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Journal of Logic and Computation Advance Access published online on March 12, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp015
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Core of Coalition Games on MV-algebras1

Tomás Kroupa

Institute of Information Theory and Automation of the ASCR, Pod Vodárenskou vezí 4, 182 08 Prague, Czech Republic; Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague.
E-mail: kroupa{at}utia.cas.cz

Received 30 September 2008.


  Abstract

Coalition games are generalized to semisimple MV-algebras. Coalitions are viewed as [0, 1]-valued functions on a set of players, which enables to express a degree of membership of a player in a coalition. Every game is a real-valued mapping on a semisimple MV-algebra. The goal is to recover the so-called core: a set of final distributions of payoffs, which are represented by measures on the MV-algebra. A class of sublinear games are shown to have a non-empty core and the core is completely characterized in certain special cases. The interpretation of games on propositional formulas in Lukasiewicz logic is introduced.

Keywords: Coalition game; core; MV-algebra

1Dedicated to the memory of Dan Butnariu.


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