Quasi-Equilibrium Pairs in Pursuit Games on a Cyclic Graph: Some Modified Cases

Abstract

In this paper, three special pursuit games on cyclic graphs are solved. These games are relevant to unsolved problems initiated by a game without a value. The following problems are proposed: (i) For a finite or infinite game without a saddle point, how should the players make their decisions? Here, we suppose that the game is played once. Thus mixed strategies are not considered. (ii) For an infinite game without a value v, i.e., V1<v2, how should the players make their decisions? To answer these questions, new concepts of quasi-equilibrium and pseudo-equilibrium are defined and it is shown that a game MDCPG has a quasi-equilibrium pair. Keywords: Pursuit games, Geometric games; Cyclic graphs; Quasi-equilibrium, Pseudo-equilibrium.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1989
Accession Number
ADA209980

Entities

People

  • Abraham Charnes
  • Di Zhang

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Animal Behavior
  • Business Administration
  • Eigenvalues
  • Equations
  • Game Theory
  • Kolmogorov Equations
  • Mathematics
  • Numbers
  • Probability
  • Probability Distributions
  • Random Walk
  • Real Numbers
  • Russian Language
  • Second World War
  • Universities
  • Zero-Sum Games

Readers

  • Game Theory.
  • Graph Algorithms and Convex Optimization.