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Abstract

The study addresses important question regarding the computational aspect of coalition formation. Almost as well known to find payoffs imputations belonging to a core, is prohibitively difficult, NP-hard task even for modern super-computers. In addition to the difficulty, the task becomes uncertain as it is unknown whether the core is non-empty. Following Shapley 1971, our Singles Party Game is convex, thus the presence of non-empty core is fully guaranteed. The article introduces a concept of coalitions, which are called nebulouses, adequate to critical coalitions, Mullat 1979. Nebulouses represent coalitions minimal by inclusion among all coalitions assembled into a semi-lattice of sets or kernels of -Monotone System,- Mullat 1971,1976,1995, Kuznetsov et al. 1982. An equivalent property to convexity, i.e., the monotonicity of the singles game allowed creating an effective procedure for finding the core by polynomial algorithm, a version of P-NP problem. Results are illustrated by MS Excel spreadsheet.



Item Type: MPRA Paper -

Original Title: How to arrange a Singles Party-

Language: English-

Keywords: stability conditions; game theory; coalition formation-

Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative GamesC - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation ModelingC - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium-





Autor: Mullat, Joseph E.

Fuente: https://mpra.ub.uni-muenchen.de/24821/



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