Kybernetika 49 no. 3, 404-419, 2013

Simple games in Łukasiewicz calculus and their cores

Petr Cintula and Tomáš Kroupa


We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness of core is completely characterized in terms of balanced systems and by the presence of strong veto players.


core, simple game, game with fuzzy coalitions, McNaughton function, Łukasiewicz logic


91A12, 06D35


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