Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A pursuit and evasion problem with measurement uncertainty

  • 45 Accesses

  • 4 Citations

Abstract

A pursuit-evasion process with uncertain state-dependent measurements, in finite, discrete time and in a finite, discrete state space, is considered. Three types of strategies which might be employed in such a process are compared, and attention is concentrated on the behavior strategy, the least well known of the three types, but often the simplest optimal strategy to employ.

A variation of the Brown-Robinson fictitious play algorithm is presented which can be used to compute behavior strategies in the case of perfect recall processes.

Two examples are given in which optimal behavior strategies are computed using the algorithm and compared with a type of plausible but nonoptimalseparation strategy.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Karlin, S.,Mathematical Methods and Theory in Games, Programming, and Economics, Chapter 6, Addison-Wesley Publishing Company, Reading, Massachusetts, 1959.

  2. 2.

    Kuhn, H. W.,Extensive Games and the Problem of Information, Contributions to the Theory of Games, Annals of Mathematical Studies, No. 28, Princeton University Press, Princeton, New Jersey, 1953.

  3. 3.

    Luce, R. D., andRaiffa, H.,Games and Decisions, Chapter 7, John Wiley and Sons, New York, 1957.

  4. 4.

    McKinsey, J.,Introduction to the Theory of Games, Chapter 6, McGraw-Hill Book Company, New York, 1952.

  5. 5.

    Robinson, J.,An Iterative Method of Solving a Game, Annals of Mathematics, Vol. 54, No. 2, 1951.

Download references

Author information

Additional information

This work was partially supported by NASA Grant No. NGR-15-005-021, NSF Grant No. GK-1970, and AFOSR Grant No. 69-1776.

Communicated by Y. C. Ho

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Utgoff, V.A., Kashyap, R.L. A pursuit and evasion problem with measurement uncertainty. J Optim Theory Appl 6, 68–87 (1970). https://doi.org/10.1007/BF00927042

Download citation

Keywords

  • State Space
  • Discrete Time
  • Optimal Strategy
  • Measurement Uncertainty
  • Discrete State