Skip to main content
SpringerLink
Log in

Game Theory and Some Interfaces with Control Theory

  • Conference paper
Optimal Control Theory and its Applications

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 105))

Abstract

The order of topics in these written notes does not follow that of the lectures; in particular, the number of subdivisions is not equal to the number of lectures. Also, the final Section 8 on the “ideal linear weights” is reproduced in the form in which it appeared in the Naval Research Logistics Quarterly (Dec. 1973, Vol. 20, pp. 645–659) rather than just the portion that was covered in the lectures.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Ho, Y.C., Decisions, Control and Extensive Games, unpublished (1973)

    Google Scholar 

  2. Ho, Y.C.,, Generalized Control Theory, lectures at Navy workshop on Differential Games, July-Aug. 1973, Annapolis, Maryland.

    Google Scholar 

  3. John J. Lawser. Properties of Dynamic Games, Ph.D. dissertation, The University of Michigan, November 1970, pp. 63–64.

    Google Scholar 

  4. Ibid., pp. 165–172.

    Google Scholar 

  5. Barfoot, C.B., “The Attrition-Rate Coefficient, Some Comments on Seth Bonder’s Paper and a Suggested Alternative Method”, Operations Research 17, 888–894 (1969).

    Article  Google Scholar 

  6. Bonder, Seth, “A Theory for Weapon System Analysis”, Proc. U.S. Army Operations Research Symposium, 111–128 (1965).

    Google Scholar 

  7. Bonder, Seth, “The Lanchester Attrition-Rate Coefficient”, Operations Research 15, 221–232 (1967).

    Article  Google Scholar 

  8. Bonder, Seth, “The Mean Lanchester Attrition Rate”, Operations Research 18, 179–181 (1970).

    Article  Google Scholar 

  9. Bonder, S. and R. Farrell, “Development of Models for Defense Systems Planning”, SRL 2147, Systems Research Laboratory, University of Michigan, Ann Arbor, Michigan (1970).

    Google Scholar 

  10. Corg, “Measuring Combat Effectiveness”, Vol. II, Technical Operations Incorporated Inc. Combat Operations Research Group, Alexandria, Va. (Jan. 1970).

    Google Scholar 

  11. Dolansky, L., “Present State of the Lanchester Theory of Combat”, Operations Research 12, 344–358 (1964).

    Article  MATH  Google Scholar 

  12. Frobenius, Georg, “Uber Matrizen aus nicht negativen Elementen”, Sitzungsberichte der Kgl Preussischen Akademie der Wissenschaften zu Berlin (1912), Berlin, pp. 456–477.

    Google Scholar 

  13. Frobenius, Georg, Gesammelte Abhandlungen, Band III (Edited by J.P. Serre ), Springer-Verlag, Berlin (1968).

    Google Scholar 

  14. Gantmacher, F.R., The Theory of Matrices (Chelsea, 1959), 2 vols.

    Google Scholar 

  15. Grubbs, Frank E. and John H. Shuford, “A New Formulation of Lanchester Combat Theory”, Operations Research 21, 926–941 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  16. Hayward, P., “The Measurement of Combat Effectiveness”, Operations Research 16, 314–323 (1968).

    Article  Google Scholar 

  17. Hero, “Comparative Analyses of Historical Studies”, Historical Evaluation and Research Office, 2223 Wisconsin Avenue, Washington, D.C. ( 15 Oct. 1964 ), Annex III-H.

    Google Scholar 

  18. Householder, A., Principles of Numerical Analysis ( McGraw-Hill, New York, 1953 ).

    MATH  Google Scholar 

  19. Kimbleton, S., “Attrition Rates for Weapons with MarkovDependent Fire”, Operations Research 19, 698–706 (1971).

    Article  MATH  Google Scholar 

  20. Koopman, B.O., “A Study of the Logical Basis of Combat Simulation”, Operations Research 18, 855–882 (1970).

    Article  MATH  Google Scholar 

  21. Lanchester, F.W., Aircraft in Warfare, the Dawn of the Fourth Arm ( Constable, London, 1916 ).

    Google Scholar 

  22. Morse, Philip M., and George E. Kimball, Methods of Operations Research ( John Wiley, New York, 1951 ).

    MATH  Google Scholar 

  23. Perron, Oskar, “Zur Theorie der Matrices”, Mathematische Annalen, Vol. 64 (1907).

    Google Scholar 

  24. RAC-TP-III, “Tacspiel War Game Procedures and Rules of Play”, Research Analysis Corp. McLean, Va. (Nov. 1963) ( Secret).

    Google Scholar 

  25. Rustagi, J. and R. Laitinen, “Moment Estimation in a MarkovDependent Firing Distribution”, Operations Research 18, 918–923 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  26. Rustagi, J. and R. Srivastava, “Parameter Estimation in a Markov Dependent Firing Distribution”, Operations Research 16, 1222–1227 (1968).

    Article  Google Scholar 

  27. Snow, R.N., “Contributions to Lanchester Attrition Theory”, Project RAND RA-15078 Douglas Aircraft Co., Santa Monica, Cal. (Apr. 1942).

    Google Scholar 

  28. Shuford, John H., “A New Probability Model for Lanchester’s Equations of Combat”, Masters Thesis submitted to the George Washington University (Dec. 1971).

    Google Scholar 

  29. Taylor, James G., “A Note on the Solution to Lanchester Type Equations with Variable Coefficients”, Operations Research 19, 709–712 (1971).

    Google Scholar 

  30. Thrall, R.M. and Associates, Final Report to U.S. Army Strategy and Tactics Analysis Group, RMT-200-R4–33 (1 May 1972 ).

    Google Scholar 

  31. Todd, J. (Editor), Survey of Numerical Analysis ( McGraw-Hill, New York, 1962 ).

    MATH  Google Scholar 

  32. United States Army Combat Developments Command Report, Measuring Combat Effectiveness, by Technical Operations Incorporated, Combat Operations Research Group, Vol. I “Firepower Potential Methodology (U)” (Confidential- NO FORN).

    Google Scholar 

  33. Varga, R., Matrix Iterative Analysis (Prentice-Hall, Englewood Cliffs, New Jersey, 1962 ).

    Google Scholar 

  34. Weiss, H.K., “Lanchester-Type Models of Warfare”, Proc. First International Conference on Operations Research (Dec. 1957), pp. 82–89.

    Google Scholar 

  35. Blackwell, David and Girshick, M.A. Theory of Games and Statis- tical Decisions. John Wiley and Sons, New York, 1954.

    Google Scholar 

  36. Burger, Ewald., Introduction to the Theory of Games. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1963.

    Google Scholar 

  37. Case, J.N., Toward a Theory of Many Player Differential Games, SIAM J. Control, Vol. 7 (1969), pp. 179–197.

    MathSciNet  MATH  Google Scholar 

  38. Copeland, A.H., Review: Theory of Games and Economic Behavior (John von Neumann and Oskar Morgenstern), Bulletin Amer. Math. Soc., Vol. 51 (1945), PP. 498–504.

    Google Scholar 

  39. Davis, M.D., Game Theory: A Nontechnical Introduction, Basic Books, Inc., New York, 1970.

    Google Scholar 

  40. Dresher, M., Tucker, A.W. and Wolfe, P. Contributions to the Theory of Games, Vol. III, Ann. Math. Studies, 39, Princeton University Press, Princeton, New Jersey,1957.

    Google Scholar 

  41. Dresher, M., Shapley, L.S. and Tucker, A.W., EDS., Advances in Game Theory, Annals of Math. Studies, No. 52, Princeton University Press, Princeton, 1964.

    Google Scholar 

  42. Dresher, Melvin, Games of Strategy: Theory and Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1961.

    Google Scholar 

  43. Eisenman, R.L., Alliance Games of N-persons, Nay. Res. Logist. Quarterly, 13 (1966), pp. 403–411.

    Article  MathSciNet  MATH  Google Scholar 

  44. Glicksman, A.M., An Introduction to Linear Programming and the Theory of Games, J. Wiley and Sons, Inc., New York, 1963.

    Google Scholar 

  45. Grotte, J.H., Computation of and Observations on the Nucleolus, the Normalized Nucleolus, and the Central Games, Masterts Thesis, Applied Mathematics Dept., Cornell University, Ithaca, New York, 1970.

    Google Scholar 

  46. Howard, Nigel, Paradoxes of Rationality: Theory of Metagames and Political Behavior, MIT Press, Cambridge, Mass. (1971).

    Google Scholar 

  47. Isaacs, R., Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, J. Wiley and Sons, Inc., New York, 1965.

    Google Scholar 

  48. Karlin, Samuel, Mathematical Methods and Theory in Games, Programming, and Economics, Vols. I and II, Addison-Wesley Publishing Company, Inc., Reading, Mass., 1959.

    Google Scholar 

  49. Kohlberg, E., On the Nucleolus of a Characteristic Function Game, SIAM J. Appl. Math., 20 (1971), pp. 62–66.

    MathSciNet  MATH  Google Scholar 

  50. Kohlberg, E., The Nucleolus as a Solution of a Minimization Problem, SIAM J. Appl. Math., to appear.

    Google Scholar 

  51. Kopelowitz, A., Computation of the Kernels of Simple Games and the Nucleolus of N-person Games, RPGTME RM 31, Dept. of Mathematics, Hebrew Univ., Jerusalem, Sept., 1967.

    Google Scholar 

  52. Kuhn, Harold W. and Tucker, Albert W., Contributions to the Theory of Games, Ann. Math. Studies, 24, Princeton University Press, Princeton, New Jersey, 1950.

    Google Scholar 

  53. Kuhn, Harold W. and Tucker, Albert W., Contributions to the Theory of Games, Vol. II, Ann. Math. Studies, 28, Princeton University Press, Princeton, New Jersey, 1953.

    Google Scholar 

  54. Lucas, W.F., Solutions for Four-person Games in Partition Function Form, SIAM J. Appl. Math., 13 (1965), pp. 118–128.

    MATH  Google Scholar 

  55. Lucas, W.F., A Game with No Solution, Bull. Amer. Soc., Vol. 74 (1968), pp. 237–239.

    Article  MATH  Google Scholar 

  56. Lucas, W.F., A Game in Partition Function Form with No Solution, J. SIAM, Vol. 16 (1968), pp. 582–585.

    MATH  Google Scholar 

  57. Lucas, W.F., The Proof That a Game May Not Have a Solution, Trans. Amer. Math. Soc., Vol. 137 (1969), pp. 219–229.

    Article  MathSciNet  MATH  Google Scholar 

  58. Lucas, W.F., Some Recent Developments in N-Person Game Theory, SIAM Review, Vol. 13 (1971).

    Google Scholar 

  59. Lucas, W.F., An Overview of the Mathematical Theory of Games, Management Science 18 (1972), pp. P3–19.

    Article  MATH  Google Scholar 

  60. Luce, R. Duncan and Raiffa, Howard, Games and Decisions: Introduction and Critical Survey, John Wiley and Sons, New York, 1957.

    Google Scholar 

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

    MATH  Google Scholar 

  62. Megiddo, N., The Kernel and the Nucleolus of a Product of Simple Games, RPGTME RM 45, Dept. of Mathematics, Hebrew Univ., Jerusalem, April, 1969.

    Google Scholar 

  63. Owen, G., Game Theory, W.B. Saunders Co., Philadelphia, 1968.

    Google Scholar 

  64. Owen, G., Political Games, Nay. Res. Logist. Quart., 18 (1971), pp. 345–355.

    Article  MathSciNet  Google Scholar 

  65. Owen, G., Optimal Threat Strategies of Bimatrix Games, Int. J. Game Th., 1, (1971), pp. 1–9.

    Article  MathSciNet  Google Scholar 

  66. Owen, G., Multilinear Extensions of Games, Management Sci., 18, (1971), pp. P64 - P79.

    Article  MathSciNet  Google Scholar 

  67. Rapoport, A., Two-Person Game Theory: The Essential Ideas, The University of Michigan Press, Ann Arbor, 1966.

    MATH  Google Scholar 

  68. Rapoport, A., N-Person Game Theory: Concepts and Applications, University of Michigan Press, Ann Arbor, 1970.

    MATH  Google Scholar 

  69. Schmeidler, D., The Nucleolus of a Characteristic Function Game, SIAM J. Appl. Math., Vol. 17 (1969), pp. 1163–1170.

    MathSciNet  MATH  Google Scholar 

  70. Schwodiauer, G., Glossary of Game Theoretical Terms, Working Paper No. 1, Dept. of Ec., New York Univ., (1971), pp. 88.

    Google Scholar 

  71. Shubik, M., ED., Game Theory and Related Approaches to Social Behavior, John Wiley and Sons, Inc., 1964.

    Google Scholar 

  72. Thrall, R.M. and Lucas, W.F., N-Person Games in Partition Function Form, Nay.Res.Logist.Quart., Vol. 10, (1963),pp. 281–298.

    Article  MathSciNet  MATH  Google Scholar 

  73. Tucker, Albert W., and Luce, R. Duncan, Contributions to the Theory of Games, Vol. IV, Ann. Math. Studies, 40, Princeton University Press, Princeton, New Jersey, 1959.

    Google Scholar 

  74. Vorobtev, N.N., The Development of Game Theory, (Translated by E. Schwodiauer) Working Paper No. 2, Dept. of Ec., New York Univ., (1971), 124 + 18 pp.

    Google Scholar 

  75. von Neumann, John and Morgenstern, Oskar, Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1st ed. 1944, 2nd ed. 1947.

    Google Scholar 

  76. Williams, John D., The Compleat Strategist: Being a Primer on the Theory of Games of Strategy, McGraw-Hill Book Comoany, New York, 1954.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Rice University, USA

    R. M. Thrall

Authors
  1. R. M. Thrall
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathematics Department, Queen’s University, Kingston, Ontario, Canada

    Bruce J. Kirby

Rights and permissions

Reprints and permissions

Copyright information

© 1974 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Thrall, R.M. (1974). Game Theory and Some Interfaces with Control Theory. In: Kirby, B.J. (eds) Optimal Control Theory and its Applications. Lecture Notes in Economics and Mathematical Systems, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-01569-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-01569-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07018-4

  • Online ISBN: 978-3-662-01569-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation