Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T13:01:13.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic pursuit-evasion games with information lag. I. Perfect observation

Published online by Cambridge University Press:  14 July 2016

Mynda Schreuer
Mynda Schreuer*
Affiliation:
University of Salzburg
Get access Rights & Permissions [Opens in a new window]

Abstract

A discrete time, scalar, pursuit-evasion game is presented in which an evader, moving according to a stationary stochastic process, is continually being followed by a pursuer. Both players have perfect observations of the evader's positions, but the observations of the pursuer are subject to a time lag. It is assumed that the strategy of the evader can be represented as an infinite moving average, and that he is restricted by a velocity constraint. The pursuer is limited to strategies linear in his information, and the payoff is taken to be the mean-square distance between pursuer and evader. Under these conditions it is shown that the game does not have a value, and subsequently the lower and upper values and corresponding strategies are found.

Keywords

PURSUIT-EVASION GAMESPREDICTION GAMESLAGGED INFORMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 248 - 256
Copyright
Copyright © Applied Probability Trust 1975 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Elion, M. (1971) Pursuit-evasion games with information lag. University of Cambridge Ph.D. thesis.Google Scholar
[2] Grenander, U. (1956) A prediction problem in game theory. Ark. Mat. 3, 371–379.CrossRefGoogle Scholar
[3] Grenander, U. (1965) Stochastic models in the theory of pursuit. Review of the International Statistical Institute , 33 (2), 177–228.CrossRefGoogle Scholar
[4] Grenander, U. (1968) A tactical study of evasive maneuvers. FOA Report , 2, (4).Google Scholar