Representation and Complexity in Boolean Games

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 con...

• Type: Conference
• Year: 2004
• Where: JELIA
• Authors: Paul E. Dunne, Wiebe van der Hoek
• Keywords: Artificial Intelligence, Boolean Form, Concise Form, Concise Form Representation, JELIA 2004