2004 | OriginalPaper | Buchkapitel
Representation and Complexity in Boolean Games
verfasst von : Paul E. Dunne, Wiebe van der Hoek
Erschienen in: Logics in Artificial Intelligence
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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Boolean games are a class of two-player games which may be defined via a Boolean form over a set of atomic actions. A particular game on some form is instantiated by partitioning these actions between the players – player 0 and player 1 – each of whom has the object of employing its available actions in such a way that the game’s outcome is that sought by the player concerned, i.e. player i tries to bring about the outcome i. In this paper our aim is to consider a number of issues concerning how such forms are represented within an algorithmic setting. We introduce a concept of concise form representation and compare its properties in relation to the more frequently used “extensive form” descriptions. Among other results we present a “normal form” theorem that gives a characterisation of winning strategies for each player. Our main interest, however, lies in classifying the computational complexity of various decision problems when the game instance is presented as a concise form. Among the problems we consider are: deciding existence of a winning strategy given control of a particular set of actions; determining whether two games are “equivalent”.