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THE PRICE OF ANARCHY FOR RESTRICTED PARALLEL LINKS

2006
*
Parallel Processing Letters
*

In this work, we present a comprehensive collection

doi:10.1142/s0129626406002514
fatcat:p4y44ee4nbelrc4xudg6ydq4zy
*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) . ...##
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Nash Equilibria, the Price of Anarchy and the Fully Mixed Nash Equilibrium Conjecture
[chapter]

2005
*
Lecture Notes in Computer Science
*

Finally,

doi:10.1007/11523468_5
fatcat:imivbt76zvc6nlmsao6tvrrgli
*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 ...##
###
The Influence of Link Restrictions on (Random) Selfish Routing
[chapter]

2008
*
Lecture Notes in Computer Science
*

In this paper we consider

doi:10.1007/978-3-540-79309-0_4
fatcat:rpojqddhzzgv7c35k7n7bdbzyy
*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*. ...##
###
Routing games with elastic traffic

2009
*
Performance Evaluation Review
*

TCP) which ultimately maximize a certain notion

doi:10.1145/1639562.1639587
fatcat:lges7ubo4bcqzngpngj3qosmf4
*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. ...##
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The Price of Anarchy for Polynomial Social Cost
[chapter]

2004
*
Lecture Notes in Computer Science
*

Moreover, we give upper bounds on

doi:10.1007/978-3-540-28629-5_44
fatcat:zjrdr6haanfa7oiowtz27dfh2q
*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*. ...##
###
The price of anarchy for polynomial social cost

2006
*
Theoretical Computer Science
*

Moreover, we give upper bounds on

doi:10.1016/j.tcs.2006.07.055
fatcat:qgiixr7fozc27dafjmfsfvmqdm
*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*. ...##
###
Altruism, selfishness, and spite in traffic routing

2008
*
Proceedings of the 9th ACM conference on Electronic commerce - EC '08
*

We show that if

doi:10.1145/1386790.1386816
dblp:conf/sigecom/ChenK08
fatcat:jopk5fwqjjdntptaels3afbaam
*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. ...##
###
The price of anarchy is independent of the network topology

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 ...

##
###
The price of anarchy is independent of the network topology

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 ...

##
###
The price of anarchy is independent of the network topology

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 ...

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

2006
*
Lecture Notes in Computer Science
*

Finally, our main result is giving a new exact

doi:10.1007/11944874_30
fatcat:gxe4nt57bzhhdj4kbiqoftd2ci
*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. ...##
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Coordination mechanisms for congestion games

2004
*
ACM SIGACT News
*

But this approach is very

doi:10.1145/1054916.1054933
fatcat:ehonaytd4rdglkzq4qromhj36m
*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*. ...##
###
Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost
[chapter]

2006
*
Lecture Notes in Computer Science
*

We prove that

doi:10.1007/11671411_13
fatcat:fnmugrwtxjbhzccltoujee4ajy
*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. ...##
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Bertrand competition in networks

2009
*
ACM SIGecom Exchanges
*

We briefly summarize our recent work characterizing

doi:10.1145/1598780.1598790
fatcat:ywii6andt5diveh3djviq2ue44
*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. ...##
###
Bertrand Competition in Networks
[chapter]

2008
*
Lecture Notes in Computer Science
*

We briefly summarize our recent work characterizing

doi:10.1007/978-3-540-79309-0_8
fatcat:akbgyw2e3fai3jaw42dktbelm4
*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. ...
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