AVOIDANCE IN ONE DIMENSION: A CONTINUOUS-MATRIX GAME

Abstract

The game is a two-person zero-sum game. On each play, each player selects any point on a line of finite length. The payoff is a trapezoidal function of the separation between the two selected points; it is constant for separations from zero to R sub 1, changes linearly between R sub 1 and R sub 2, and is zero for separations greater than R sub 2. The derivation and proof of the solution are interesting due to the discontinuities in the slope of the payoff function. The solution includes the special cases of triangular (R sub 1 = 0) and rectangular (R sub 1 = R sub 2) payoff functions. The game is related to search theory in its applicability to the barrier problem. Uniform distribution along the barrier is not in general an optimal strategy for either the maximizer (detector) or the avoider (transitor). In selecting optimal strategies the detec or must have more information on the payoff function (lateral range curve) than is required by the transitor.

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Document Details

Document Type
Technical Report
Publication Date
Jan 11, 1962
Accession Number
AD0277843

Entities

People

  • Robert D. Arnold

Organizations

  • Center for Naval Analyses

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Detection
  • Detectors
  • Discontinuities
  • Equations
  • Frequency
  • Government Procurement
  • Governments
  • Integrals
  • Matrix Games
  • Probability
  • Search Theory
  • Zero-Sum Games

Readers

  • Calculus or Mathematical Analysis
  • Game Theory.