Accession Number : AD0694446

Title :   ON ASYMPTOTIC BEHAVIOR OF SOME NUCLEI OF n-PERSON GAMES AND THE PIECEWISE LINEARITY OF THE NUCLEOLUS.

Descriptive Note : Research rept.,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP

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

Report Date : AUG 1969

Pagination or Media Count : 19

Abstract : In a previous paper the authors developed a new class of solution concepts in n-person game theory as optimal solutions to specially constructed linear programming problems whose constraint matrices and hence optimal solutions depend on a certain parameter, c. In this paper asymptotic results are obtained for the limiting payoff configuration as c approaches infinity. It is shown that the limiting payoff configuration in general shares some properties with Schmeidler's solution concept of the nucleolus and under additional assumptions does converge to the nucleolus. By using recent results of Kohlberg, a new proof is obtained for the author's theorem of the piecewise linearity of the nucleolus as a function of the characteristic function of n-person games. (Author)

Descriptors :   (*GAME THEORY, *LINEAR PROGRAMMING), DECISION THEORY, SET THEORY, OPTIMIZATION, REAL VARIABLES, CONVERGENCE

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE