ON WEAKLY BALANCED GAMES AND DUALITY THEORY

Abstract

The notion of a 'weakly balanced game' under very general conditions involving no topology whatever is defined. The work of Schmeidler is extended by establishing duality results for a pair of (possibly) infinite dimensional linear programming problems arising from a generalized game. A necessary and sufficient condition is given in order that a separating hyperplane argument can be employed to prove the existence of a candidate core member for a weakly balanced game. This candidate is shown to be in the core if and only if the game is balanced. No use is made of topological ideas, but conditions are given under which the core member takes on values in a bounded set. The Charnes-Kortanek M-operator is used to characterize the redundancy of certain coalition values in restriction core membership.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1968
Accession Number
AD0666815

Entities

People

  • Abraham Charnes
  • Kenneth O. Kortanek
  • Mark Eisner

Organizations

  • Northwestern University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Computer Programming
  • Contracts
  • Convex Sets
  • Inequalities
  • Linear Programming
  • Mathematical Programming
  • Military Research
  • Numbers
  • Real Numbers
  • Redundancy
  • Security
  • Theorems
  • Topology
  • United States
  • United States Government
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Game Theory.
  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design