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

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)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1969
Accession Number
AD0694446

Entities

People

  • Abraham Charnes
  • K. O. Kortanek

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computer Programming
  • Contracts
  • Cooperation
  • Game Theory
  • Interdisciplinary Science
  • Linear Programming
  • Linearity
  • Mathematical Analysis
  • Mathematics
  • Operations Research
  • Systems Science
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Game Theory.
  • Operations Research
  • Statistical inference.