On the impact of combinatorial structure on congestion games

Ackermann, Heiner; Röglin, Heiko; Vöcking, Berthold

doi:10.1145/1455248.1455249

Cited by 179 publications

(251 citation statements)

References 13 publications

Supporting

Mentioning

250

Contrasting

Order By: Relevance

“…On the other hand, Fabrikant et al [10] have studied the complexity of computing Nash equilibria in general congestion games proving that such a problem is PLS-complete. Ackermann et al [1] have shown that such result still holds if we restrict to unweighted congestion games with linear delay functions. From these results it follows that there exist linear congestion games with initial states such that any improvement sequence starting from these states needs an exponential number of steps to reach a Nash equilibrium.…”

Section: Related Workmentioning

confidence: 74%

“…Moreover from their completeness proof and from previous results about local search problems, it follows that there exist congestion games with initial states such that any improvement sequence starting from these states needs an exponential number of steps in order to reach a Nash equilibrium. More recently, Ackermann et al [1] show that the previous negative result holds even in the restricted case of linear unweighted congestion games. Furthermore, as already remarked, in the more general setting of weighted congestion games Nash equilibria may not exist.…”

Section: Introductionmentioning

confidence: 92%

“…On the one hand, Ackermann et al [1] showed that for matroid congestion games (a special class of congestion games including also the singleton congestion games) the convergence time to Nash equilibria is polynomial. On the other hand, Fabrikant et al [10] have studied the complexity of computing Nash equilibria in general congestion games proving that such a problem is PLS-complete.…”

Section: Related Workmentioning

confidence: 99%

“…Moreover, it is worth noticing that computing in polynomial time best responses still remains possible for some interesting classes of congestion games in which the strategies are represented in a succinct way. For instance, consider the well studied class of network congestion games [1,10] in which we are given a directed graph G whose edges represent the resources, and every player is associated to a pair of nodes u, v ∈ G that she aims at connecting; in such a setting, the strategies associated to a player aiming at connecting u to v are all the simple paths from u to v, and computing the best response is basically a shortest path problem.…”

Section: Definitions and Notationmentioning

confidence: 99%

See 3 more Smart Citations

On best response dynamics in weighted congestion games with polynomial delays

Fanelli

Moscardelli

2011

Distrib. Comput.

View full text Add to dashboard Cite

We investigate the speed of convergence of best response dynamics to approximately optimal solutions in weighted congestion games with polynomial delay functions. Awerbuch et al. (Fast convergence to nearly optimal solutions in potential games. ACM Conference on Electronic Commerce, 2008) showed that the convergence time of such dynamics to Nash equilibrium may be exponential in the number of players n even for unweighted players and linear delay functions. Nevertheless, we show that (n log log W ) (where W is the sum of all the players' weights) best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every O(n) steps each player performs a constant (and non-null) number of best responses. For congestion games in which computing a best response is a polynomial time solvable problem, such a dynamics naturally implies a polynomial time distributed algorithm for the problem of computing the social optimum in congestion games, approximating the optimal solution by a constant factor.

show abstract

Section: Related Workmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 92%

Section: Related Workmentioning

confidence: 99%

Section: Definitions and Notationmentioning

confidence: 99%

See 2 more Smart Citations

On best response dynamics in weighted congestion games with polynomial delays

Fanelli

Moscardelli

2011

Distrib. Comput.

View full text Add to dashboard Cite

show abstract

“…In particular, the problem of computing a pure Nash equilibrium has been shown to be PLS-complete in congestion games by Fabrikant et al (2004) and in some of their special cases by Ackermann et al (2008), where congestion games, introduced by Rosenthal (1973), is a well-known and significative class of games represented in succinct form for which existence of pure Nash equilibria is always guaranteed. Moreover, the problem of computing a (mixed) Nash equilibrium has been shown to be PPAD-complete for any number of players (Chen et al 2009;Daskalakis et al 2009;Daskalakis and Papadimitriou 2005), even in games represented in standard normal form, i.e., by explicitly listing the utility of each player in any possible strategy profile.…”

Section: Introductionmentioning

confidence: 99%

On the performance of mildly greedy players in cut games

Bilò

Paladini

2015

J Comb Optim

View full text Add to dashboard Cite

We continue the study of the performance of mildly greedy players in cut games initiated by Christodoulou et al. (Theoret Comput Sci 438:13-27, 2012), where a mildly greedy player is a selfish agent who is willing to deviate from a certain strategy profile only if her payoff improves by a factor of more than 1 + , for some given ≥ 0. Hence, in presence of mildly greedy players, the classical concepts of pure Nash equilibria and best-responses generalize to those of (1 + )-approximate pure Nash equilibria and (1 + )-approximate best-responses, respectively. We first show that the -approximate price of anarchy, that is the price of anarchy of (1 + )-approximate pure Nash equilibria, is at least 1 2+ and that this bound is tight for any ≥ 0. Then, we evaluate the approximation ratio of the solutions achieved after a (1 + )-approximate one-round walk starting from any initial strategy profile, where a (1 + )-approximate one-round walk is a sequence of (1 + )-approximate bestresponses, one for each player. We improve the currently known lower bound on this ratio from min 1 4+2 , 4+2 up to min 1 2+ , 2 (1+ )(2+ ) and show that this is again tight for any ≥ 0. An interesting and quite surprising consequence of our results is that the worst-case performance guarantee of the very simple solutions generated after a (1 + )-approximate one-round walk is the same as that of (1 + )-approximate pure Nash equilibria when ≥ 1 and of that of subgame perfect equilibria (i.e., Nash equilibria for greedy players with farsighted, rather than myopic, rationality) when = 1.

show abstract

Algorithmic Game Theory and Applications

Nayak

2007

Handbook of Applied Algorithms

View full text Add to dashboard Cite

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 ...

show abstract

On the impact of combinatorial structure on congestion games

Cited by 179 publications

References 13 publications

On best response dynamics in weighted congestion games with polynomial delays

On best response dynamics in weighted congestion games with polynomial delays

On the performance of mildly greedy players in cut games

Algorithmic Game Theory and Applications

Contact Info

Product

Resources

About