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On the Complexity of Succinct Zero-Sum Games

Lance Fortnow, Russell Impagliazzo, Valentine Kabanets, Christopher Umans
2008 Computational Complexity  
We complement the known EXPhardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum  ...  the value, of a given succinct zero-sum game.  ...  Acknowledgements We want to thank Joe Kilian for bringing (FKS95) to our attention, and Christos Papadimitriou for answering our questions on linear programming and zerosum games.  ... 
doi:10.1007/s00037-008-0252-2 fatcat:ijcjcbihlbcthpot2xs34nqbya

On the Complexity of Succinct Zero-Sum Games

L. Fortnow, R. Impagliazzo, V. Kabanets, C. Umans
20th Annual IEEE Conference on Computational Complexity (CCC'05)  
We complement the known EXPhardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum  ...  the value, of a given succinct zero-sum game.  ...  Acknowledgements We want to thank Joe Kilian for bringing (FKS95) to our attention, and Christos Papadimitriou for answering our questions on linear programming and zerosum games.  ... 
doi:10.1109/ccc.2005.18 dblp:conf/coco/FortnowIKU05 fatcat:arkvozqt4ndqbicfhrxxmnghqy

Complexity, appeal and challenges of combinatorial games

Aviezri S. Fraenkel
2004 Theoretical Computer Science  
Studying the precise nature of the complexity of games enables gamesters to attain a deeper understanding of the di culties involved in certain new and old open game problems, which is a key to their solution  ...  Substantiations of these assertions are illustrated on hand of many sample games, leading to a deÿnition of the tractability, polynomiality and e ciency of subsets of games.  ...  The game is a sum of its piles. But it is succinct.  ... 
doi:10.1016/j.tcs.2002.11.001 fatcat:iay4nt562re2xniyhtt6l2p2cy

Linear Game Theory : Reduction of complexity by decomposing large games into partial games [article]

Tatsuya Iwase, Takahiro Shiga
2016 arXiv   pre-print
Previous studies in algorithmic game theory propose succinct games that enable small descriptions of payoff matrices and reduction of complexities.  ...  Finally, experiments on simple example games are shown to verify the proposed method.  ...  Thus, the computational complexity theory only focuses on succinct games that can avoid full descriptions of payoff matrices and allow brief representations of large games.  ... 
arXiv:1609.00481v2 fatcat:gclqmm34drhaxoqwhyidhl5pni

The Circuit-Input Game, Natural Proofs, and Testing Circuits With Data

Brynmor Chapman, Ryan Williams
2015 Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science - ITCS '15  
Several results are known on the existence of small-support strategies for zero-sum games, in particular the above circuit-input game.  ...  We revisit a natural zero-sum game from several prior works. A circuit player, armed with a collection of Boolean circuits, wants to compute a function f with one (or some) of its circuits.  ...  Acknowledgements We thank the ITCS reviewers for their helpful comments. In particular, one reviewer improved an earlier version of Theorem 2.3.  ... 
doi:10.1145/2688073.2688115 dblp:conf/innovations/ChapmanW15 fatcat:dxgjg4xysnebvjhabo7uss6caa

Pseudorandomness and the Minimum Circuit Size Problem

Rahul Santhanam, Michael Wagner
2020 Innovations in Theoretical Computer Science  
We explore the possibility of basing one-way functions on the average-case hardness of the fundamental Minimum Circuit Size Problem (MCSP[s]), which asks whether a Boolean function on n bits specified  ...  circuits with membership queries over the uniform distribution is hard; MCSP[2 n ] is zero-error hard on average for some > 0; Cryptographic succinct hitting set generators exist. 3.  ...  Let M be a r ×c matrix with entries in [−1, 1] representing the payoffs of a zero-sum game. Let v(M ) denote the value of the game. Let δ < 1 be a parameter.  ... 
doi:10.4230/lipics.itcs.2020.68 dblp:conf/innovations/Santhanam20 fatcat:pgatorc5k5hlrknytijhfgjufy

Stochastic selfish routing

Evdokia Nikolova, Nicolas Stier-Moses
2012 ACM SIGecom Exchanges  
We also show that succinct representations of equilibria always exist even though the game is non-additive, i.e., the cost along a path is not a sum of costs over edges of the path as is typically assumed  ...  We embark on an agenda to investigate how stochastic delays and risk aversion transform traditional models of routing games and the corresponding equilibrium concepts.  ...  The work of the first author was supported by the National Science Foundation grant number 0931550.  ... 
doi:10.1145/2325713.2325717 fatcat:xd5wh5iysbcv3n5g2ihx3jqrjm

Stochastic Selfish Routing [chapter]

Evdokia Nikolova, Nicolas E. Stier-Moses
2011 Lecture Notes in Computer Science  
We also show that succinct representations of equilibria always exist even though the game is non-additive, i.e., the cost along a path is not a sum of costs over edges of the path as is typically assumed  ...  We embark on an agenda to investigate how stochastic delays and risk aversion transform traditional models of routing games and the corresponding equilibrium concepts.  ...  The work of the first author was supported by the National Science Foundation grant number 0931550.  ... 
doi:10.1007/978-3-642-24829-0_28 fatcat:bcaywmtuandlpikdmlglkuhvxu

Computing correlated equilibria in multi-player games

Christos H. Papadimitriou
2005 Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05  
Our algorithm is based on a variant of the existence proof due to Hart and Schmeidler [23] , and employs linear programming duality, the ellipsoid algorithm, Markov chain steady state computations, as  ...  For anonymous games and graphical games of bounded tree-width, we provide a different polynomial-time algorithm for optimizing an arbitrary linear function over the set of correlated equilibria of the  ...  6.3, and Bernhard von Stengel for suggesting the study of polymatrix games.  ... 
doi:10.1145/1060590.1060598 dblp:conf/stoc/Papadimitriou05 fatcat:u34pwid6yfciposqudgm3tiqqe

Computing correlated equilibria in multi-player games

Christos H. Papadimitriou, Tim Roughgarden
2008 Journal of the ACM  
Our algorithm is based on a variant of the existence proof due to Hart and Schmeidler [23] , and employs linear programming duality, the ellipsoid algorithm, Markov chain steady state computations, as  ...  For anonymous games and graphical games of bounded tree-width, we provide a different polynomial-time algorithm for optimizing an arbitrary linear function over the set of correlated equilibria of the  ...  6.3, and Bernhard von Stengel for suggesting the study of polymatrix games.  ... 
doi:10.1145/1379759.1379762 fatcat:yj3pqoopfjg4peh7zfnuo422vu

A Uniform Min-Max Theorem with Applications in Cryptography [chapter]

Salil Vadhan, Colin Jia Zheng
2013 Lecture Notes in Computer Science  
We present a new, more constructive proof of von Neumann's Min-Max Theorem for two-player zero-sum game -specifically, an algorithm that builds a near-optimal mixed strategy for the second player from  ...  Consider a zero-sum game between two players where for every mixed strategy V for Player 1 (as a distribution over his strategy space V), Player 2 has a response W ∈ W that guarantees E [F (V, W )] ≥ 0  ...  Acknowledgments We thank Kai-Min Chung for many helpful discussions, especially on SNARGs.  ... 
doi:10.1007/978-3-642-40041-4_6 fatcat:onfjuic7vbf5dk45rptnoderme

A Sampling-Based Approach to Computing Equilibria in Succinct Extensive-Form Games [article]

Miroslav Dudik, Geoffrey Gordon
2012 arXiv   pre-print
games or some of their succinct representations such as multi-agent influence diagrams.  ...  We prove convergence guarantees and explore the utility of our approach on several moderately sized multi-player games.  ...  Acknowledgements The authors gratefully acknowledge support from the DARPA grant number HR0011-07-10026, the Computer Science Study Panel program, and the ARO grant number W911NF-08-1-0301.  ... 
arXiv:1205.2649v1 fatcat:dscmewj56rf53pskjbh2q57q2y

The Game World Is Flat: The Complexity of Nash Equilibria in Succinct Games [chapter]

Constantinos Daskalakis, Alex Fabrikant, Christos H. Papadimitriou
2006 Lecture Notes in Computer Science  
In view of empirically successful algorithms available for this problem, this is in essence a positive result -even though, due to the complexity of the reductions, it is of no immediate practical significance  ...  We further extend this conclusion to extensive form games and network congestion games, two classes which do not fall into the same succinct representation framework, and for which no positive algorithmic  ...  Succinct Games in PPAD We now explore how the mapping described in Theorem 1 can be used in deriving complexity results for the problem of computing a Nash equilibrium in succinct games. Proof.  ... 
doi:10.1007/11786986_45 fatcat:7gxgonperzcwri4qnco5laqqdm

Page 9767 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
A family of two-person zero-sum games is solved. The title of the paper describes the setting.  ...  The paper considers a zero sum game where the players choose a distribution on the unit interval but where the second player (think of it as nature) has given moment values for the first n moments.  ... 

A pseudo-quasi-polynomial algorithm for solving mean-payoff parity games [article]

Laure Daviaud and Marcin Jurdzinski and Ranko Lazic
2018 arXiv   pre-print
The game is zero-sum and hence the aim of the other player is to either foil the parity objective or to maximize the mean payoff.  ...  The former provides normal forms for and succinct representations of winning strategies, and the latter enables the application to mean-payoff parity games of the order-theoretic machinery that underpins  ...  Acknowledgements This research has been supported by the EPSRC grant EP/P020992/1 (Solving Parity Games in Theory and Practice).  ... 
arXiv:1803.04756v3 fatcat:hqlmukazujfmnkqu2vxsz54nkq
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