Game Theory and Some Interfaces with Control Theory

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


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.


Differential Game Level Curve Ideal Weight Nash Bargaining Solution Effectiveness Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ho, Y.C., Decisions, Control and Extensive Games, unpublished (1973)Google Scholar
  2. [2]
    Ho, Y.C.,, Generalized Control Theory, lectures at Navy workshop on Differential Games, July-Aug. 1973, Annapolis, Maryland.Google Scholar
  3. 1.
    John J. Lawser. Properties of Dynamic Games, Ph.D. dissertation, The University of Michigan, November 1970, pp. 63–64.Google Scholar
  4. 2.
    Ibid., pp. 165–172.Google Scholar
  5. [1]
    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).CrossRefGoogle Scholar
  6. [2]
    Bonder, Seth, “A Theory for Weapon System Analysis”, Proc. U.S. Army Operations Research Symposium, 111–128 (1965).Google Scholar
  7. [3]
    Bonder, Seth, “The Lanchester Attrition-Rate Coefficient”, Operations Research 15, 221–232 (1967).CrossRefGoogle Scholar
  8. [4]
    Bonder, Seth, “The Mean Lanchester Attrition Rate”, Operations Research 18, 179–181 (1970).CrossRefGoogle Scholar
  9. [5]
    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. [6]
    Corg, “Measuring Combat Effectiveness”, Vol. II, Technical Operations Incorporated Inc. Combat Operations Research Group, Alexandria, Va. (Jan. 1970).Google Scholar
  11. [7]
    Dolansky, L., “Present State of the Lanchester Theory of Combat”, Operations Research 12, 344–358 (1964).zbMATHCrossRefGoogle Scholar
  12. [8]
    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. [9]
    Frobenius, Georg, Gesammelte Abhandlungen, Band III (Edited by J.P. Serre ), Springer-Verlag, Berlin (1968).Google Scholar
  14. [10]
    Gantmacher, F.R., The Theory of Matrices (Chelsea, 1959), 2 vols.Google Scholar
  15. [11]
    Grubbs, Frank E. and John H. Shuford, “A New Formulation of Lanchester Combat Theory”, Operations Research 21, 926–941 (1973).MathSciNetzbMATHCrossRefGoogle Scholar
  16. [12]
    Hayward, P., “The Measurement of Combat Effectiveness”, Operations Research 16, 314–323 (1968).CrossRefGoogle Scholar
  17. [13]
    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. [14]
    Householder, A., Principles of Numerical Analysis ( McGraw-Hill, New York, 1953 ).zbMATHGoogle Scholar
  19. [15]
    Kimbleton, S., “Attrition Rates for Weapons with MarkovDependent Fire”, Operations Research 19, 698–706 (1971).zbMATHCrossRefGoogle Scholar
  20. [16]
    Koopman, B.O., “A Study of the Logical Basis of Combat Simulation”, Operations Research 18, 855–882 (1970).zbMATHCrossRefGoogle Scholar
  21. [17]
    Lanchester, F.W., Aircraft in Warfare, the Dawn of the Fourth Arm ( Constable, London, 1916 ).Google Scholar
  22. [18]
    Morse, Philip M., and George E. Kimball, Methods of Operations Research ( John Wiley, New York, 1951 ).zbMATHGoogle Scholar
  23. [19]
    Perron, Oskar, “Zur Theorie der Matrices”, Mathematische Annalen, Vol. 64 (1907).Google Scholar
  24. [20]
    RAC-TP-III, “Tacspiel War Game Procedures and Rules of Play”, Research Analysis Corp. McLean, Va. (Nov. 1963) ( Secret).Google Scholar
  25. [21]
    Rustagi, J. and R. Laitinen, “Moment Estimation in a MarkovDependent Firing Distribution”, Operations Research 18, 918–923 (1970).MathSciNetzbMATHCrossRefGoogle Scholar
  26. [22]
    Rustagi, J. and R. Srivastava, “Parameter Estimation in a Markov Dependent Firing Distribution”, Operations Research 16, 1222–1227 (1968).CrossRefGoogle Scholar
  27. [23]
    Snow, R.N., “Contributions to Lanchester Attrition Theory”, Project RAND RA-15078 Douglas Aircraft Co., Santa Monica, Cal. (Apr. 1942).Google Scholar
  28. [24]
    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. [25]
    Taylor, James G., “A Note on the Solution to Lanchester Type Equations with Variable Coefficients”, Operations Research 19, 709–712 (1971).Google Scholar
  30. [26]
    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. [27]
    Todd, J. (Editor), Survey of Numerical Analysis ( McGraw-Hill, New York, 1962 ).zbMATHGoogle Scholar
  32. [28]
    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. [29]
    Varga, R., Matrix Iterative Analysis (Prentice-Hall, Englewood Cliffs, New Jersey, 1962 ).Google Scholar
  34. [30]
    Weiss, H.K., “Lanchester-Type Models of Warfare”, Proc. First International Conference on Operations Research (Dec. 1957), pp. 82–89.Google Scholar
  35. 1.
    Blackwell, David and Girshick, M.A. Theory of Games and Statis- tical Decisions. John Wiley and Sons, New York, 1954.Google Scholar
  36. 2.
    Burger, Ewald., Introduction to the Theory of Games. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1963.Google Scholar
  37. 3.
    Case, J.N., Toward a Theory of Many Player Differential Games, SIAM J. Control, Vol. 7 (1969), pp. 179–197.MathSciNetzbMATHGoogle Scholar
  38. 4.
    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. 5.
    Davis, M.D., Game Theory: A Nontechnical Introduction, Basic Books, Inc., New York, 1970.Google Scholar
  40. 6.
    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. 7.
    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. 8.
    Dresher, Melvin, Games of Strategy: Theory and Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1961.Google Scholar
  43. 9.
    Eisenman, R.L., Alliance Games of N-persons, Nay. Res. Logist. Quarterly, 13 (1966), pp. 403–411.MathSciNetzbMATHCrossRefGoogle Scholar
  44. 10.
    Glicksman, A.M., An Introduction to Linear Programming and the Theory of Games, J. Wiley and Sons, Inc., New York, 1963.Google Scholar
  45. 11.
    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. 12.
    Howard, Nigel, Paradoxes of Rationality: Theory of Metagames and Political Behavior, MIT Press, Cambridge, Mass. (1971).Google Scholar
  47. 13.
    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. 14.
    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. 15.
    Kohlberg, E., On the Nucleolus of a Characteristic Function Game, SIAM J. Appl. Math., 20 (1971), pp. 62–66.MathSciNetzbMATHGoogle Scholar
  50. 16.
    Kohlberg, E., The Nucleolus as a Solution of a Minimization Problem, SIAM J. Appl. Math., to appear.Google Scholar
  51. 17.
    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. 18.
    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. 19.
    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. 20.
    Lucas, W.F., Solutions for Four-person Games in Partition Function Form, SIAM J. Appl. Math., 13 (1965), pp. 118–128.zbMATHGoogle Scholar
  55. 21.
    Lucas, W.F., A Game with No Solution, Bull. Amer. Soc., Vol. 74 (1968), pp. 237–239.zbMATHCrossRefGoogle Scholar
  56. 22.
    Lucas, W.F., A Game in Partition Function Form with No Solution, J. SIAM, Vol. 16 (1968), pp. 582–585.zbMATHGoogle Scholar
  57. 23.
    Lucas, W.F., The Proof That a Game May Not Have a Solution, Trans. Amer. Math. Soc., Vol. 137 (1969), pp. 219–229.MathSciNetzbMATHCrossRefGoogle Scholar
  58. 24.
    Lucas, W.F., Some Recent Developments in N-Person Game Theory, SIAM Review, Vol. 13 (1971).Google Scholar
  59. 25.
    Lucas, W.F., An Overview of the Mathematical Theory of Games, Management Science 18 (1972), pp. P3–19.zbMATHCrossRefGoogle Scholar
  60. 26.
    Luce, R. Duncan and Raiffa, Howard, Games and Decisions: Introduction and Critical Survey, John Wiley and Sons, New York, 1957.Google Scholar
  61. 27.
    McKinsey, J.C.C., Introduction to the Theory of Games, McGraw-Hill Book Company, New York, 1952.zbMATHGoogle Scholar
  62. 28.
    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. 29.
    Owen, G., Game Theory, W.B. Saunders Co., Philadelphia, 1968.Google Scholar
  64. 30.
    Owen, G., Political Games, Nay. Res. Logist. Quart., 18 (1971), pp. 345–355.MathSciNetCrossRefGoogle Scholar
  65. 31.
    Owen, G., Optimal Threat Strategies of Bimatrix Games, Int. J. Game Th., 1, (1971), pp. 1–9.MathSciNetCrossRefGoogle Scholar
  66. 32.
    Owen, G., Multilinear Extensions of Games, Management Sci., 18, (1971), pp. P64 - P79.MathSciNetCrossRefGoogle Scholar
  67. 33.
    Rapoport, A., Two-Person Game Theory: The Essential Ideas, The University of Michigan Press, Ann Arbor, 1966.zbMATHGoogle Scholar
  68. 34.
    Rapoport, A., N-Person Game Theory: Concepts and Applications, University of Michigan Press, Ann Arbor, 1970.zbMATHGoogle Scholar
  69. 35.
    Schmeidler, D., The Nucleolus of a Characteristic Function Game, SIAM J. Appl. Math., Vol. 17 (1969), pp. 1163–1170.MathSciNetzbMATHGoogle Scholar
  70. 36.
    Schwodiauer, G., Glossary of Game Theoretical Terms, Working Paper No. 1, Dept. of Ec., New York Univ., (1971), pp. 88.Google Scholar
  71. 37.
    Shubik, M., ED., Game Theory and Related Approaches to Social Behavior, John Wiley and Sons, Inc., 1964.Google Scholar
  72. 38.
    Thrall, R.M. and Lucas, W.F., N-Person Games in Partition Function Form, Nay.Res.Logist.Quart., Vol. 10, (1963),pp. 281–298.MathSciNetzbMATHCrossRefGoogle Scholar
  73. 39.
    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. 40.
    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. 41.
    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. 42.
    Williams, John D., The Compleat Strategist: Being a Primer on the Theory of Games of Strategy, McGraw-Hill Book Comoany, New York, 1954.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRice UniversityUSA

Personalised recommendations