Annals of Operations Research

, Volume 109, Issue 1–4, pp 15–40 | Cite as

A Game Theoretical Multiple Resource Interaction Approach to Resource Allocation in an Air Campaign

  • Debasish Ghose
  • Jason L. Speyer
  • Jeff S. Shamma

Abstract

In this paper we propose a multiple resource interaction model in a game-theoretical framework to solve resource allocation problems in theater level military campaigns. An air raid campaign using SEAD aircraft and bombers against an enemy target defended by air defense units is considered as the basic platform. Conditions for the existence of saddle point in pure strategies is proved and explicit feedback strategies are obtained for a simplified model with linear attrition function limited by resource availability. An illustrative example demonstrates the key features.

air campaign modeling resource interaction models resource allocation military campaigns applied game theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T. Basar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edn. (Academic Press, London, 1995).Google Scholar
  2. [2]
    L.D. Berkovitz and M. Dresher, A game-theory analysis of tactical air war, Operations Research 7 (1959) 599-620.Google Scholar
  3. [3]
    D. Blackwell, On multi-component attrition games, Naval Research Logistics Quarterly 1 (1954) 210-216.Google Scholar
  4. [4]
    J. Bracken and J.T. McGill, Defense applications of mathematical programs with optimization problems in the constraints, Operations Research 22 (1974) 1086-1096.Google Scholar
  5. [5]
    J.M. Danskin, The Theory of Max-Min and its Applications to Weapons Allocation Problems (Springer, New York, 1967).Google Scholar
  6. [6]
    P.K. Davis and J.H. Bigelow, Experiments inMulti-Resolution Modeling (MRM), RAND Publication MR-1004-DARPA, Santa Monica, CA (1998).Google Scholar
  7. [7]
    K. Fan, Minimax theorems, Proc. Nat. Acad. Sci. 39 (1953) 42-47.Google Scholar
  8. [8]
    F. Forgo, J. Szep and F. Szidarovszky, Introduction to the Theory of Games: Concepts, Methods, Applications (Kluwer Academic, Dordrecht, 1999).Google Scholar
  9. [9]
    D. Ghose, M. Krichman, J.S. Shamma and J.L. Speyer, Modeling of a SEAD assisted air campaign as an integrated temporal and spatial resource allocation problem, Technical Report, Mechanical and Aerospace Engineering Department, University of California at Los Angeles (April 2000).Google Scholar
  10. [10]
    D. Ghose, M. Krichman, J.L. Speyer and J.S. Shamma, Game theoretic campaign modeling and analysis, in: Proceedings of the IEEE Conference on Decision and Control (CDC '2000), Sydney, Australia (December 2000) pp. 2556-2561.Google Scholar
  11. [11]
    D. Ghose, J.L. Speyer and J.S. Shamma, A game theoretical model for temporal resource allocation in an air campaign, in: Proceedings of the JFACC Symposium on Advances in Enterprise Control, Minneapolis, MN (2000) pp.129-138.Google Scholar
  12. [12]
    D. Ghose, J.L. Speyer and J.S. Shamma, A game theoretical analysis of a multiple resource interaction model for resource allocation in an air campaign, Technical Report, Mechanical and Aerospace Engineering Department, University of California at Los Angeles (October 2000).Google Scholar
  13. [13]
    R.J. Hillestad and L. Moore, The theater-level campaign model: A research prototype for a new generation of combat analysis model, RAND Technical Report MR-388-AF/A, Rand Publication, Santa Monica, CA (1996).Google Scholar
  14. [14]
    R.D. Luce and H. Raiffa, Games and Decisions (Wiley, New York, 1957).Google Scholar
  15. [15]
    G. Owen, Game Theory, 3rd edn. (Academic Press, New York, 1995).Google Scholar
  16. [16]
    E. van Damme, Stability and Perfection of Nash Equilibria (Springer, Berlin, 1987).Google Scholar
  17. [17]
    D. Vaughan, J. Kvitky, K. Henry, M. Gabriele, G. Park, G. Halverson and B. Schweitzer, Capturing the essential factors in reconnaissance and surveillance force sizing and mix, Project Air Force, RAND Documented Briefing, DB 199-AF, Rand Publication, Santa Monica, CA (1998).Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Debasish Ghose
    • 1
  • Jason L. Speyer
    • 2
  • Jeff S. Shamma
    • 2
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Mechanical and Aerospace Engineering DepartmentUniversity of California at Los AngelesLos AngelesUSA

Personalised recommendations