Accession Number : AD0651037

Title :   ON A CLASS OF CONVEX AND NON-ARCHIMEDEAN SOLUTION CONCEPTS FOR N-PERSON GAMES.

Descriptive Note : Systems research memo.,

Corporate Author : NORTHWESTERN UNIV EVANSTON ILL TECHNOLOGICAL INST

Personal Author(s) : Charnes,A. ; Kortanek,K.

Report Date : MAR 1967

Pagination or Media Count : 24

Abstract : Recently D. Schmeidler developed an interesting solution concept, called the nucleolus of a game, for characteristic function n-person games taking values in the real number field. By using elementary topology Schmeidler proves existence and uniqueness properties and also shows that the nucleolus belongs to the core of the game. This paper develops a general class of solution concepts termed nuclei which generalize the nucleolus and which are defined for n-person games which take values in any arbitrarily ordered field. These nuclei are in general independent of any topological considerations and possess unicity properties as well as core membership. When a topology is introduced, a wide class of convex nuclei is presented which is contained in the core and which correspond to a class of (strictly) convex functions of the excesses of the game values over the payoff values on coalitions. Finally, by introducing non-Archimedean elements to the base field, preemptive nuclei are constructed which correspond to only a few (arbitrarily chosen) preemptive orderings on the excesses and which are unique and contained in the core.

Descriptors :   (*GAME THEORY, *LINEAR PROGRAMMING), (*TOPOLOGY, *REAL NUMBERS), VALUE ENGINEERING, POLYNOMIALS, THEOREMS, INEQUALITIES, SET THEORY, MATRICES(MATHEMATICS), VECTOR ANALYSIS, SEQUENCES(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE