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Bilinear Games: Polynomial Time Algorithms for Rank Based Subclasses
[article]
2011
arXiv
pre-print
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(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]
2010
Lecture Notes in Computer Science
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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
2012
Theoretical Computer Science
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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
2017
Conference on Uncertainty in Artificial Intelligence
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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]
2022
arXiv
pre-print
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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
2018
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
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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]
2012
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
1994
Handbook of Game Theory with Economic Applications
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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]
2022
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
2018
Neural Information Processing Systems
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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
2016
Computers & electrical engineering
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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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