On the Impact of Combinatorial Structure on Congestion Games

Ackermann, Heiner; Röglin, Heiko; Vöcking, Berthold

doi:10.1109/focs.2006.55

Cited by 83 publications

(133 citation statements)

References 11 publications

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“…For cost functions of the form f (x) = cr(x)/x, where cr(x) is a non-decreasing concave function we also prove PLS-completeness in undirected networks. Thus we extend the results of [7,1] to the non-increasing case. For the case of Matroid Cost Sharing Games, where tractability of Pure Nash Equilibria is known by [1] we give a greedy polynomial time algorithm that computes a Pure Nash Equilibrium with social cost at most the potential of the optimal strategy profile.…”

supporting

confidence: 61%

“…No assumption on the cost functions is made. These games generalize k-Threshold Games introduced by Ackermann et al [1].…”

Section: Resultsmentioning

confidence: 96%

“…In a seminal paper Fabrikant et al [7] proved that the above problem is PLS-complete even in the case where the strategies of the players are paths in a directed network. Later, Ackermann et al [1] extended the above result to the case of undirected networks with linear cost functions. However, both results use cost functions on the resources that are non-decreasing (delays) and do not carry over to Cost Sharing Games.…”

Section: Introductionmentioning

confidence: 93%

“…Moreover, Ackermann et al [1] introduce Matroid Congestion Games as a class of games where best response dynamics converge in polynomially many steps.…”

Section: Related Workmentioning

confidence: 99%

“…Apart from the results mentioned in the introduction [7,1], there has been several works on the relation between PLS and PNE. Skopalik et al [16] proves that even computing an approximate PNE is PLS complete for Congestion Games.…”

Section: Related Workmentioning

confidence: 99%

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The Complexity of Equilibria in Cost Sharing Games

Syrgkanis

2010

Lecture Notes in Computer Science

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Abstract. We study Congestion Games with non-increasing cost functions (Cost Sharing Games) from a complexity perspective and resolve their computational hardness, which has been an open question. Specifically we prove that when the cost functions have the form f (x) = cr/x (Fair Cost Allocation) then it is PLS-complete to compute a Pure Nash Equilibrium even in the case where strategies of the players are paths on a directed network. For cost functions of the form f (x) = cr(x)/x, where cr(x) is a non-decreasing concave function we also prove PLS-completeness in undirected networks. Thus we extend the results of [7,1] to the non-increasing case. For the case of Matroid Cost Sharing Games, where tractability of Pure Nash Equilibria is known by [1] we give a greedy polynomial time algorithm that computes a Pure Nash Equilibrium with social cost at most the potential of the optimal strategy profile. Hence, for this class of games we give a polynomial time version of the Potential Method introduced in [2] for bounding the Price of Stability.

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supporting

confidence: 61%

“…No assumption on the cost functions is made. These games generalize k-Threshold Games introduced by Ackermann et al [1].…”

Section: Resultsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 93%

“…Moreover, Ackermann et al [1] introduce Matroid Congestion Games as a class of games where best response dynamics converge in polynomially many steps.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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The Complexity of Equilibria in Cost Sharing Games

Syrgkanis

2010

Lecture Notes in Computer Science

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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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Computing approximate Nash equilibria in network congestion games

2011

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We consider the problem of computing ε-approximate Nash equilibria in network congestion games. The general problem is known to be PLS-complete for every ε > 0, but the reductions are based on artificial and steep delay functions with the property that already two players using the same resource cause a delay that is significantly larger than the delay for a single player. We consider network congestion games with delay functions such as polynomials, exponential functions, and functions from queuing theory. We analyse which approximation guarantees can be achieved for such congestion games by the method of randomized rounding. Our results show that the success of this method depends on different criteria depending on the class of functions considered. For example, queuing theoretical functions admit good approximations if the equilibrium load of every resource is bounded away appropriately from its capacity.

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On the Impact of Combinatorial Structure on Congestion Games

Cited by 83 publications

References 11 publications

The Complexity of Equilibria in Cost Sharing Games

The Complexity of Equilibria in Cost Sharing Games

Algorithmic Game Theory and Applications

Computing approximate Nash equilibria in network congestion games

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