Relaxing Exclusive Control in Boolean Games

Francesco Belardinelli
(IBISC, Université d'Evry and IRIT, CNRS, Toulouse)
Umberto Grandi
(IRIT, University of Toulouse)
Andreas Herzig
(IRIT, CNRS, Toulouse)
Dominique Longin
(IRIT, CNRS, Toulouse)
Emiliano Lorini
(IRIT, CNRS, Toulouse)
Arianna Novaro
(IRIT, University of Toulouse)
Laurent Perrussel
(IRIT, University of Toulouse)

In the typical framework for boolean games (BG) each player can change the truth value of some propositional atoms, while attempting to make her goal true. In standard BG goals are propositional formulas, whereas in iterated BG goals are formulas of Linear Temporal Logic. Both notions of BG are characterised by the fact that agents have exclusive control over their set of atoms, meaning that no two agents can control the same atom. In the present contribution we drop the exclusivity assumption and explore structures where an atom can be controlled by multiple agents. We introduce Concurrent Game Structures with Shared Propositional Control (CGS-SPC) and show that they ac- count for several classes of repeated games, including iterated boolean games, influence games, and aggregation games. Our main result shows that, as far as verification is concerned, CGS-SPC can be reduced to concurrent game structures with exclusive control. This result provides a polynomial reduction for the model checking problem of specifications in Alternating-time Temporal Logic on CGS-SPC.

In Jérôme Lang: Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017, Electronic Proceedings in Theoretical Computer Science 251, pp. 43–56.
Published: 25th July 2017.

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