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Smoothed Efficient Algorithms and Reductions for Network Coordination Games

Shant Boodaghians, Rucha Kulkarni, Ruta Mehta, Michael Wagner
2020 Innovations in Theoretical Computer Science  
We study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case, even when each player has two strategies.  ...  Further, we define a notion of a smoothness-preserving reduction among search problems, and obtain reductions from 2-strategy network coordination games to local-max-cut, and from k-strategy games (k arbitrary  ...  Finding a pure Nash equilibrium in a network coordination game is complete for the class PLS (Polynomial Local Search) [12] .  ... 
doi:10.4230/lipics.itcs.2020.73 dblp:conf/innovations/BoodaghiansKM20 fatcat:ku274ytagreeff77sy7eg5lnua

Computing Nash Equilibria: Approximation and Smoothed Complexity [article]

Xi Chen, Xiaotie Deng, Shang-Hua Teng
2006 arXiv   pre-print
Furthermore, we prove, unless PPAD is in RP, that the smoothed complexity of the Lemke-Howson algorithm or any algorithm for computing a Nash equilibrium of a bimatrix game is polynomial in n and 1/\sigma  ...  In other words, no algorithm with time polynomial in n and 1/\epsilon can compute an \epsilon-approximate Nash equilibrium of an n by nbimatrix game, unless PPAD is in P.  ...  The bimatrix game is in smoothed polynomial time if there exists an algorithm J with polynomial smoothed time-complexity for computing a Nash equilibrium.  ... 
arXiv:cs/0602043v2 fatcat:rjauce5pwbhr7e6ceejmva334a

Computing Nash Equilibria: Approximation and Smoothed Complexity

Xi Chen, Xiaotie Deng, Shang-hua Teng
2006 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)  
In other words, no algorithm with time polynomial in n and 1/ can compute an -approximate Nash equilibrium of an n×n bimatrix game, unless PPAD ⊆ P.  ...  Furthermore, we prove that it is unlikely, unless PPAD ⊆ RP, that the smoothed complexity of the Lemke-Howson algorithm or any algorithm for computing a Nash equilibrium of a bimatrix game is polynomial  ...  The bimatrix game is in smoothed polynomial time if there exists an algorithm J with polynomial smoothed time-complexity for computing a Nash equilibrium.  ... 
doi:10.1109/focs.2006.20 dblp:conf/focs/ChenDT06 fatcat:kit3shzrebhofnyrq4ota665ji

Smoothed Efficient Algorithms and Reductions for Network Coordination Games [article]

Shant Boodaghians, Rucha Kulkarni, Ruta Mehta
2019 arXiv   pre-print
To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case.  ...  Second, we define a notion of smoothness-preserving reduction among search problems, and obtain reductions from 2-strategy network coordination games to local-max-cut, and from k-strategy games (with arbitrary  ...  We would like to thank Pravesh Kothari for the insightful discussions in the initial stages of this work.  ... 
arXiv:1809.02280v4 fatcat:u5iezhj4j5b4vjuf3fzyq4qgji

Congestion Games with Complementarities [chapter]

Matthias Feldotto, Lennart Leder, Alexander Skopalik
2017 Lecture Notes in Computer Science  
We consider congestion games with different aggregation functions. In particular, we study L_p norms and analyze the existence and complexity of (approximate) pure Nash equilibria.  ...  We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in modern networked environments.  ...  computed in polynomial time.  ... 
doi:10.1007/978-3-319-57586-5_19 fatcat:h7fqtbxfxvexvl5pbnoz2qnizm

Strong Price of Anarchy and Coalitional Dynamics [article]

Yoram Bachrach, Vasilis Syrgkanis, Eva Tardos, Milan Vojnovic
2013 arXiv   pre-print
Additionally, we show that in potential games the strong price of anarchy is close to the price of stability, the quality of the best Nash equilibrium.  ...  We introduce a framework for studying the effect of cooperation on the quality of outcomes in utility games.  ...  In the context of utility-maximization games one example is that of network contribution games under the restriction that friendship value functions v e (·, ·) are increasing in both coordinates.  ... 
arXiv:1307.2537v1 fatcat:f5ceczy2uvb5bilrytsngs7n5m

Intrinsic Robustness of the Price of Anarchy

Tim Roughgarden
2015 Journal of the ACM  
Smoothness arguments also have automatic implications for the inefficiency of approximate and Bayesian-Nash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomial-length  ...  Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with non-polynomial cost functions, and the first *  ...  Our techniques also imply performance guarantees for approximate Nash equilibria and Bayes-Nash equilibria in these classes of games as well as, under mild extra conditions, for polynomial-length best-response  ... 
doi:10.1145/2806883 fatcat:lx6nlwhv5jd2vdry57jigwnql4

Intrinsic robustness of the price of anarchy

Tim Roughgarden
2012 Communications of the ACM  
Smoothness arguments also have automatic implications for the inefficiency of approximate and Bayesian-Nash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomial-length  ...  Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with non-polynomial cost functions, and the first *  ...  Our techniques also imply performance guarantees for approximate Nash equilibria and Bayes-Nash equilibria in these classes of games as well as, under mild extra conditions, for polynomial-length best-response  ... 
doi:10.1145/2209249.2209274 fatcat:eybaf62r2jgh7kxi3ff7asvtsa

Intrinsic robustness of the price of anarchy

Tim Roughgarden
2009 Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09  
Smoothness arguments also have automatic implications for the inefficiency of approximate and Bayesian-Nash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomial-length  ...  Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with non-polynomial cost functions, and the first *  ...  Our techniques also imply performance guarantees for approximate Nash equilibria and Bayes-Nash equilibria in these classes of games as well as, under mild extra conditions, for polynomial-length best-response  ... 
doi:10.1145/1536414.1536485 dblp:conf/stoc/Roughgarden09 fatcat:hl3tzhlklzhvvns6xmhnm6gptm

Intrinsic Robustness of the Price of Anarchy

Tim Roughgarden
2016 Proceedings of the 2016 ACM Conference on Economics and Computation - EC '16  
Smoothness arguments also have automatic implications for the inefficiency of approximate and Bayesian-Nash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomial-length  ...  Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with non-polynomial cost functions, and the first *  ...  Our techniques also imply performance guarantees for approximate Nash equilibria and Bayes-Nash equilibria in these classes of games as well as, under mild extra conditions, for polynomial-length best-response  ... 
doi:10.1145/2940716.2940797 dblp:conf/sigecom/Roughgarden16 fatcat:biri6vhwkjg23m3rhtinjd5b74

Settling the Complexity of Computing Two-Player Nash Equilibria [article]

Xi Chen, Xiaotie Deng, Shang-Hua Teng
2007 arXiv   pre-print
We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed version) introduced by Papadimitriou  ...  The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time.  ...  We would like to thank everyone who asked about the smoothed complexity of the Lemke-Howson algorithm, especially John Reif for being the first player to ask us this question.  ... 
arXiv:0704.1678v1 fatcat:bv5kllzvurg7fjlt2gq7d6nolu

Synchronisation Games on Hypergraphs

Sunil Simon, Dominik Wojtczak
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
Moreover, in the pure coordination setting, we show that a strong equilibrium exists and can be computed in polynomial time when the game possesses a certain acyclic structure.  ...  in pseudo-polynomial time.  ...  We are grateful to Krzysztof Apt for useful discussions and also thank the anonymous reviewers for their valuable comments.  ... 
doi:10.24963/ijcai.2017/57 dblp:conf/ijcai/SimonW17 fatcat:zfgg7cefsbbpjnbmcqbbaue6fy

Complexity Theory, Game Theory, and Economics: The Barbados Lectures [article]

Tim Roughgarden
2019 arXiv   pre-print
No background in game theory is assumed.  ...  The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have  ...  For the first positive result, we'll review the famous Minimax theorem, and see how it leads to a polynomial-time algorithm for computing a Nash equilibrium of a two-player zero-sum game.  ... 
arXiv:1801.00734v2 fatcat:r6sz7jskqjbs7gxof52fbjikom

Approximate Equilibrium and Incentivizing Social Coordination [article]

Elliot Anshelevich, Shreyas Sekar
2014 arXiv   pre-print
For non-trivial versions of our game, stable solutions like Nash Equilibrium may not exist, or may be socially inefficient even when they do exist.  ...  Towards this end, we consider coordination games where agents have different intrinsic preferences but they stand to gain if others choose the same strategy as them.  ...  Acknowledgements This work was supported in part by NSF awards CCF-0914782, CCF-1101495, CNS-1017932, and CNS-1218374.  ... 
arXiv:1404.4718v1 fatcat:4bwoi2gh35hedoy4imi7lu56e4

On the complexity of constrained Nash equilibria in graphical games

Gianluigi Greco, Francesco Scarcello
2009 Theoretical Computer Science  
In particular, for this latter case, restrictions on players' interactions and on constraints are identified, that make the computation of Nash equilibria an easy problem, for which polynomial and highlyparallelizable  ...  A widely accepted rational behavior for non-cooperative players is based on the notion of Nash equilibrium.  ...  in polynomial time, for games having tree-like dependency graphs and a bounded number of smooth constraints (Theorem 5.5).  ... 
doi:10.1016/j.tcs.2009.05.030 fatcat:e5fwu7ypxrgpnb7d3umyagi7zm
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