Nonsymmetric variants of the prekernel and the prenucleolus

A solution on a class of TU games that satisfies the axioms of the pre-nucleolus or -kernel except the equal treatment property and is single valued for two-person games, is a nonsymmetric pre-nucleolus (NSPN) or -kernel (NSPK). We investigate the NSPKs and NSPNs and their relations to the positive prekernel and to the positive core. It turns out that any NSPK is a subsolution of the positive prekernel. Moreover, we show that an arbitrary NSPK, when applied to a TU game, intersects the set of preimputations whose dissatisfactions coincide with the dissatisfactions of an arbitrary element of any other NSPK applied to this game. This result also provides a new proof of sufficiency of the characterizing conditions for NSPKs introduced by Orshan (Non-symmetric prekernels, discussion paper 60. Center for Rationality, The Hebrew University of Jerusalem, 1994). Any NSPN belongs to ??its?? NSPK. Several classes of NSPNs are presented, all of them being subsolutions of the positive core. We show that any NSPN is a subsolution of the positive core provided that it satisfies the equal treatment property on an infinite subset of the universe of potential players. Moreover, we prove that, for any game whose prenucleolus is in its anticore, any NSPN coincides with the prenucleolus.     

The consistent Shapley value in hyperplane games from a global standpoint

It is proved that the consistent Shapley value for hyperplane games is characterized by Pareto-optimality, symmetry, covariancy, and global consistency. A dynamic process based on global consistency is given. It leads the players to the value from any arbitrary payoff vector.Submitted as an M. Sc. thesis, The Hebrew University of Jerusalem.     

The prenucleolus and the reduced game property: Equal treatment replaces anonymity

In his paper, Sobolev [1975] characterized the prenucleolus as the unique solution concept, defined over the class of cooperative games that satisfies single valuedness, anonymity, covariance under strategic equivalence and reduced game property (consistency).In this paper we show that anonymity can be weakened and replaced by a requirement of equal treatment (symmetry).     

The positive core of a cooperative game

The positive core is a nonempty extension of the core of transferable utility games. If the core is nonempty, then it coincides with the core. It shares many properties with the core. Six well-known axioms that are employed in some axiomatizations of the core, the prenucleolus, or the positive prekernel, and one new intuitive axiom, characterize the positive core for any infinite universe of players. This new axiom requires that the solution of a game, whenever it is nonempty, contains an element that is invariant under any symmetry of the game.     

Polymeric UV-Absorbers of 2-Hydroxybenzophenone Type. I. Polyesters on the Base of 2-Hydroxy-4-(2,3-epoxypropoxy)benzophenone

Some polyester light stabilizers were synthetized by the co-polymerization of an equimolar mixture of 2-hydroxy-4-(2,3-epoxypropoxy)benzophenone with cyclic anhydrides of di-carboxylic acids. This synthesis was carried out in melt by using potassium benzoate or tert-amines as catalysts. The catalytic efficiency of potassium benzoate in heterogeneous phase increases with its surface area. In comparison with potassium benzoate, tert-amines show a higher catalytic effect in homogeneous medium. According to the UV spectra of the products, the 2-hydroxybenzophenone structural units of light stabilizers are not subject to destruction during the polymerization of an equimolar mixture of epoxide with anhydrides. The efficiency of UV stabilization of the stabilizers prepared in polypropylene is comparable with the efficiency of 2-hydroxy-4-n-octyloxybenzophenone with the exception of those samples which contain the structural units of maleinic anhydride and glycidyl-β-naphthyi ether. In contrast to 2-hydroxy-4-n-octyloxybenzophenone, the high molecular weight UV absorbers exhibit a lower extractibility from polypropylene sheets with trichloroethylene.