Representing Strategic Games and Their Equilibria in Many-Valued Logics

0456358 - ÚI 2017 RIV GB eng J - Článek v odborném periodiku
Běhounek, Libor - Cintula, Petr - Fermüller, C. - Kroupa, Tomáš
Representing Strategic Games and Their Equilibria in Many-Valued Logics.
Logic Journal of the IGPL. Roč. 24, č. 3 (2016), s. 238-267. ISSN 1367-0751. E-ISSN 1368-9894
Grant CEP: GA ČR GAP402/12/1309; GA MŠMT 7AMB13AT014; GA ČR(CZ) GF15-34650L
Grant ostatní: Austrian Science Fund(AT) P25417-G15; Austrian Science Fund(AT) I1897-N25
Institucionální podpora: RVO:67985807 ; RVO:67985556
Klíčová slova: strategic games * many-valued logics * Nash equilibria * Lukasiewicz games
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.575, rok: 2016

We introduce the notion of logical A-games for a fairly general class of algebras A of real truth-values. This concept generalizes the Boolean games as well as the recently defined Lukasiewicz games of Marchioni and Wooldridge. We demonstrate that a wide range of strategic n-player games can be represented as logical A-games. Moreover we show how to construct, under rather general conditions, propositional formulas in the language of A that correspond to pure and mixed Nash equilibria of logical A-games.
Trvalý link: http://hdl.handle.net/11104/0256881