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

Calculus of Bargaining Solution on Boolean Tables

Abstract. This article reports not only a theoretical solution of bargaining problem as used by game theoreticians but also an adequate calculus. By adequate calculus we understand an algorithm that can lead us to the result within reasonable timetable using either the computing power of nowadays computers or widely accepted classical Hamiltonian method of function maximization with constraints. Our motive is quite difficult to meet but we hope to move in this direction in order to close the gap at least for one nontrivial situation on Boolean Tables. JEL classification: C7

Maximum Principle for Survey Data Analysis *

The note addresses a principle of data cleaning. An implementation procedure of the principle contains a recommendation that might be well suited for clarifying and illustrating the results of survey data analysis

A STUDY OF INFRASPECIFIC GROUPS OF THE BALTIC EAST COAST AUTUMN HERRING BY TWO NEW METHODS BASED ON CLUSTER ANALYSIS

In the Baltic Sea the autumn spawning herring forms a smaller number of groups than the spring herring does. This is probably connected with the different location of their spawning grounds. Spawning grounds of the spring herring are concentrated in favorable sites near the coast (in gulf, estuaries, etc.) while between such spawning centers gaps occur usually. Contrary to it, in most parts of the Baltic spawning places of the autumn herring form a continuous chain situated in the open sea. Therefore, differences in environment conditions between the autumn spawning grounds of neighboring areas are small and in large districts the characters of the autumn herring do not reveal essential differences. For instance, there is no significant difference between the autumn herrings caught on various grounds off the Polish coasts (2,5). The autumn herring of the Swedish Baltic coasts can be divided into four groups (that of the Gulf of Bothnia, that of the Bothnia Sea, the herring of the Swedish east coast and that of the Swedish south coast), between which a gradual transition occurs [1]. Environmental conditions in various parts of the northeastern Baltic differ considerably. Spawning grounds of the autumn herring in these parts are disconnected b