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LP-based Covering Games with Low Price of Anarchy [article]

Georgios Piliouras, Tomas Valla, Laszlo A. Vegh
2012 arXiv   pre-print
In particular, we describe a vertex cover game with a price of anarchy of 2.  ...  studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]).  ...  Our game approach extends even to this setting, with the same price of anarchy d.  ... 
arXiv:1203.0050v1 fatcat:ppcxryvn5fb3zguzesoamxivn4

LP-Based Covering Games with Low Price of Anarchy [chapter]

Georgios Piliouras, Tomáš Valla, László A. Végh
2012 Lecture Notes in Computer Science  
Each one of these papers was thoroughly reviewed by two experts, in accordance with the high standards of this journal.  ...  Online algorithms need to make decisions based on information that is provided to them as the algorithms execute, without knowledge of the information that will be provided to them in the future.  ...  technique based on the use of adaptive constructions to compute new lower bounds for several variants of the online bin packing problem.  ... 
doi:10.1007/978-3-642-35311-6_14 fatcat:neldp3gg3nfmpmbbzgtre3pqfi

LP-Based Covering Games with Low Price of Anarchy

Georgios Piliouras, Tomáš Valla, László A Végh
2014 Theory of Computing Systems  
The authors of [3] proposed an algorithm for the GWPM problem based on the weighted prefix table that works in O(nz 2 log z + nσ ) time.  ...  In the most common definition of the problem (see [3, 13] ), we are to find all fragments of the text that give a positive answer to the WEIGHTED CONSENSUS problem with the pattern.  ...  Acknowledgments This work was supported by the "Algorithms for text processing with errors and uncertainties" project carried out within the HOMING programme of the Foundation for Polish Science co-financed  ... 
doi:10.1007/s00224-014-9587-z fatcat:qw4rfbnyozh5loesaa23kopx24

Non-cooperative facility location and covering games

Jean Cardinal, Martin Hoefer
2010 Theoretical Computer Science  
In general the cost of pure-strategy Nash equilibria in this game can be prohibitively high, as both prices of anarchy and stability are in Θ(k).  ...  We study a general class of non-cooperative games coming from combinatorial covering and facility location problems. A game for k players is based on an integer programming formulation.  ...  Acknowledgement Part of this work was done during a visit at Dortmund University. I am grateful to Piotr Krysta and Patrick Briest for enlightening discussions on the topic.  ... 
doi:10.1016/j.tcs.2010.02.005 fatcat:fszqswohdzgchiwrs7zn43xbou

Non-cooperative Facility Location and Covering Games [chapter]

Martin Hoefer
2006 Lecture Notes in Computer Science  
In general the cost of pure-strategy Nash equilibria in this game can be prohibitively high, as both prices of anarchy and stability are in Θ(k).  ...  We study a general class of non-cooperative games coming from combinatorial covering and facility location problems. A game for k players is based on an integer programming formulation.  ...  Acknowledgement Part of this work was done during a visit at Dortmund University. I am grateful to Piotr Krysta and Patrick Briest for enlightening discussions on the topic.  ... 
doi:10.1007/11940128_38 fatcat:fgnvrvoltzh3rkysf34cou3sme

Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round [article]

Paul Dütting, Thomas Kesselheim, Éva Tardos
2015 arXiv   pre-print
Our goal is to show that a wide class of approximation algorithms yields this way mechanisms with low Price of Anarchy.  ...  The seminal result of Lucier and Borodin [SODA 2010] shows that combining a greedy algorithm that is an α-approximation algorithm with a pay-your-bid payment rule yields a mechanism whose Price of Anarchy  ...  combinatorial characterization of algorithms with low price of anarchy.  ... 
arXiv:1511.09208v1 fatcat:r7clduspyjeq7ito6tzrnsnuia

Existence Theorems and Approximation Algorithms for Generalized Network Security Games

V.S. Anil Kumar, Rajmohan Rajaraman, Zhifeng Sun, Ravi Sundaram
2010 2010 IEEE 30th International Conference on Distributed Computing Systems  
We design a general LP-based framework for approximating the NP-complete problem of finding a socially optimal configuration in our game.  ...  For local and global games, we also characterize the price of anarchy in terms of the maximum degree and vertex expansion of the contact network; these suggest natural heuristics to aid a network planner  ...  Therefore, ensuring that the system has efficient NE is desirable (equivalently, a low price of anarchy (PoA)) for network planners.  ... 
doi:10.1109/icdcs.2010.70 dblp:conf/icdcs/KumarRSS10 fatcat:zpqexm5zmjaobnwe3ykvynim2e

Minimally invasive mechanism design: Distributed covering with carefully chosen advice

Maria-Florina Balcan, Sara Krehbiel, Georgios Piliouras, Jinwoo Shin
2012 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)  
We show that with an arbitrary advice vector, a set cover game quickly converges to an equilibrium with cost of the same order as the square of the social cost of the advice vector.  ...  We apply this approach to a broad family of potential games modeling vertex cover and set cover optimization problems in a distributed setting.  ...  Our Contribution We show indeed that the high price of anarchy results for the case of vertex cover and set cover games can be largely circumvented.  ... 
doi:10.1109/cdc.2012.6426061 dblp:conf/cdc/BalcanKPS12 fatcat:wme7xbkvjbgr7ppynrqgahsq7m

Utility Design for Distributed Resource Allocation – Part II: Applications to Submodular, Covering, and Supermodular Problems [article]

Dario Paccagnan, Jason R. Marden
2021 arXiv   pre-print
In all these cases we obtain tight expressions for the price of anarchy that often match or improve the guarantees associated to state-of-the-art approximation algorithms.  ...  I showed how to design local utilities so as to maximize the associated performance guarantees [Paccagnan et al., TAC 2019] which we measure by the price of anarchy.  ...  We identify the game introduced above with the tuple G = (R, {v r } r∈R , N, {A i } i∈N , f ) . (3) Given a distribution rule f , we measure its performance adapting the notion of price of anarchy [14  ... 
arXiv:1807.01343v4 fatcat:osymwg7rlre7hbnaawe3bdtsde

Game couplings: Learning dynamics and applications

Maria-Florina Balcan, Florin Constantin, Georgios Piliouras, Jeff S. Shamma
2011 IEEE Conference on Decision and Control and European Control Conference  
Furthermore, we extend the price of anarchy framework in this setting, to account both for the social welfare within each subgame as well as that of the coupled game.  ...  of anarchy.  ...  Game Couplings In the preliminaries section, we went over a number of beneficial system level properties such as a low price of anarchy and the existence of a pure Nash equilibrium.  ... 
doi:10.1109/cdc.2011.6161365 dblp:conf/cdc/BalcanCPS11 fatcat:xatrmvpnzfhm7oxx4rnxuodb7y

Near Optimality in Covering and Packing Games by Exposing Global Information [article]

Maria-Florina Balcan, Sara Krehbiel, Georgios Piliouras, Jinwoo Shin
2011 arXiv   pre-print
Covering and packing problems can be modeled as games to encapsulate interesting social and engineering settings. These games have a high Price of Anarchy in their natural formulation.  ...  This paper studies general classes of covering and packing games with learning dynamics models that incorporate a central authority who broadcasts weak, socially beneficial signals to agents that otherwise  ...  As a step in that direction, here we provide a centralized LP-rounding-based poly-time algorithm to find a low-cost configuration s ad for the covering game as follows. 1.  ... 
arXiv:1109.3606v1 fatcat:ymrzh2eyyzczfpa7hbwqh4yx3m

Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

Chi-Kin Chau, Khaled Elbassioni
2017 IEEE Transactions on Control of Network Systems  
We quantify the inefficiency of distributed decision-making processes under a cost-sharing mechanism by the strong price of anarchy (SPoA), comparing a worst-case stable coalition structure and a social  ...  In particular, we derive SPoA for common fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games, and usage based cost-sharing  ...  In general, the strong price of anarchy of usage based costsharing can be Ω(K). Theorem 5.  ... 
doi:10.1109/tcns.2017.2763747 fatcat:filr6bkmmzgynj4unfvt7on5ju

Efficient Black-Box Reductions for Separable Cost Sharing

Tobias Harks, Martin Hoefer, Anja Schedel, Manuel Surek
2020 Mathematics of Operations Research  
In cost-sharing games with delays, a set of agents jointly uses a subset of resources.  ...  Hence, in these domains, any approximation algorithm yields a separable cost-sharing protocol with price of stability bounded by the approximation factor.  ...  For n ≥ 3 players, there is a generalized series-parallel graph with fixed edge costs and no player-specific delays, so that the unique optimal Steiner forest is not enforceable.  ... 
doi:10.1287/moor.2020.1050 fatcat:lgsdyh5frndixnsdpvhqchu7si

Efficient Black-Box Reductions for Separable Cost Sharing [article]

Tobias Harks, Martin Hoefer, Anja Huber, Manuel Surek
2018 arXiv   pre-print
In cost sharing games with delays, a set of agents jointly allocates a finite subset of resources.  ...  Hence, in these domains any approximation algorithm can be used to obtain a separable cost sharing protocol with a price of stability bounded by the approximation factor.  ...  More general separable protocols have been studied mostly in terms of the price of anarchy, e.g., for scheduling (or matroid games) [6, 13, 19, 24, 52] or single-source network design with [20, 21]  ... 
arXiv:1802.10351v1 fatcat:plpke443crcu5h5qxzydtmcmoe

Composable and efficient mechanisms

Vasilis Syrgkanis, Eva Tardos
2013 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13  
We define the class of smooth mechanisms, related to smooth games defined by Roughgarden, that can be thought of as mechanisms that generate approximately market clearing prices.  ...  We initiate the study of efficient mechanism design with guaranteed good properties even when players participate in multiple different mechanisms simultaneously or sequentially.  ...  price of anarchy.  ... 
doi:10.1145/2488608.2488635 dblp:conf/stoc/SyrgkanisT13 fatcat:uofukrqtijalli7v3i33shth4a
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