A MULTIMOVE INFINITE GAME WITH LINEAR PAYOFF

Abstract

This paper analyzes a multimove infinite game with linear payoff function. The game had its origin in the consideration of a military problem, but is presented here solely for its mathematical interest. It is symmetric in every respect except that the initial conditions of the two players are different. On each move, each player allocates his resources to tasks that might be described roughly as attacking, defending, and scoring. His resources for the next move are diminished by the amount that his opponent's attack exceeds his own defense, while his score cumulates from move to move. The value of the game and the optimal strategies for the players are rigorously derived in the present paper. It is shown that one player has a pure optimal strategy and the other player must randomize.

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Document Details

Document Type
Technical Report
Publication Date
Sep 22, 1958
Accession Number
AD0606465

Entities

People

  • Leonard D. Berkovitz
  • Melvin Dresher

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Coefficients
  • Computations
  • Continuity
  • Distribution Functions
  • Equations
  • Hard Copy
  • Inequalities
  • Microfiche
  • Probability
  • Probability Distributions
  • Sequences
  • Step Functions
  • Triangles
  • Varistors

Readers

  • Game Theory.
  • Military History / Militaries and War Studies
  • Operations Research