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THE PRICE OF ANARCHY FOR RESTRICTED PARALLEL LINKS

MARTIN GAIRING, THOMAS LÜCKING, MARIOS MAVRONICOLAS, BURKHARD MONIEN
2006 Parallel Processing Letters  
In this work, we present a comprehensive collection of bounds on Price of Anarchy for the model of restricted parallel links.  ...  In the model of restricted parallel links, n users must be routed on m parallel links under the restriction that the link for each user be chosen from a certain set of allowed links for the user.  ...  The Price of Anarchy for Restricted Parallel Links Consider now a link j ∈ [m] with c j < 1 OPT (w, c) .  ... 
doi:10.1142/s0129626406002514 fatcat:p4y44ee4nbelrc4xudg6ydq4zy

Nash Equilibria, the Price of Anarchy and the Fully Mixed Nash Equilibrium Conjecture [chapter]

Martin Gairing, Thomas Lücking, Burkhard Monien, Karsten Tiemann
2005 Lecture Notes in Computer Science  
Finally, the price of anarchy found its way into congestion games [4, 11] .  ...  The network consists of a single source and a single destination which are connected by parallel links.  ...  Fig. 2 . 2 Pure and mixed price of anarchy for the KP-model Fig. 3 . 3 Pure price of anarchy for the KP-model with restricted strategy sets analysis significantly simpler and allows the investigation  ... 
doi:10.1007/11523468_5 fatcat:imivbt76zvc6nlmsao6tvrrgli

The Influence of Link Restrictions on (Random) Selfish Routing [chapter]

Martin Hoefer, Alexander Souza
2008 Lecture Notes in Computer Science  
In this paper we consider the influence of link restrictions on the price of anarchy for several social cost functions in the following model of selfish routing.  ...  For total latency cost, we show the tight result that the price of anarchy is essentially Θ (n √ m/t).  ...  Our main result states that the price of anarchy for general restrictions behaves similarly as for clustered restrictions.  ... 
doi:10.1007/978-3-540-79309-0_4 fatcat:rpojqddhzzgv7c35k7n7bdbzyy

Routing games with elastic traffic

Peter Key, Alexandre Proutiere
2009 Performance Evaluation Review  
TCP) which ultimately maximize a certain notion of the network utility. We analyze the existence and the performance of the Nash Equilibria (NEs) of the resulting routing games.  ...  In this paper, we introduce and investigate a novel class of multipath routing games with elastic traffic.  ...  We now restrict our attention to parallel link networks where all links have unit capacity.  ... 
doi:10.1145/1639562.1639587 fatcat:lges7ubo4bcqzngpngj3qosmf4

The Price of Anarchy for Polynomial Social Cost [chapter]

Martin Gairing, Thomas Lücking, Marios Mavronicolas, Burkhard Monien
2004 Lecture Notes in Computer Science  
Moreover, we give upper bounds on the Price of Anarchy.  ...  We prove the Fully Mixed Nash Equilibrium Conjecture for identical users and two links, and establish an approximate version of the conjecture for arbitrary many links.  ...  We also obtain an upper bound on the Price of Anarchy for the general case of polynomials with non-negative coefficients. We then generalize these results to the case of many links.  ... 
doi:10.1007/978-3-540-28629-5_44 fatcat:zjrdr6haanfa7oiowtz27dfh2q

The price of anarchy for polynomial social cost

Martin Gairing, Thomas Lücking, Marios Mavronicolas, Burkhard Monien
2006 Theoretical Computer Science  
Moreover, we give upper bounds on the Price of Anarchy.  ...  We prove the Fully Mixed Nash Equilibrium Conjecture for identical users and two links, and establish an approximate version of the conjecture for arbitrary many links.  ...  We also obtain an upper bound on the Price of Anarchy for the general case of polynomials with non-negative coefficients. We then generalize these results to the case of many links.  ... 
doi:10.1016/j.tcs.2006.07.055 fatcat:qgiixr7fozc27dafjmfsfvmqdm

Altruism, selfishness, and spite in traffic routing

Po-An Chen, David Kempe
2008 Proceedings of the 9th ACM conference on Electronic commerce - EC '08  
We show that if the average of the coefficients for the altruistic components of all users isβ, then the price of anarchy is bounded by 1/β, for single commodity parallel link networks, and arbitrary convex  ...  We extend this result to give more precise bounds on the price of anarchy for specific classes of latency functions, even for β < 0 modeling spiteful behavior.  ...  Acknowledgments We would like to thank Tim Roughgarden and Pierre-Olivier Weill for useful discussions and references, and several anonymous referees for detailed and useful comments.  ... 
doi:10.1145/1386790.1386816 dblp:conf/sigecom/ChenK08 fatcat:jopk5fwqjjdntptaels3afbaam

The price of anarchy is independent of the network topology

Tim Roughgarden
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
for any multicommodity flow network is achieved by a singlecommodity instance on a network of parallel links.  ...  These are the first tight analyses of the price of anarchy for significant classes of latency functions outside the class of linear functions.  ...  Acknowledgements We thank Amir Ronen for substantially simplifying our original proof of Theorem 3.8,Éva Tardos for helpful discussions and for suggestions on an earlier draft of this paper, and the anonymous  ... 
doi:10.1145/509907.509971 dblp:conf/stoc/Roughgarden02 fatcat:seq2vrqa5rdnll7zanwlt6pdle

The price of anarchy is independent of the network topology

Tim Roughgarden
2003 Journal of computer and system sciences (Print)  
for any multicommodity flow network is achieved by a singlecommodity instance on a network of parallel links.  ...  These are the first tight analyses of the price of anarchy for significant classes of latency functions outside the class of linear functions.  ...  Acknowledgements We thank Amir Ronen for substantially simplifying our original proof of Theorem 3.8,Éva Tardos for helpful discussions and for suggestions on an earlier draft of this paper, and the anonymous  ... 
doi:10.1016/s0022-0000(03)00044-8 fatcat:je7elvdlvzcjnprxruoitityse

The price of anarchy is independent of the network topology

Tim Roughgarden
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
for any multicommodity flow network is achieved by a singlecommodity instance on a network of parallel links.  ...  These are the first tight analyses of the price of anarchy for significant classes of latency functions outside the class of linear functions.  ...  Acknowledgements We thank Amir Ronen for substantially simplifying our original proof of Theorem 3.8,Éva Tardos for helpful discussions and for suggestions on an earlier draft of this paper, and the anonymous  ... 
doi:10.1145/509967.509971 fatcat:fxi7dp36zfc5zdzce54lhtqvne

Wardrop Equilibria and Price of Stability for Bottleneck Games with Splittable Traffic [chapter]

Vladimir Mazalov, Burkhard Monien, Florian Schoppmann, Karsten Tiemann
2006 Lecture Notes in Computer Science  
Finally, our main result is giving a new exact price of stability for Wardrop/bottleneck games on parallel links with M/M/1 latency functions.  ...  For the price of stability, we give an independence result with regard to the network topology.  ...  We would like to thank Marios Mavronicolas for many helpful comments.  ... 
doi:10.1007/11944874_30 fatcat:gxe4nt57bzhhdj4kbiqoftd2ci

Coordination mechanisms for congestion games

Marek Chrobak, Elias Koutsoupias
2004 ACM SIGACT News  
But this approach is very restricted; it does not even improve the price of anarchy on the two parallel links network.  ...  The price of anarchy in this case is 4/3. A similar situation occurs on the example with the two parallel links.  ... 
doi:10.1145/1054916.1054933 fatcat:ehonaytd4rdglkzq4qromhj36m

Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost [chapter]

Dimitris Fotakis, Spyros Kontogiannis, Paul Spirakis
2006 Lecture Notes in Computer Science  
We prove that for any network of m uniformly related links and for identical users, the price of anarchy is Θ( log m log log m ).  ...  Thus, we essentially indicate the limits of the applicability of this greedy approach. We also study the price of anarchy for the objective of maximum latency.  ...  We wish to thank Burkhard Monien for suggesting the significance and the possibility of obtaining stronger results on the efficient computation of PNE in series-parallel networks.  ... 
doi:10.1007/11671411_13 fatcat:fnmugrwtxjbhzccltoujee4ajy

Bertrand competition in networks

Shuchi Chawla, Feng Niu, Tim Roughgarden
2009 ACM SIGecom Exchanges  
We briefly summarize our recent work characterizing the efficiency of equilibria in pricing games in two-sided combinatorial markets.  ...  single-sink parallel-link network).  ...  The value of consumer u for path p is simply u + Q p . In the unrelated values model consumer values are arbitrary. We study these models in single-source single-sink parallel link networks.  ... 
doi:10.1145/1598780.1598790 fatcat:ywii6andt5diveh3djviq2ue44

Bertrand Competition in Networks [chapter]

Shuchi Chawla, Tim Roughgarden
2008 Lecture Notes in Computer Science  
We briefly summarize our recent work characterizing the efficiency of equilibria in pricing games in two-sided combinatorial markets.  ...  single-sink parallel-link network).  ...  The value of consumer u for path p is simply u + Q p . In the unrelated values model consumer values are arbitrary. We study these models in single-source single-sink parallel link networks.  ... 
doi:10.1007/978-3-540-79309-0_8 fatcat:akbgyw2e3fai3jaw42dktbelm4
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