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Optimal Cost-Sharing in Weighted Congestion Games [chapter]

Vasilis Gkatzelis, Konstantinos Kollias, Tim Roughgarden
2014 Lecture Notes in Computer Science  
We identify how to share costs locally in weighted congestion games with polynomial cost functions to minimize the worst-case price of anarchy (POA).  ...  ) congestion games.  ...  Which cost-sharing rule minimizes the worst-case POA in weighted congestion games?  ... 
doi:10.1007/978-3-319-13129-0_6 fatcat:kunosk57uvaojhb3ye57rohv2y

Tight Bounds for Cost-Sharing in Weighted Congestion Games [chapter]

Martin Gairing, Konstantinos Kollias, Grammateia Kotsialou
2015 Lecture Notes in Computer Science  
This work studies the price of anarchy and the price of stability of cost-sharing methods in weighted congestion games.  ...  We then turn to the price of stability and prove an upper bound for the Shapley value cost-sharing method, which holds for general sets of cost functions and which is tight in special cases of interest  ...  By Nash's famous theorem, a MNE is guaranteed to exist in every weighted congestion game. However, existence of a PNE is not guaranteed for some cost-sharing methods.  ... 
doi:10.1007/978-3-662-47666-6_50 fatcat:ifsd7oxvxzdm5jvev22xjn5rti

Sharing Non-Anonymous Costs of Multiple Resources Optimally [article]

Max Klimm, Daniel Schmand
2015 arXiv   pre-print
In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs.  ...  costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users.  ...  In forthcoming work, Gkatzelis et al. [5] examined optimal cost sharing rules for weighted congestion games with polynomial cost functions.  ... 
arXiv:1412.4456v2 fatcat:d6rnam2wejdgbaonohv4sxeily

Restoring Pure Equilibria to Weighted Congestion Games [chapter]

Konstantinos Kollias, Tim Roughgarden
2011 Lecture Notes in Computer Science  
We propose a new way of assigning costs to players with weights in congestion games that recovers the important properties of the unweighted model.  ...  Weighted variants of congestion games that rely on sharing costs proportional to players' weights do not generally have pure-strategy Nash equilibria.  ...  This worst-case POA is larger, but only slightly, than the one in weighted congestion games with proportional cost sharing that have PNE.  ... 
doi:10.1007/978-3-642-22012-8_43 fatcat:asc7k45syvbkdaanslwp3rrzai

Sharing Non-anonymous Costs of Multiple Resources Optimally [chapter]

Max Klimm, Daniel Schmand
2015 Lecture Notes in Computer Science  
In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs.  ...  costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users.  ...  In forthcoming work, Gkatzelis et al. [5] examined optimal cost sharing rules for weighted congestion games with polynomial cost functions.  ... 
doi:10.1007/978-3-319-18173-8_20 fatcat:blceikiywbb2dngiag5m5bhwya

Fast convergence to nearly optimal solutions in potential games

Baruch Awerbuch, Yossi Azar, Amir Epstein, Vahab Seyed Mirrokni, Alexander Skopalik
2008 Proceedings of the 9th ACM conference on Electronic commerce - EC '08  
We extend these results for congestion games to other potential games including weighted congestion games with linear delay functions, cut games (also called party affiliation games) and market sharing  ...  in asymmetric congestion games is exponential [23].  ...  In weighted congestion games, player i has weighted demand w i . We denote by l e (S), the congestion(load) on resource e in a state S, i.e., l e (S) = i|e∈S i w i .  ... 
doi:10.1145/1386790.1386832 dblp:conf/sigecom/AwerbuchAEMS08 fatcat:7gwjunsbbrdzvpf5f6yxgd5fha

Reconciling the Overlay and Underlay Tussle

Jin Xiao, Raouf Boutaba
2014 IEEE/ACM Transactions on Networking  
For weighted games, we find that weighted Shapley potential can achieve linear time convergence to an operable state.  ...  Furthermore, we analyze the interaction of overlays and underlays as a two-stage congestion game and recommend simple operational guidelines to ensure global stability.  ...  It is known that weighted congestion games do not have pure Nash equilibrium in general.  ... 
doi:10.1109/tnet.2013.2281276 fatcat:zi4t24oh7feklpmso22wcnup5y

The Complexity of Equilibria in Cost Sharing Games [chapter]

Vasilis Syrgkanis
2010 Lecture Notes in Computer Science  
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.  ...  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  ...  The Cost Sharing Game with Fair Cost Allocation constructed in the MAX CUT reduction is a 2-Congestable Cost Sharing Game.  ... 
doi:10.1007/978-3-642-17572-5_30 fatcat:6nenxvzk5jhproi64tox7qupdm

A Unifying Approximate Potential for Weighted Congestion Games [article]

Yiannis Giannakopoulos, Diogo Poças
2022 arXiv   pre-print
We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability.  ...  We demonstrate the power of our tool by applying it to recover the recent result of Caragiannis and Fanelli [ICALP'19] for polynomial congestion games; improve upon the bounds for fair cost sharing games  ...  Fix a fair cost sharing game with unit minimum weight ( min = 1), and let max , be the maximum weight and the maximum total load.  ... 
arXiv:2005.10101v3 fatcat:jd6l5yehp5f4xj5gwrgzd25zuu

Exact Price of Anarchy for Polynomial Congestion Games [chapter]

Sebastian Aland, Dominic Dumrauf, Martin Gairing, Burkhard Monien, Florian Schoppmann
2006 Lecture Notes in Computer Science  
The given values also hold for weighted and unweighted network congestion games.  ...  We show exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions.  ...  In both cases they define social cost as expected maximum latency. For a survey on weighted congestion games we refer to [13] .  ... 
doi:10.1007/11672142_17 fatcat:blqhhxartbab3kfvwil6vzsxn4

Selfish unsplittable flows

Dimitris Fotakis, Spyros Kontogiannis, Paul Spirakis
2005 Theoretical Computer Science  
Motivated by this question we generalize the model of in: , to the case of weighted congestion games.  ...  On the other hand, we prove that any weighted network congestion game with linear edge delays admits a pure Nash equilibrium that can be found in pseudo-polynomial time.  ...  A weighted congestion game associated with this model is a game in strategic form with the set of users N and user demands (w i ) i∈N , the action sets ( i ) i∈N and cost functions ( i r i ) i∈N,r i ∈  ... 
doi:10.1016/j.tcs.2005.09.024 fatcat:3tv776hihfe43i75glvs5ipns4

Competitive equilibrium and stable coalition in overlay environments

Shan Jiang, Jianxin Liao, Jun Gong, Jingyu Wang, Tonghong Li
2015 2015 IEEE 40th Conference on Local Computer Networks (LCN)  
In this paper, we adopt game theoretic approaches to analyze this hybrid interaction.  ...  Secondly, we model another situation of the hybrid interaction as a 1-leadern-follower Stackelberg-Nash game, where TE is the leader and coexisting overlays are followers, and prove that the cost at Stackelberg-Nash  ...  Thus, is defined by: , (11) where is the equivalent weight between congestion and delay, i.e., when sharing cost, 1 unit congestion equals to units delay.  ... 
doi:10.1109/lcn.2015.7366331 dblp:conf/lcn/JiangLGWL15 fatcat:g5vtmmqmq5gt3pg5lfh6m3wmlu

Restoring Pure Equilibria to Weighted Congestion Games

Konstantinos Kollias, Tim Roughgarden
2015 ACM Transactions on Economics and Computation  
This worst-case POA is slightly larger than that in weighted congestion games with proportional cost shares that have PNE.  ...  Arbitrary Congestion-Type Games The (weighted) Shapley shares in Definitions 3.1 and 3.2 can be generalized to arbitrary congestion-type games.  ...  Its cost function is c e and the weight of the corresponding player is w e . Let l, r be the left and right children of e, with corresponding player weights w l = z 1 · w e and w r = z 2 · w e .  ... 
doi:10.1145/2781678 fatcat:rfwcr6znsvgntmorwy4yjz3taq

The Efficiency of Best-Response Dynamics [article]

Michal Feldman and Yuval Snappir and Tami Tamir
2020 arXiv   pre-print
We study the inefficiency of various deviator rules in network formation games and job scheduling games (both are congestion games, where BR dynamics always converges to a pure NE).  ...  For some classes of games, we compute optimal deviator rules. Furthermore, we define and study a new class of deviator rules, called local deviator rules.  ...  • e 2 has cost 3 + and is shared by n players with the weights {a i } n i=1 corresponding to the Partition instance. • e 3 has cost 9 + and is shared by 6 unit-weight players. • e 4 has cost 2 and is  ... 
arXiv:2002.11461v1 fatcat:jp55zmdmcvbdhnbyjeu7tvwaae

On Spectrum Selection Games in Cognitive Radio Networks

Ilaria Malanchini, Matteo Cesana, Nicola Gatti
2009 GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference  
The cost of spectrum mobility is also accounted in the analytical framework. Numerical results are reported to assess the quality of the game equilibria.  ...  In this paper, a game theoretic framework is proposed to evaluate spectrum management functionalities in Cognitive Radio Networks.  ...  Moreover, the game is non-weighted, since users congest the resources with the same weight and with linear cost functions.  ... 
doi:10.1109/glocom.2009.5425335 dblp:conf/globecom/MalanchiniCG09 fatcat:xrh5eibu5bcfngmn4imdcc53mu
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