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A Potential Reduction Algorithm for Two-person Zero-sum Mean Payoff Stochastic Games [article]

Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Kazuhisa Makino
2015 arXiv   pre-print
We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies.  ...  Given a positive real ϵ, let us call a stochastic game ϵ-ergodic, if its values from any two initial positions differ by at most ϵ.  ...  implies that the algorithm constructs the sets I τ and F τ .  ... 
arXiv:1508.03455v1 fatcat:f4jeqlhy6zcn5p74v6mjenlfsy

A potential reduction algorithm for two-person zero-sum mean payoff stochastic games [article]

Endre Borosz, Khaled Elbassionix, Vladimir Gurvich, Kazuhisa Makino, University, My, University, My
We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies.  ...  Given a positive real , let us call a stochastic game -ergodic, if its values from any two initial positions dier by at most .  ...  Main Result Given an undiscounted zero-sum stochastic game, we try to reduce the range of its local values by a potential transformation x ∈ R V .  ... 
doi:10.34657/1863 fatcat:r6zjlptrjvgxvfxkr6jj7rclma

On Nash equilibria and improvement cycles in pure positional strategies for Chess-like and Backgammon-like n-person games

Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Kazuhisa Makino
2012 Discrete Mathematics  
The standard Chess and Backgammon are two-person (n = 2) zero-sum games in which c is defined as a draw.  ...  Furthermore, an arbitrary real-valued utility (called also payoff) function u : I × A → R is defined for a Backgammon-like game. Remark 1.  ...  Acknowledgments The first author is thankful to the US National Science Foundation for the partial support; grants CMMI-0856663 and IIS-0803444.  ... 
doi:10.1016/j.disc.2011.11.011 fatcat:nln7wfafsbfqff4nqlbr25ag7a

On Minmax Theorems for Multiplayer Games [chapter]

Yang Cai, Constantinos Daskalakis
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
These games are polymatrix-that is, graphical games in which every edge is a two-player game between its endpoints-in which every outcome has zero total sum of players' payoffs.  ...  all edges are constant-sum games, and invoking a recent result of [Daskalakis, Papadimitriou 2009] for these games.  ...  Acknowledgements We thank Ozan Candogan and Adam Kalai for useful discussions.  ... 
doi:10.1137/1.9781611973082.20 dblp:conf/soda/CaiD11 fatcat:kkpyegftf5bipjhxia2mcwrjye

Sparse Zero-Sum Games as Stable Functional Feature Selection

Nataliya Sokolovska, Olivier Teytaud, Salwa Rizkalla, Karine Clément, Jean-Daniel Zucker, Zhen Wang
2015 PLoS ONE  
In particular, the approach is based on feature subsets ranking by a thresholding stochastic bandit. We provide a theoretical analysis of the introduced algorithm.  ...  In this contribution, we propose a framework based on a sparse zerosum game which performs a stable functional feature selection.  ...  In our contribution we consider bimatrix (two-player) zero-sum games, and refer to them, for short, as "matrix games".  ... 
doi:10.1371/journal.pone.0134683 pmid:26325268 pmcid:PMC4556702 fatcat:jc25tgezojcwli323bjqar7kse

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information [chapter]

Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Kazuhisa Makino
2010 Lecture Notes in Computer Science  
We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = VB ∪ VW ∪ VR, E), with local rewards r : E → R, and three types of vertices  ...  Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the value and optimal strategies of both players are obvious for every initial position, since  ...  Introduction BWR-games We consider two-person zero-sum stochastic games with perfect information and mean payoff: Let G = (V, E) a digraph whose vertex-set V is partitioned into three subsets V = V B  ... 
doi:10.1007/978-3-642-13036-6_26 fatcat:qmlkvvzs7rhcfgokebmahdg5ma

Combinatorial structure and randomized subexponential algorithms for infinite games

Henrik Björklund, Sergei Vorobyov
2005 Theoretical Computer Science  
The complexity of solving infinite games, including parity, mean payoff, and simple stochastic, is an important open problem in verification, automata, and complexity theory.  ...  We introduce new classes of recursively local-global (RLG) and partial recursively local-global (PRLG) functions, and show that strategy evaluation functions for simple stochastic, mean payoff, and parity  ...  Acknowledgments We are grateful to Leonid Khachiyan, Vladimir Gurvich, and Endre Boros for inspiring discussions and illuminating ideas. We thank DIMACS for providing a creative environment.  ... 
doi:10.1016/j.tcs.2005.07.041 fatcat:u3gsujjxkjflzfu5ndcr6cgqru

Adaptive Two-stage Learning Algorithm for Repeated Games

Wataru Fujita, Koichi Moriyama, Ken-ichi Fukui, Masayuki Numao
2016 Proceedings of the 8th International Conference on Agents and Artificial Intelligence  
Adaptive Two-stage Learning Algorithm for Repeated Games.  ...  Reinforcement learning algorithms are widely studied with a goal of identifying strategies of gaining large payoffs in games; however, existing algorithms learn slowly because they require a large number  ...  ACKNOWLEDGEMENTS This work was supported in part by the Management Expenses Grants for National Universities Corporations from the Ministry of Education, Culture, Sports, Science and Technology of Japan  ... 
doi:10.5220/0005711000470055 dblp:conf/icaart/FujitaMFN16 fatcat:d4a4zavutzaklbvsd62za3zqbm

Efficient Stackelberg Strategies for Finitely Repeated Games [article]

Eshwar Ram Arunachaleswaran, Natalie Collina, Michael Kearns
2022 arXiv   pre-print
More precisely, we give efficient algorithms for finding approximate Stackelberg equilibria in finite-horizon repeated two-player games, along with rates of convergence depending on the horizon T.  ...  We complement these results by showing that approximating the Stackelberg value in three-player finite-horizon repeated games is a computationally hard problem via a reduction from the balanced vertex  ...  algorithm is an approximately optimal Stackelberg GPA in a two player zero-sum game.  ... 
arXiv:2207.04192v2 fatcat:gc6vb2l7kjdenp73t6da4s2ifq

Game Theory Meets Information Security Management [chapter]

Andrew Fielder, Emmanouil Panaousis, Pasquale Malacaria, Chris Hankin, Fabrizio Smeraldi
2014 IFIP Advances in Information and Communication Technology  
We finally compare the game theoretic defense method with a method which implements a stochastic optimization algorithm.  ...  We have formulated general-sum games that represent our cyber security environment, and we have proven that the defender's Nash strategy is also minimax.  ...  This means D minimaximizes the utility of the attacker in the zero-sum game where the defender's strategy is as in G: D = argmin D max A U A (D, A).  ... 
doi:10.1007/978-3-642-55415-5_2 fatcat:5gnkkdfyjfg3rmmnqktjgdfmse

Multi-Agent Inverse Reinforcement Learning: Suboptimal Demonstrations and Alternative Solution Concepts [article]

Sage Bergerson
2021 arXiv   pre-print
These solutions include the correlated equilibrium, logistic stochastic best response equilibrium and entropy regularized mean field NE.  ...  Traditional formalisms of game theory provide computationally tractable behavioral models, but assume agents have unrealistic cognitive capabilities.  ...  Acknowledgements I would like to thank Tamay Besiroglu for his mentorship throughout this research; I would also like to thank Lawrence Chan (Center for Human Compatible AI, UC Berkeley) for his helpful  ... 
arXiv:2109.01178v1 fatcat:v635kuj4wfg4nndxvclbaubv2q

Cyclic games and linear programming

Sergei Vorobyov
2008 Discrete Applied Mathematics  
New efficient algorithms for solving infinite-duration two-person adversary games with the decision problem in NP ∩ coNP, based on linear programming (LP), LP-representations, combinatorial LP, linear  ...  Preliminaries on cyclic games Mean payoff games An MPG is played on a finite directed edge-weighted graph G = (V , E, w), where the set of vertices V is partitioned into two nonempty subsets V MAX , V  ...  A further reduction from discounted payoff to simple stochastic games (SSGs) is described in [56] .  ... 
doi:10.1016/j.dam.2008.04.012 fatcat:5fmgypimu5cs3ahclgd4lsc4si

Multiagent systems: algorithmic, game-theoretic, and logical foundations

2009 ChoiceReviews  
Computing Nash equilibria of two-player, general-sum games 91 4.2.1 Complexity of computing a sample Nash equilibrium 91 4.2.2 An LCP formulation and the Lemke-Howson algorithm 93 4.2.3 Searching the  ...  perfect equilibrium 85 3.4.7 ǫ-Nash equilibrium 85 3.5 History and references 87 4 Computing Solution Concepts of Normal-Form Games 89 4.1 Computing Nash equilibria of two-player, zero-sum games 89 4.2  ...  We will introduce a particular way of tying the two notions together, which has several conceptual and technical advantages.  ... 
doi:10.5860/choice.46-5662 fatcat:pr2pmv7k2bad3pp5bxgogecgnq

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)  
CHAPTER IV ZERO-SUM STOCHASTIC GAMES by Koos Vrieze INTRODUCTION In this paper we give a survey on zero-sum stochastic games.  ...  By definition the payoffs to player 2 are the negatives of these expressions. As solution concept for zero-sum stochastic games the usual concept for zero-sum games in normal form is adopted.  ...  In the Nash demand game corresponding to a two-person bargaining game (S,d), each player proposes an outcome in P(S,d).  ... 
doi:10.2307/2982790 fatcat:ynwbj5p5fzeoxdhc6ed626rgxe

Integrity assurance in resource-bounded systems through stochastic message authentication

Aron Laszka, Yevgeniy Vorobeychik, Xenofon Koutsoukos
2015 Proceedings of the 2015 Symposium and Bootcamp on the Science of Security - HotSoS '15  
We propose a formal game-theoretic framework for optimal stochastic message authentication, providing provable integrity guarantees for resource-bounded systems based on an existing MAC scheme.  ...  Assuring communication integrity is a central problem in security.  ...  We introduce a game-theoretic model to achieve two ends: first, provide algorithmic means to compute an optimal stochastic authentication strategy, accounting for the relative importance of messages, and  ... 
doi:10.1145/2746194.2746195 dblp:conf/hotsos/LaszkaVK15 fatcat:qoykg27krbgj3gm6my3yyb7tyy
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