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Combining local search techniques and path following for bimatrix games [article]

Nicola Gatti, Giorgio Patrini, Marco Rocco, Tuomas Sandholm
2012 arXiv   pre-print
In this paper, we combine path following algorithms with local search techniques to design new algorithms for finding exact and approximate NEs.  ...  We show that our algorithms largely outperform the state of the art and that almost all the known benchmark game classes are easily solvable or approximable (except for the GAMUT CovariantGameRand class  ...  Acknowledgements Tuomas Sandholm was funded under NSF grants IIS-0964579, CCF-1101668, and IIS-0905390.  ... 
arXiv:1210.4858v1 fatcat:wlkdzjzwerhp7fsvh2g6y3ri6e

Combining local search techniques and path following for bimatrix games

Nicola Gatta, Giorgio Patrini, Marco Rocco, Tuomas W Sandholm
2018
In this paper, we combine path following algorithms with local search techniques to design new algorithms for finding exact and approximate NEs.  ...  We show that our algorithms largely outperform the state of the art and that almost all the known benchmark game classes are easily solvable or approximable (except for the GAMUT CovariantGame– Rand class  ...  Acknowledgements Tuomas Sandholm was funded under NSF grants IIS-0964579, CCF-1101668, and IIS-0905390.  ... 
doi:10.1184/r1/6604193 fatcat:fsd7civqdfhfnk6teu2pjjpg7q

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 Kyle Burke, Li-Sha Huang, Jon Kelner, Rajmohan Rajaraman, Dan Spielman, Ravi Sundaram, Paul Valiant, and Vijay Vazirani for helpful comments and suggestions.  ... 
arXiv:0704.1678v1 fatcat:bv5kllzvurg7fjlt2gq7d6nolu

Settling the complexity of computing two-player Nash equilibria

Xi Chen, Xiaotie Deng, Shang-Hua Teng
2009 Journal of the ACM  
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 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  ...  Acknowledgments We would like to thank the three referees for their great suggestions. We would like to thank Kyle  ... 
doi:10.1145/1516512.1516516 fatcat:4csizuhga5h4jnbkrickxw6d2y

Computing Nash Equilibria in Bimatrix Games: GPU-Based Parallel Support Enumeration

Safraz Rampersaud, Lena Mashayekhy, Daniel Grosu
2014 IEEE Transactions on Parallel and Distributed Systems  
To address this issue, we design a GPU-based parallel support enumeration algorithm for computing Nash equilibria in bimatrix games.  ...  Unfortunately, computing these equilibria even for moderately sized games is computationally expensive.  ...  ACKNOWLEDGMENT This research was supported in part by NSF grants DGE-0654014 and CNS-1116787.  ... 
doi:10.1109/tpds.2014.2307887 fatcat:gdyxywzwenchrok7jfbrtds4xq

Computing Nash equilibria in bimatrix games: GPU-based parallel support enumeration

Safraz Rampersaud, Lena Mashayekhy, Daniel Grosu
2012 2012 IEEE 31st International Performance Computing and Communications Conference (IPCCC)  
To address this issue, we design a GPU-based parallel support enumeration algorithm for computing Nash equilibria in bimatrix games.  ...  Unfortunately, computing these equilibria even for moderately sized games is computationally expensive.  ...  ACKNOWLEDGMENT This research was supported in part by NSF grants DGE-0654014 and CNS-1116787.  ... 
doi:10.1109/pccc.2012.6407775 dblp:conf/ipccc/RampersaudMG12 fatcat:thxdpchrpffohittfjq7lpscxy

On incremental deployability [article]

Ioannis Avramopoulos
2018 arXiv   pre-print
For example, we show that incremental deployability is at least as general a concept as the Nash equilibrium (in that the latter can be derived from the former).  ...  organization beyond its predominant market (and finance)-based character.  ...  Acknowledgments My account on YouTube has kept me company, through recommendations (for example, on music to listen to or on technical material to study) and through positive "clockwork orange" experiments  ... 
arXiv:1805.10115v1 fatcat:2ovf2na3jnbz3dwmrtiphdp6oy

Multiple UCAVs cooperative air combat simulation platform based on PSO, ACO, and game theory

Haibin Duan, Xingxing Wei, Zhuoning Dong
2013 IEEE Aerospace and Electronic Systems Magazine  
ACKNOWLEDGMENTS The authors also thank the anonymous referees for their comments and suggestions, which led to the better presentation of this work.  ...  In this way, ants make better use of their pheromone trail information; without local updating, all ants search in a narrow neighborhood of the best previous tour. (6) (7) where  is the local pheromone  ...  PSO has been successfully applied as a (nonlinear) optimization technique and has become increasingly popular due to its combination of simplicity (in terms of its implementation), low computational cost  ... 
doi:10.1109/maes.2013.6678487 fatcat:geay2ex5une3xbroz6lefptgbu

A Glimpse at Paul G. Spirakis [chapter]

Ioannis Chatzigiannakis, Dimitris Fotakis, Spyros Kontogiannis, Othon Michail, Sotiris Nikoletseas, Grammati Pantziou, Christos Zaroliagis
2015 Lecture Notes in Computer Science  
We are indebted to Eleni Spiraki (Paul's sister) for her great help in the preparation of this article.  ...  Spirakis and his colleagues have established novel techniques for constructing approximate equilibria in normalized bimatrix games, which essentially hold the record so far for the two most popular notions  ...  in bimatrix games [48] .  ... 
doi:10.1007/978-3-319-24024-4_1 fatcat:vmn7swilvjdcdjs6lir335pch4

Local Search Methods for Finding a Nash Equilibrium in Two-Player Games

Sofia Ceppi, Nicola Gatti, Giorgio Patrini, Marco Rocco
2010 2010 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology  
In this paper, we present, to the best of our knowledge, the first anytime algorithm based on the combination of support enumeration methods and local search techniques to find a Nash equilibrium in two-player  ...  The algorithm searches for a Nash equilibrium and, if it is stopped before it has found an equilibrium, it returns the best approximate equilibrium found so far.  ...  We proposed the first anytime algorithm based on the combination of support enumeration methods and local search techniques.  ... 
doi:10.1109/wi-iat.2010.57 dblp:conf/iat/CeppiGPR10 fatcat:ftl7s76v4be2vmn6j676gfvdoy

Evolutionary stability implies asymptotic stability under multiplicative weights [article]

Ioannis Avramopoulos
2016 arXiv   pre-print
, which are well-known to be equipped with a convex potential function, and finding strict local maxima of quadratic programming problems, are special cases of the problem of computing evolutionarily stable  ...  states in nonlinear population games.  ...  on tackling systems problems with machine learning techniques (SysML) in 2008.  ... 
arXiv:1601.07267v2 fatcat:hv2q7rsxorfphgrivc2yzodtym

Two-agent cooperative search using game models with endurance-time constraints

P. B. Sujit, Debasish Ghose
2010 Engineering optimization (Print)  
Here, two agents are considered which are performing the search operation and formulate the game as a bimatrix game.  ...  Non-cooperative Nash equilibrium strategy A non-cooperative bimatrix game for two players or agents Basar and Olsder (1995) is defined as a game consisting of two search effectiveness matrices, M 1 =  ... 
doi:10.1080/03052150903369837 fatcat:je4i3stbmvaatb27mmz2o5prum

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

Tim Roughgarden
2019 arXiv   pre-print
theory in game theory and economics.  ...  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  ...  General Bimatrix Games A general bimatrix game is defined by two independent payoff matrices, an m × n matrix A for Alice and an x Aŷ ≥ x Aŷ − ∀x , and (1.7) x Bŷ ≥x By − ∀y . (1.8) It has long been known  ... 
arXiv:1801.00734v2 fatcat:r6sz7jskqjbs7gxof52fbjikom

The Mechanics of n-Player Differentiable Games [article]

David Balduzzi, Sebastien Racaniere, James Martens, Jakob Foerster, Karl Tuyls, Thore Graepel
2018 arXiv   pre-print
In this paper, we develop new techniques to understand and control the dynamics in general games. The key result is to decompose the second-order dynamics into two components.  ...  The decomposition motivates Symplectic Gradient Adjustment (SGA), a new algorithm for finding stable fixed points in general games.  ...  We thank Guillame Desjardins, Csaba Szepesvari and especially Alistair Letcher for useful feedback.  ... 
arXiv:1802.05642v2 fatcat:kcg2iirbujbehdgz6ctg65um3i

Surveys in Game Theory and Related Topics

V. J. Baston, H. J. M. Peters, O. J. Vrieze
1988 Journal of the Royal Statistical Society: Series A (Statistics in Society)  
,n}, and one searches for a probability measure agreeing in some way with the more-probable-than relation.  ...  Consequently the set of all regular mxn-bimatrix games is, as a finite union of open sets, disconnected and the number of equilibrium points is locally constant on the set of regular games.  ...  We call the described pair of strategies a sirrrple Nash equilibrium for (x,1-x). A pair of strategies actually determines a "path" in the "game tree" \ A [ = 2.  ... 
doi:10.2307/2982790 fatcat:ynwbj5p5fzeoxdhc6ed626rgxe
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