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Logic Journal of IGPL Advance Access published online on May 18, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Logics for Qualitative Coalitional Games

Thomas Ågotnes*

University of Bergen, Norway.
E-mail: thomas.agotnes{at}infomedia.uib.no

Wiebe Van Der Hoek and Michael Wooldridge

University of Liverpool, United Kingdom.
E-mail: wiebe{at}csc.liv.ac.uk,mjw{at}csc.liv.ac.uk

*Corresponding author. Address: Department of Information Science and Media Studies, University of Bergen, PB 7800, 5007 Bergen, Norway.


  Abstract

Qualitative Coalitional Games (QCGs) are a variant of coalitional games in which an agent's desires are represented as goals that are either satisfied or unsatisfied, and each choice available to a coalition is a set of goals, which would be jointly satisfied if the coalition made that choice. A coalition in a QCG will typically form in order to bring about a set of goals that will satisfy all members of the coalition. Our goal in this paper is to develop and study logics for reasoning about QCGs. We begin by introducing a logic for reasoning about "static" QCGs, where participants play a single game, and we then introduce and study Temporal QCGs (TQCGs), i.e., games in which a sequence of QCGs is played. In order to represent and reason about such games, we introduce a linear time temporal logic of QCGs, called L(TQCG). We give a complete axiomatisation of L(TQCG), use it to investigate the properties of TQCGs, identify its expressive power, establish its complexity, characterise classes of TQGCs with formulas from our logical language, and use it to formulate several (temporal) solution concepts for TQCGs.

Key Words: modal logic • temporal logic • coalitional games • repeated games


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