Internet, are operated and built by thousands of large and small entities (autonomous agents), which collaborate to process and deliver end-to-end flows originating from and terminating at any of them. The distributed nature of the Internet implies a lack of coordination among its users. Instead, each user attempts to obtain maximum performance according to his own parameters and objectives.Methods from game theory and mathematical economics have been proven to be a powerful modeling tool, which can be applied to understand, control, and efficiently design such dynamic, complex networks. Game theory provides a good starting point for computer scientists in their endeavor to understand selfish rational behavior in complex networks with many agents (players). Such scenarios are readily modeled using techniques from game theory, where players with potentially conflicting goals participate in a common setting with well-prescribed interactions.Nash equilibrium [73,74] distinguishes itself as the predominant concept of rationality in noncooperative settings. So, game theory and its various concepts of equilibria provide a rich framework for modeling the behavior of selfish agents in these kinds of distributed or networked environments; they offer mechanisms to achieve efficient and desirable global outcomes in spite of the selfish behavior.Mechanism design, a subfield of game theory, asks how one can design systems so that agents' selfish behavior results to desired systemwide goals. Algorithmic mechanism design additionally considers computational tractability to the set of concerns of mechanism design. Work on algorithmic mechanism design has focused on the complexity of centralized implementations of game-theoretic mechanisms for distributed optimization problems. Moreover, in such huge and heterogeneous networks, each agent does not have access to (and may not process) complete information. 286 ALGORITHMIC GAME THEORY AND APPLICATIONSThe notion of bounded rationality for agents and the design of corresponding incomplete-information distributed algorithms have been successfully utilized to capture the aspect of lack of global knowledge in information networks.In this chapter, we review some of the most thrilling algorithmic problems and solutions, and corresponding advances, achieved on the account of game theory. The areas addressed are the following.Congestion games A central problem arising in the management of large-scale communication networks is that of routing traffic through the network. However, due to the large size of these networks, it is often impossible to employ a centralized traffic management. A natural assumption to make in the absence of central regulation is that network users behave selfishly and aim at optimizing their own individual welfare. One way to address this problem is to model this scenario as a noncooperative multiplayer game and formalize it using congestion game. Congestion games (either unweighted or weighted) offer ...

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Selfish unsplittable flows

Cited by 171 publications

References 19 publications

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Window-Games between TCP Flows

Algorithmic Game Theory and Applications

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