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

2015
*
arXiv
*
pre-print

We suggest

arXiv:1508.03455v1
fatcat:f4jeqlhy6zcn5p74v6mjenlfsy
*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 . ...##
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A potential reduction algorithm for two-person zero-sum mean payoff stochastic games
[article]

2019

We suggest

doi:10.34657/1863
fatcat:r6zjlptrjvgxvfxkr6jj7rclma
*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 . ...##
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On Nash equilibria and improvement cycles in pure positional strategies for Chess-like and Backgammon-like n-person games

2012
*
Discrete Mathematics
*

The standard Chess and Backgammon are

doi:10.1016/j.disc.2011.11.011
fatcat:nln7wfafsbfqff4nqlbr25ag7a
*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. ...##
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On Minmax Theorems for Multiplayer Games
[chapter]

2011
*
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms
*

These

doi:10.1137/1.9781611973082.20
dblp:conf/soda/CaiD11
fatcat:kkpyegftf5bipjhxia2mcwrjye
*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. ...##
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Sparse Zero-Sum Games as Stable Functional Feature Selection

2015
*
PLoS ONE
*

In particular, the approach is based on feature subsets ranking by

doi:10.1371/journal.pone.0134683
pmid:26325268
pmcid:PMC4556702
fatcat:jc25tgezojcwli323bjqar7kse
*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*". ...##
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A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information
[chapter]

2010
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/978-3-642-13036-6_26
fatcat:qmlkvvzs7rhcfgokebmahdg5ma
*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 ...##
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Combinatorial structure and randomized subexponential algorithms for infinite games

2005
*
Theoretical Computer Science
*

The complexity of solving infinite

doi:10.1016/j.tcs.2005.07.041
fatcat:u3gsujjxkjflzfu5ndcr6cgqru
*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. ...##
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Adaptive Two-stage Learning Algorithm for Repeated Games

2016
*
Proceedings of the 8th International Conference on Agents and Artificial Intelligence
*

Adaptive

doi:10.5220/0005711000470055
dblp:conf/icaart/FujitaMFN16
fatcat:d4a4zavutzaklbvsd62za3zqbm
*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 ...##
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Efficient Stackelberg Strategies for Finitely Repeated Games
[article]

2022
*
arXiv
*
pre-print

More precisely, we give efficient

arXiv:2207.04192v2
fatcat:gc6vb2l7kjdenp73t6da4s2ifq
*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*. ...##
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Game Theory Meets Information Security Management
[chapter]

2014
*
IFIP Advances in Information and Communication Technology
*

We finally compare the

doi:10.1007/978-3-642-55415-5_2
fatcat:5gnkkdfyjfg3rmmnqktjgdfmse
*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*). ...##
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Multi-Agent Inverse Reinforcement Learning: Suboptimal Demonstrations and Alternative Solution Concepts
[article]

2021
*
arXiv
*
pre-print

These solutions include the correlated equilibrium, logistic

arXiv:2109.01178v1
fatcat:v635kuj4wfg4nndxvclbaubv2q
*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 ...##
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Cyclic games and linear programming

2008
*
Discrete Applied Mathematics
*

New efficient

doi:10.1016/j.dam.2008.04.012
fatcat:5fmgypimu5cs3ahclgd4lsc4si
*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] . ...##
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Multiagent systems: algorithmic, game-theoretic, and logical foundations

2009
*
ChoiceReviews
*

Computing Nash equilibria of

doi:10.5860/choice.46-5662
fatcat:pr2pmv7k2bad3pp5bxgogecgnq
*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. ...##
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Surveys in Game Theory and Related Topics

1988
*
Journal of the Royal Statistical Society: Series A (Statistics in Society)
*

CHAPTER IV

doi:10.2307/2982790
fatcat:ynwbj5p5fzeoxdhc6ed626rgxe
*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). ...##
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Integrity assurance in resource-bounded systems through stochastic message authentication

2015
*
Proceedings of the 2015 Symposium and Bootcamp on the Science of Security - HotSoS '15
*

We propose

doi:10.1145/2746194.2746195
dblp:conf/hotsos/LaszkaVK15
fatcat:qoykg27krbgj3gm6my3yyb7tyy
*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 ...
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