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Multiagent influence diagrams for representing and solving games
 Games and Economic Behavior
, 2001
"... The traditional representations of games using the extensive form or the strategic (normal) form obscure much of the structure that is present in realworld games. In this paper, we propose a new representation language for general multiplayer games — multiagent influence diagrams (MAIDs). This rep ..."
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Cited by 157 (2 self)
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The traditional representations of games using the extensive form or the strategic (normal) form obscure much of the structure that is present in realworld games. In this paper, we propose a new representation language for general multiplayer games — multiagent influence diagrams (MAIDs). This representation extends graphical models for probability distributions to a multiagent decisionmaking context. MAIDs explicitly encode structure involving the dependence relationships among variables. As a consequence, we can define a notion of strategic relevance of one decision variable to another: ¢¡ is strategically relevant to if, to optimize the decision rule at, the decision maker needs to take into consideration the decision rule at ¡. We provide a sound and complete graphical criterion for determining strategic relevance. We then show how strategic relevance can be used to detect structure in games, allowing a large game to be broken up into a set of interacting smaller games, which can be solved in sequence. We show that this decomposition can lead to substantial savings in the computational cost of finding Nash equilibria in these games. 1
Multiagent Systems: Algorithmic, GameTheoretic, and Logical Foundations
, 2009
"... formatted differently than the book—and in particular has different page numbering—and has not been fully copy edited. Please treat the printed book as the definitive version. You are invited to use this electronic copy without restriction for onscreen viewing, but are requested to print it only un ..."
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Cited by 106 (11 self)
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formatted differently than the book—and in particular has different page numbering—and has not been fully copy edited. Please treat the printed book as the definitive version. You are invited to use this electronic copy without restriction for onscreen viewing, but are requested to print it only under one of the following circumstances: You live in a place that does not offer you access to the physical book; The cost of the book is prohibitive for you; You need only one or two chapters. Finally, we ask you not to link directly to the PDF or to distribute it electronically. Instead, we invite you to link to
Fast Algorithms for Finding Randomized Strategies in Game Trees
, 1994
"... Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computation ..."
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Cited by 90 (12 self)
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Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computationally intractable. The approach is to generate the normal form of the game (the matrix containing the payoff for each strategy combination), and then solve a linear program (LP) or a linear complementarity problem (LCP). The size of the normal form, however, is typically exponential in the size of the game tree, thus making this method impractical in all but the simplest cases. This paper describes a new representation of strategies which results in a practical linear formulation of the problem of twoplayer games with perfect recall (i.e., games where players never forget anything, which is a standard assumption). Standard LP or LCP solvers can then be applied to find optimal randomized strategies. The resulting algorithms are, in general, exponentially better than the standard ones, both in terms of time and in terms of space.
A GameTheoretic Classification of Interactive Complexity Classes (Extended Abstract)
 IN PROCEEDINGS OF THE TENTH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 1995
"... Gametheoretic characterizations of complexity classes have often proved useful in understanding the power and limitations of these classes. One wellknown example tells us that PSPACE can be characterized by twoperson, perfectinformation games in which the length of a played game is polynomial i ..."
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Cited by 18 (1 self)
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Gametheoretic characterizations of complexity classes have often proved useful in understanding the power and limitations of these classes. One wellknown example tells us that PSPACE can be characterized by twoperson, perfectinformation games in which the length of a played game is polynomial in the length of the description of the initial position [Chandra et al., Journal of the ACM, 28 (1981), pp. 114133]. In this paper, we investigate the connection between game theory and interactive computation. We formalize the notion of a polynomially definable game system for the language L, which, informally, consists of two arbitrarily powerful players P 1 and P 2 and a ...
Memoryless determinacy of parity and mean payoff games: A simple proof
 THEORETICAL COMPUTER SCIENCE
, 2004
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Rational behaviour and strategy construction in infinite multiplayer games
, 2005
"... We study infinite games played by arbitrarily many players on a directed graph. Equilibrium states capture rational behaviour in these games. Instead of the wellknown notion of a Nash equilibrium, we focus on the notion of a subgame perfect equilibrium. We argue that the latter one is more appropri ..."
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Cited by 12 (5 self)
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We study infinite games played by arbitrarily many players on a directed graph. Equilibrium states capture rational behaviour in these games. Instead of the wellknown notion of a Nash equilibrium, we focus on the notion of a subgame perfect equilibrium. We argue that the latter one is more appropriate for the kind of games we study, and we show the existence of a subgame perfect equilibrium in any infinite game with ωregular winning conditions. As, in general, equilibria are not unique, it is appealing to compute one with a maximal payoff. This problem corresponds naturally to the problem of deciding given a game and two payoff vectors whether the game has an equilibrium with a payoff in between the given thresholds. We show that this problem is decidable for games with ωregular winning conditions played on a finite graph and analyse its complexity. Moreover, we establish that any subgame perfect equilibrium of a game with ωregular winning conditions played on a finite graph can be implemented by finitestate strategies. Finally, we consider logical definability. We state that if we fix the number of players together with an ωregular winning condition for each of them and two payoff vectors the property that a game has a subgame perfect equilibrium with a payoff in between the given thresholds is definable in the modal µcalculus.
Positional Determinacy of Infinite Games
"... We survey results on determinacy of games and on the existence of positional winning strategies for parity games and Rabin games. We will then discuss some new... ..."
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Cited by 6 (0 self)
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We survey results on determinacy of games and on the existence of positional winning strategies for parity games and Rabin games. We will then discuss some new...
Operations Research
, 1987
"... Fear appeal as a tactic of persuasion has been studied primarily from a positivistic and nondiscursive perspective. This study examines the use of fear appeal in a natural discursive setting of fundamentalist rhetoric. More specifically, we examine the interactional problems facing Jewish fundament ..."
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Cited by 5 (0 self)
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Fear appeal as a tactic of persuasion has been studied primarily from a positivistic and nondiscursive perspective. This study examines the use of fear appeal in a natural discursive setting of fundamentalist rhetoric. More specifically, we examine the interactional problems facing Jewish fundamentalist preachers who attempt to manipulate fear and identify several discursive strategies that aim at solving these problems. General conclusions point to the power of a discursive perspective in examining fear appeal and its sophisticated application in rhetoric. Acknowledgement