serial: Journal of Logic and Computation vol.21, 3 (2011), p. 479-492
project(s): 1M0572, GA MŠk, GA102/08/0567, GA ČR
keywords: coalition game, core, MV-algebra
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 Łukasiewicz logic is introduced.