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Bilinear Games: Polynomial Time Algorithms for Rank Based Subclasses [article]

Jugal Garg and Albert Xin Jiang and Ruta Mehta
2011 arXiv   pre-print
(GEB'96), this paper defines bilinear games, and proposes efficient algorithms for its rank based subclasses.  ...  In this paper, we give polynomial time algorithms to compute Nash equilibrium for special classes of bilinear games: (i) Rank-1 games (i.e., rank(A+B)=1).  ...  We would like to thank Milind Sohoni for helpful comments and corrections.  ... 
arXiv:1109.6182v1 fatcat:cuairizybbhvzjmvb3d7dgalgy

Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses [chapter]

Spyros Kontogiannis, Paul Spirakis
2010 Lecture Notes in Computer Science  
This subclass entirely contains the most popular subclass of polynomial-time solvable bimatrix games, namely, all the constantsum games (rank−0 games).  ...  For mutually concave bimatrix games, we provide a polynomial-time computation of a Nash equilibrium, based on the polynomial tractability of convex quadratic programming.  ...  We then proceed to determine new subclasses of bimatrix games which admit polynomial-time algorithms, or at least FPTAS, for finding any NE.  ... 
doi:10.1007/978-3-642-15369-3_24 fatcat:ukvdyvu6qffhrhkm3tfyeuvrtm

On mutual concavity and strategically-zero-sum bimatrix games

Spyros Kontogiannis, Paul Spirakis
2012 Theoretical Computer Science  
We conclude our discussion with a comparison of MC-games (or, SZS-games) to k-rank games, which are known to admit for 2NASH a FPTAS when k is fixed [18] , and a polynomialtime algorithm for k = 1 [2].  ...  This gives an alternative explanation of the polynomial-time tractability of 2NASH for these games, not depending on the solvability of zero-sum games.  ...  Nevertheless, it should be noted that for the intersection of MC-games of fixed rank, rather than giving a FPTAS, we find in polynomial time an exact NE point via the optimal solution to our convex quadratic  ... 
doi:10.1016/j.tcs.2012.01.016 fatcat:ihoq65e2nzdlpfv3nyhpujdnfa

Complexity of Solving Decision Trees with Skew-Symmetric Bilinear Utility

Hugo Gilbert, Olivier Spanjaard
2017 Conference on Uncertainty in Artificial Intelligence  
We show that determining an SSB optimal plan is NP-hard if one only considers deterministic plans while it is polynomial time if one allows randomized plans.  ...  We study the complexity of solving decision trees with a Skew-Symmetric Bilinear (SSB) utility function.  ...  Dinkelbach's method The second algorithm has not the polynomial time guarantee of the first one, but is more efficient in practice.  ... 
dblp:conf/uai/GilbertS17 fatcat:4s676h2ut5bltb4v2rdococely

Sampling Equilibria: Fast No-Regret Learning in Structured Games [article]

Daniel Beaglehole, Max Hopkins, Daniel Kane, Sihan Liu, Shachar Lovett
2022 arXiv   pre-print
As an immediate corollary, we give a polylogarithmic time meta-algorithm to compute approximate Nash Equilibria for these games that is exponentially faster than prior methods in several important settings  ...  This gives the first efficient no-regret algorithms for problems such as the (discrete) Colonel Blotto game, matroid congestion, matroid security, and basic dueling games.  ...  Acknowledgements We thank Thuy Duong Vuong, Nima Anari, and Kuikui Liu for helpful discussions on MCMC-based approaches for Dueling games and Colonel Blotto, and Saeed Seddighin for discussions on algorithms  ... 
arXiv:2201.10758v7 fatcat:k4rubua6czhm3pnmir4bh262me

An FPTAS for Computing Nash Equilibrium in Resource Graph Games

Hau Chan, Albert Xin Jiang
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
As a consequence, our FPTAS provides new approximation results for security games, network congestion games, and bilinear games.  ...  We consider the problem of computing a mixed-strategy Nash equilibrium (MSNE) in resource graph games (RGGs), a compact representation for games with an exponential number of strategies.  ...  A natural question arises: are there subclasses of RGGs for which MSNE can be computed (or approximated) in polynomial time?  ... 
doi:10.24963/ijcai.2018/21 dblp:conf/ijcai/ChanJ18 fatcat:5hs7oh44n5aolnztwrbe6mz4ea

Quantum XOR Games [article]

Oded Regev, Thomas Vidick
2012 arXiv   pre-print
We give examples showing that quantum XOR games exhibit a wide range of behaviors that are known not to exist for standard XOR games, such as cases in which the use of entanglement leads to an arbitrarily  ...  By invoking two deep extensions of Grothendieck's inequality, we present an efficient algorithm that gives a constant-factor approximation to the best performance players can obtain in a given game, both  ...  We are grateful to David Pérez-García for suggesting the family of games (T n ). We also thank him and Carlos Palazuelos for many useful discussions.  ... 
arXiv:1207.4939v1 fatcat:a2flgg5gr5cshpwiu4gs4a4wge

Team Belief DAG: A Concise Representation for Team-Correlated Game-Theoretic Decision Making [article]

Brian Hu Zhang, Gabriele Farina, Tuomas Sandholm
2022 arXiv   pre-print
of our TB-DAG to solve for a team correlated equilibrium in an adversarial team games recovers almost exactly their algorithm.  ...  In particular, like the LP-based algorithm of Zhang & Sandholm (2022), the size of our representation scales with the amount of information uncommon to the team; in fact, using linear programming on top  ...  Acknowledgements This material is based on work supported by the National Science Foundation under grants IIS-1718457, IIS-1901403, and CCF-1733556, and the ARO under award W911NF2010081.  ... 
arXiv:2202.00789v3 fatcat:ljwn7bksiza3ldprkaqk7wa7rq

Tight last-iterate convergence rates for no-regret learning in multi-player games [article]

Noah Golowich, Sarath Pattathil, Constantinos Daskalakis
2020 arXiv   pre-print
We study the question of obtaining last-iterate convergence rates for no-regret learning algorithms in multi-player games.  ...  We also show that the O(1/√(T)) rate is tight for all p-SCLI algorithms, which includes OG as a special case.  ...  Acknowledgements We thank Yossi Arjevani for a helpful conversation. References [Ahl79] L.V. Ahlfors. Complex Analysis. McGraw-Hill, 1979.  ... 
arXiv:2010.13724v1 fatcat:ybwuvqiwi5cu3nmiebh7arh75i

Noncommutative Nullstellensätze and Perfect Games [article]

Adam Bene Watts, John William Helton, Igor Klep
2021 arXiv   pre-print
For these games we show the question of whether or not a game has a perfect commuting operator strategy reduces to instances of the subgroup membership problem and, for linear systems games, we further  ...  The main results of this paper are two characterizations, based on Nullstellensatz, which apply to games with perfect commuting operator strategies.  ...  for a subclass of imitation games known as mirror games.  ... 
arXiv:2111.14928v2 fatcat:kowtpz72ibcrli4ctll43uiwde

Chapter 20 Zero-sum two-person games [chapter]

T.E.S. Raghavan
1994 Handbook of Game Theory with Economic Applications  
Indeed p(x, y) is a polynomial game with value 0 whose optimal strategy for the maximizer serves as an optimal strategy for the original game K(x, y). [] Bell.shaped kernels. Let K:R2---~ R.  ...  If each player selects his masterplan based on the outcome of his independently chosen random device we enter into a new game called a mixed extension of the game.  ... 
doi:10.1016/s1574-0005(05)80052-9 fatcat:br7nlpdmmvbaplmusdnozhksgi

On Last-Iterate Convergence Beyond Zero-Sum Games [article]

Ioannis Anagnostides, Ioannis Panageas, Gabriele Farina, Tuomas Sandholm
2022 arXiv   pre-print
First, we use a regret-based analysis to show that in a class of games that includes constant-sum polymatrix and strategically zero-sum games, dynamics such as optimistic mirror descent (OMD) have bounded  ...  Moreover, for potential games we establish convergence to an ϵ-equilibrium after O(1/ϵ^2) iterations for mirror descent under a broad class of regularizers, as well as optimal O(1) regret bounds for OMD  ...  Part of this work was done while Ioannis Panageas was visiting the Simons Institute for the Theory of Computing.  ... 
arXiv:2203.12056v1 fatcat:vwlvt2iiqff3ddqlgwhoxscnbu

An Overview of Multi-Agent Reinforcement Learning from Game Theoretical Perspective [article]

Yaodong Yang, Jun Wang
2021 arXiv   pre-print
directions based on recent advances.  ...  We expect this work to serve as a stepping stone for both new researchers who are about to enter this fast-growing domain and existing domain experts who want to obtain a panoramic view and identify new  ...  algorithms for team games.  ... 
arXiv:2011.00583v3 fatcat:3k3smfqopvejnn4wdpnc2gbpzi

Ex ante coordination and collusion in zero-sum multi-player extensive-form games

Gabriele Farina, Andrea Celli, Nicola Gatti, Tuomas Sandholm
2018 Neural Information Processing Systems  
that is dramatically faster than the prior state-of-the-art algorithm for this problem.  ...  By reasoning over the auxiliary game, we devise an anytime algorithm, fictitious team-play, that is guaranteed to converge to an optimal coordinated strategy for the team against an optimal opponent, and  ...  This material is based on work supported by the National Science Foundation under grants IIS-1718457, IIS-1617590, and CCF-1733556, and the ARO under award W911NF-17-1-0082.  ... 
dblp:conf/nips/FarinaC0S18 fatcat:qh4xcsjpqjak3plomyfnwj7yke

Efficient privacy preserving predicate encryption with fine-grained searchable capability for Cloud storage

Xu An Wang, Fatos Xhafa, Weiyi Cai, Jianfeng Ma, Fushan Wei
2016 Computers & electrical engineering  
Indeed, Cloud data centres store each time more sensitive data such as personal data, organizational and enterprise data, transactional data, etc.  ...  A new transformation of PEto-PEFKS is also proposed and used to construct an efficient PEFKS scheme based on the transformation from the proposed PE scheme.  ...  by given a group generator G: Lemma 1 . 1 If for a polynomial time adversary A, there exists Adv Game real A −Adv Game 0 A = , then with advantage , we can construct a polynomial time simulator B breaking  ... 
doi:10.1016/j.compeleceng.2016.05.012 fatcat:6omnffbjbraxffc57qbb7vnt5y
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