How to arrange a Singles Party

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.