Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
simple game; game with fuzzy coalitions; core; McNaughton function; Łukasiewicz logic
simple game; game with fuzzy coalitions; core; McNaughton function; Łukasiewicz logic
Summary:
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.
References:
[1] Aguzzoli, S.: Geometric and Proof-theoretic Issues in Łukasiewicz Propositional Logics. PhD. Thesis, University of Siena 1998.
[2] Aubin, J.-P.: Coeur et valeur des jeux flous à paiements latéraux. Comptes rendus de l'Académie des Sciences, Série A 279 (1974), 891-894. MR 0368799 | Zbl 0297.90128
[3] Aumann, R. J., Shapley, L. S.: Values of Non-atomic Games. Princeton University Press, Princeton 1974. MR 0378865 | Zbl 0311.90084
[4] Azrieli, Y., Lehrer, E.: On some families of cooperative fuzzy games. Internat. J. Game Theory 36 (2007), 1, 1-15. DOI 10.1007/s00182-007-0093-2 | MR 2332449 | Zbl 1128.91005
[5] Branzei, R., Dimitrov, D., Tijs, S.: Models in Cooperative Game Theory. Lecture Notes in Econom. and Math. Systems 556, Springer-Verlag, Berlin 2005. MR 2162897 | Zbl 1142.91017
[6] Butnariu, D., Klement, E. P.: Triangular Norm Based Measures and Games with Fuzzy Coalitions. Kluwer, Dordrecht 1993. MR 2867321 | Zbl 0804.90145
[7] Butnariu, D., Kroupa, T.: Shapley mappings and the cumulative value for $n$-person games with fuzzy coalitions. European J. Oper. Res. 186 (2008), 1, 288-299. DOI 10.1016/j.ejor.2007.01.033 | MR 2363872 | Zbl 1138.91320
[8] Cignoli, R. L. O., D'Ottaviano, I. M. L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. Trends in Logic - Studia Logica Library 7, Kluwer Academic Publishers, Dordrecht 2000. MR 1786097 | Zbl 0937.06009
[9] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Trends in Logic - Studia Logica Library 8, Kluwer Academic Publishers, Dordrecht 2000. MR 1790096 | Zbl 1087.20041
[10] McNaughton, R.: A theorem about infinite-valued sentential logic. J. Symbolic Logic 16 (1051), 1-13. DOI 10.2307/2268660 | MR 0041799 | Zbl 0135.24807
[11] Mundici, D.: Averaging the truth-value in Łukasiewicz logic. Studia Logica 55 (1995), 1, 113-127. DOI 10.1007/BF01053035 | MR 1348840 | Zbl 0836.03016
[12] Peleg, B., Sudhölter, P.: Introduction to the Theory of Cooperative Games. Second edition. Theory and Decision Library. Series C: Game Theory, Mathematical Programming and Operations Research 34, Springer, Berlin 2007. MR 2364703
[13] Riečan, B., Mundici, D.: Probability on MV-algebras. In: Handbook of Measure Theory, Vol. I, II, North-Holland, Amsterdam 2002, pp. 869-909. MR 1954631 | Zbl 1017.28002
[14] Rose, A., Rosser, J. B.: Fragments of many-valued statement calculi. Trans. AMS 87 (1958), 1-53. DOI 10.1090/S0002-9947-1958-0094299-1 | MR 0094299 | Zbl 0085.24303
[15] Webster, R.: Convexity. Oxford Science Publications. The Clarendon Press Oxford University Press, New York 1994. MR 1443208 | Zbl 1052.68785
[16] Wegener, I.: The Complexity of Boolean Functions. Wiley-Teubner Series in Computer Science. John Wiley and Sons, Chichester 1987. MR 0905473 | Zbl 0623.94018
Search
Partner of
