ON GAMES OF SURVIVAL

Abstract

In a game of survival, two players with limited resources play a zero-sum game repeatedly until one of them is ruined. The solution of the survival game gives one a measure of the value of resources in terms of survival probabilities. In this paper the zero-sum game is expressed as a finite matrix, but with (possibly) incommensurable entries; hence the number of different distributions of resources that can occur during a single play may be infinite. The existence of a value and optimal strategies is proved, using the theory of semi-martingales. A simple approximation to the solution is described, and several examples are discussed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 10, 1956
Accession Number
AD0604629

Entities

People

  • J. Milnor
  • Lloyd Shapley

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Convergence
  • Convex Sets
  • Corporations
  • Equations
  • Guarantees
  • Inequalities
  • Intervals
  • Matrix Games
  • Numbers
  • Plastic Explosives
  • Probability
  • Probability Distributions
  • Random Variables
  • Random Walk
  • Sequences
  • Theorems
  • Zero-Sum Games

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Game Theory.