The genesis of differential games in light of Isaacs' contributions

Journal of Optimization Theory and Applications

Volumn 124, Issue 3, 2005, Pages 523-559

  Breitner, M H ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Contributions of Rufus P. Isaacs; Differential games; Dynamic games; Dynamic programming; History; Maximum principle

Indexed keywords

GAME THEORY; MAXIMUM PRINCIPLE;

BACKWARD ANALYSIS; CALIFORNIA; CONTRIBUTION OF RUFU P ISAAC; DIFFERENTIAL GAMES; DYNAMIC GAME; DYNAMIC GAME THEORIES; PAPER SURVEYS; PURSUIT EVASION; THEORY OF DYNAMICS; ZERO SUMS;

DYNAMIC PROGRAMMING;

EID: 21344434321     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-004-1173-0     Document Type: Review

References (194)

1. ISAACS, R. P., Games of Pursuit, Paper P-257, RAND Corporation, Santa Monica, California, 1951.
2. BELLMAN, R. E., Eye of the Hurricane: An Autobiography, World Scientific, Singapore, 1984.
3. ISAACS, R. P., Differential Games, I: Introduction, Research Memorandum RM-1391, RAND Corporation, Santa Monica, California, 1954.
4. ISAACS, R. P., Differential Games, II: The Definition and Formulation, Research Memorandum RM-1399, RAND Corporation, Santa Monica, California, 1954.
5. ISAACS, R. P., Differential Games, III: The Basic Principles of the Solution Process, Research Memorandum RM-1411, RAND Corporation, Santa Monica, California, 1954.
6. ISAACS, R. P., Differential Games, IV: Mainly Examples, Research Memorandum RM-1486, RAND Corporation, Santa Monica, California, 1955.
7. ISAACS, R. P., Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control, and Optimization, John Wiley and Sons, New York, NY, 1965; Revised 2nd Edition, John Wiley and Sons, New York, NY, 1967; Revised and Extended 3rd Edition, Krieger, Huntington, NY, 1975; Paperback Republication of the 1st Edition, Dover, Mineola, NY, 1999.
8. ISAACS, R. P., The Finite Differences of Polygenic Functions, Bulletin of the American Mathematical Society, Vol. 47, pp. 444-448, 1941; see also PhD. Thesis, Faculty of Pure Science, Columbia University, New York, NY, 1942.
9. KASNER, E., and NEWMAN, J. R., Mathematics and the Imagination (with Drawings and Diagrams by Rufus Isaacs), Simon and Schuster, New York, NY, 1940; Last Reprint: Tempus Books of Microsoft Press, Redmond, Washington, 1989.
10. ISAACS, R. P., A Finite Difference Function Theory, Revista de la Universidad Nacional de Tucuman, Vol. 2A, pp. 177-201, 1941; see also PhD Thesis, Faculty of Pure Science, Columbia University, New York, NY, 1942.
11. ISAACS, R. P., Planar Elasticity as a Potential Theory, Revista de la Universidad Nacional de Tucuman, Vol. 6A, pp. 263-272, 1948.
12. ISAACS, R. P., Monodiffric Functions, Proceedings of a Symposium on the Construction and Applications of Conformal Maps, University of California, Los Angeles, California, 1949; Edited by the National Bureau of Standards, Applied Mathematics Series, US Government Printing Office, Washington, DC, Vol. 18, pp. 257-266, 1952.
13. ISAACS, R. P., Airfoil Theory for Flows of Variable Velocity, Journal of the Aeronautical Sciences, Vol. 12, pp. 113-117, 1945.
14. ISAACS, R. P., Airfoil Theory for Rotary Wing Aircraft, Journal of the Aeronautical Sciences, Vol. 13, pp. 218-220, 1946.
15. 29
16. ISAACS, R. P., Recent Progress in Compressible Fluid Theory, American Mathematical Monthly, Vol. 55, pp. 140-144, 1948.
17. ISAACS, R. P., Transstability Flutter of Supersonic Aircraft Panels, Report AL-127, North American Aviation, Los Angeles, California, 1948; see also Paper P-101, RAND Corporation, Santa Monica, California, 1949.
18. ISAACS, R. P., A Static Stability Analysis for Thin Buckled Beams at Supersonic Speeds, Report AL-172, North American Aviation, Los Angeles, California, 1948.
19. VON NEUMANN, J., and MORGENSTERN, O., Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944.
20. BELLMAN, R. E., Symmetric Three-Person Games and the Concept of an Independent Point, Paper P-220, RAND Corporation, Santa Monica, California, 1951.
21. BELLMAN, R. E., On Some Dynamic Linear Programming Problems, Paper P-230, RAND Corporation, Santa Monica, California, 1951.
22. BELLMAN, R. E., On the Theory of Dynamic Programming, Proceedings of the National Academy of Sciences of the USA, Vol. 38, pp. 716-719, 1952.
23. BELLMAN, R. E., An Introduction to the Theory of Dynamic Programming, Report R-245, RAND Corporation, Santa Monica, California, 1953.
24. BELLMAN, R. E., On an Application of the Theory of Dynamic Programming to Bottleneck Problems in Production and Allocation, Research Memorandum RM-1069, RAND Corporation, Santa Monica, California, 1953.
25. BELLMAN, R. E., Dynamic Programming of Continuous Processes, Report R-271, RAND Corporation, Santa Monica, California, 1954.
26. BELLMAN, R. E., Dynamic Programming and Its Application to Variational Problems in Mathematical Economics, Paper P-796, RAND Corporation, Santa Monica, California, 1956.
27. BELLMAN, R. E., Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.
28. BELLMAN, R. E., and BLACKWELL, D. H., Some Two-Person Games Involving Bluffing, Proceedings of the National Academy of Sciences of the USA, Vol. 35, pp. 600-605, 1948.
29. BELLMAN, R. E., and BLACKWELL, D. H., On Games Involving Bluffing, Paper P-168, RAND Corporation, Santa Monica, California, 1950.
30. BELLMAN, R. E., and DREYFUS, S. E. Applied Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1962.
31. BELLMAN, R. E., FLEMING, W. H., and WIDDER, D. V., Variational Problems with Constraints, Annali di Matematica Pura ed Applicata, Vol. 41 (Fourth Series), pp. 301-323, 1956.
32. BELLMAN,. R. E., GLICKSBERG, I. L., and GROSS, O. A., On Some Variational Problems Occurring in the Theory of Dynamic Programming, Proceedings of the National Academy of Sciences of the USA, Vol. 39, pp. 298-301, 1953.
33. BELLMAN, R. E., GLICKSBERG, I. L., and GROSS, O. A., On Some Variational Problems Occuring in the Theory of Dynamic Programming, Rendiconti del Circolo Matematico di Palermo, Vol. 3 (Second Series), pp. 363-397, 1954.
34. BELLMAN, R. E., GLICKSBERG, I. L., and GROSS, O. A., On Some Nonlinear Integral Equations Occurring in the Theory of Dynamic Programming, Proceedings of the National Academy of Sciences of the USA, Vol. 41, pp. 227-229, 1955.
35. BELLMAN, R. E., GLICKSBERG, I. L., and GROSS, O. A., Some Aspects of the Mathematical Theory of Control Processes (Survey Report), Report R-313, RAND Corporation, Santa Monica, California, 1958.
36. BELLMAN, R. E., and KARUSH, R., Dynamic Programming: A Bibliography of Theory and Application, Research Memorandum RM-3951, RAND Corporation, Santa Monica, California, 1964.
37. BELLMAN, R. E., and SHIFFMAN, M., On the Min-Max of a Special Integral, Paper P-232, RAND Corporation, Santa Monica, California, 1951.
38. BERKOVITZ, L. D., A Variational Approach to Differential Games, Research Memorandum RM-2772, RAND Corporation, Santa Monica, California, 1961;
39. see also Annals of Mathematics Studies, Vol. 52, pp. 127-174, 1964.
40. BERKOVITZ, L. D., A Survey of Certain Aspects of the Mathematics of Control Problems, Research Memorandum RM-3309, RAND Corporation, Santa Monica, California, 1962.
41. BERKOVITZ, L. D., and FLEMING, W. H., On Differntial Games with Integral Payoff; see Ref. 118, pp. 413-435, 1957.
42. BLACKWELL, D. H., and GIRSHICK, M. A., Theory of Games and Statistical Decisions, John Wiley and Sons, New York, NY, 1954.
43. DANSKIN, J. M., An Extension of the Brown-Robinson Iterative Process for Finding the Value of a Game, Paper P-293, RAND Corporation, Santa Monica, California, 1952.
44. DANSKIN, J. M., Another Proof of the Minmax Theorem for Continuous Payoffs, Research Memorandum RM-818, RAND Corporation, Santa Monica, California, 1952.
45. DANSKIN, J. M., The Theory of Max-Min and Its Application to Weapons Allocation Problems, Springer, Berlin, Germany, 1967.
46. DARLING, D. A., The Continuous Pursuit Problem, Unpublished Notes, 1954.
47. DRESHER, M., Mathematical Theory of Zero-Sum Two-Person Games with a Finite Number or a Continuum of Strategies, Report R-115, RAND Corporation, Santa Monica, California, 1949.
48. DRESHER, M., An Analysis of Three-Move Finite Games, Paper P-245, RAND Corporation, Santa Monica, California, 1951.
49. DRESHER, M., Games of Strategy: Theory and Applications (Includes Bibliography), Report R-360, RAND Corporation, Santa Monica, California, 1961; see also Prentice-Hall, Englewood Cliffs, New Jersey, 1961.
50. DRESHER, M., and KARLIN, S., Solutions of Convex Games as Fixed Points, Paper P-255, RAND Corporation, Santa Monica, California, 1951.
51. FLEMING, W. H., On Weak Convergence of Strategies in Certain Games over a Function Space, Research Memorandum RM-745, RAND Corporation, Santa Monica, California, 1952.
52. FLEMING, W. H., Minmax Theorem for a Class of Games over a Function Space, Research Memorandum RM-814, RAND Corporation, Santa Monica, California, 1952.
53. FLEMING, W. H., Reduction of Certain Games over Function Space, Research Memorandum RM-897, RAND Corporation, Santa Monica, California, 1952.
54. FLEMING, W. H., On a Class of Games over Function Space and Related Variational Problems, Annals of Mathematics, Vol. 60, pp. 578-594, 1954.
55. FLEMING, W. H., A Note on Differential Games of Prescribed Duration; see also Ref. 118, pp. 407-412, 1957.
56. FLEMING, W. H., The Convergence Problem for Differential Games, Journal of Mathematical Analysis and Applications, Vol. 3, pp. 102-116, 1961.
57. FLEMING, W. H., The Convergence Problem for Differential Games, II, Annals of Mathematics Studies, Vol. 52, pp. 195-210, 1964.
58. GLICKSBERG, I. L., and GROSS, O. A., Notes on the Game with Rational Payoff, Research Memorandum RM-491, RAND Corporation, Santa Monica, California, 1950.
59. GLICKSBERG, I. L., and GROSS, O. A., A Class of Games with Unique Density Function Solutions, Research Memorandum RM-501, RAND Corporation, Santa Monica, California, 1950.
60. GLICKSBERG, I. L., and GROSS, O. A., Continuous Games with Given Strategies, Research Memorandum RM-510, RAND Corporation, Santa Monica, California, 1951.
61. GLICKSBERG, I. L., and GROSS, O. A., The Pathological Nature of Certain Games with Rational Payoff, Research Memorandum RM-549, RAND Corporation, Santa Monica, California, 1951.
62. GLICKSBERG, I. L., and GROSS, O. A., Continuous Games with Given Unique Solutions, Research Memorandum RM-620, RAND Corporation, Santa Monica, California, 1951.
63. GLICKSBERG, I. L., and GROSS, O. A., Solution Sets for Games on the Square, Research Memorandum RM-901, RAND Corporation, Santa Monica, California, 1952.
64. GROSS, O. A., The Derivatives of the Value of a Game, Research Memorandum RM-1286, RAND Corporation, Santa Monica, California, 1954.
65. HAUSNER, M., Optimal Strategies in Games of Survival, Research Memorandum RM-777, RAND Corporation, Santa Monica, California, 1952;
66. see also Games of Survival, Research Memorandum RM-776, RAND Corporation, Santa Monica, California, 1952.
67. ISAACS, R. P., A Pursuit Game with Incomplete Information, Research Memorandum RM-791, RAND Corporation, Santa Monica, California, 1952.
68. ISAACS, R. P., Optimal Horse Race Bets, American Mathematical Monthly, Vol. 60, pp. 310-315, 1953.
69. ISAACS, R. P., A Game of Aiming and Evasion: General Discussion and the Marksman's Strategies, Research Memorandum RM-1385, RAND Corporation, Santa Monica, California, 1953.
70. ISAACS, R. P., A Card Game with Bluffing, American Mathematical Monthly, Vol. 62, pp. 99-108, 1955.
71. ISAACS, R. P., The Problem of Aiming and Evasion, Naval Reserve Logistics Quarterly, Vol. 2, pp. 47-67, 1955.
72. ISAACS, R. P., Some Simple Methods for Pursuit and Similar Maneuvering Problems, Internal Memorandum 9, Institute for Defense Analyses (IDA), Weapons Systems Evaluation Group, Washington, DC, 1961.
73. ISAACS, R. P., The Solution to a Game Occurring in a Naval Appointment Problem, Report OEG 479-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
74. ISAACS, R. P., The Interdiction Game with a Parameter Unknown to One Player, Report OEG 482-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
75. ISAACS, R. P., On Bang-Bang-Bang Surfaces in Differential Games, Report OEG 499-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
76. PONTRYAGIN, L. S., BOLTYANSKU, V. G., GAMKRELIDZE, R. V., and MISHCHENKO, E. F., The Mathematical Theory of Optimal Processes (in Russian), Fizmatgiz, Moscow, Russia, 1961; see also Interscience (Wiley), New York, NY, 1962 (in English).
77. 30
78. ISAACS, R. P., Jeux Differentiels: Theorie des Jeux Appliquées aux Domaines de la Guerre, des Poursuites, du Controle et de L'Optimisation, Revised Edition, Dunod, Paris, France, 1968 (in French).
79. ISAACS, R. P., and KARLIN, S., A Game of Aiming and Evasion, Research Memorandum RM-1316, RAND Corporation, Santa Monica, California, 1953.
80. KARLIN, S., Reduction of Certain Classes of Games to Integral Equations, Paper P-241, RAND Corporation, Santa Monica, California, 1951.
81. KARLIN, S., The Theory of Infinite Games, Paper P-248, RAND Corporation, Santa Monica, California, 1951.
82. KARLIN, S., Continuous Games, Proceedings of the National Academy of Sciences of the USA, Vol. 37, pp. 220-223, 1951.
83. KARLIN, S., On a Class of Games, Paper P-254, RAND Corporation, Santa Monica, California, 1952.
84. KARLIN, S., The Theory of Infinite Games, Annals of Mathematics, Vol. 58 (Second Series), pp. 371-401, 1953.
85. KARLIN, S., Mathematical Methods and Theory in Games, Programming, and Economics, Addison-Wesley, Reading, Massachusetts, 1959.
86. MILNOR, J. W., Games against Nature, Research Memorandum RM-679, RAND Corporation, Santa Monica, California, 1951.
87. MILNOR, J. W., Reasonable Outcomes for N-person Games, Research Memorandum RM-916, RAND Corporation, Santa Monica, California, 1953.
88. MILNOR, J. W., Sums of Positional Games, Contributions to the Theory of Games, Vol. 2, Annals of Mathematics Studies, Vol. 28, pp. 291-301, 1953.
89. MILNOR, J. W., and SHAPLEY, L. S., On Games of Survival, Paper P-622, RAND Corporation, Santa Monica, California, 1955.
90. MILNOR, J. W., and SHAPLEY, L. S., On Games of Survival, Contributions to the Theory of Games, Vol. 3, Annals of Mathematics Studies, Vol. 39, pp. 15-45, 1957.
91. SCARF, H. E., On Differential Games with Survival Payoff; see also Ref. 118, pp. 393-405, 1957.
92. SHAPLEY, L. S., A Value for N-Person Games, Paper P-295, RAND Corporation, Santa Monica, California, 1952.
93. SHAPLEY, L. S., Quota Solutions of N-Person Games, Paper P-297, RAND Corporation, Santa Monica, California, 1952.
94. SHAPLEY, L. S., Notes on the N-Person Game, III: Some Variants of the von Neumann-Morgenstern Definition of Solution, Research Memorandum RM-817, RAND Corporation, Santa Monica, California, 1952.
95. SHAPLEY, L. S., Notes on the N-Person Game, IV: A Theorem on C-Stable Sets, Research Memorandum RM-881, RAND Corporation, Santa Monica, California, 1952.
96. SHAPLEY, L. S., An Example of an Infinite, Nonconstant-Sum Game, Research Memorandum RM-898, RAND Corporation, Santa Monica, California, 1952.
97. SHAPLEY, L. S., Notes on the N-Person Game, V: Stable-Set Solutions Including an Arbitrary Closed Component, Research Memorandum RM-1005, RAND Corporation, Santa Monica, California, 1953.
98. SHAPLEY, L. S., A Value for N-Person Games, Contributions to the Theory of Games, Vol. 2, Annals of Mathematics Studies, Vol. 28, pp. 307-317, 1953.
99. SHAPLEY, L. S., MILNOR, J. W., and SHAPIRO, N. Z., Values of Large Games, Research Memoranda RM-2648 and RM-2649, RAND Corporation, Santa Monica, California, 1960 and 1961.
100. BERKOVITZ, L. D., Letter to the Author, November 15, 2002.
101. BERKOVITZ, L. D., E-mail Discussion with the Author, 2002.
102. FLEMING, W. H., E-mail Discussion with the Author, 2002.
103. FLEMING, W. H., Comments on Michael H. Breitner's Draft Paper Rufus P. Isaacs and the Early Years of Differential Games: A Survey and Discussion Paper, Short Paper, Brown University, Providence, Rhode Island, 2002.
104. ISAACS, R. P., Some Fundamentals of Differential Games/Differential Games: Their Scope, Nature and Future, Topics in Differential Games, Edited by A. Blaquière, North-Holland, Amsterdam, Holland, pp. 1-42, 1973 (pp. 2-19 are an unaltered reprint of Ref. 142).
105. FRIEDMAN, A., Differential Games, John Wiley and Sons, New York, NY, 1971.
106. KRASOVSKIJ, N. N., and SUBBOTIN, A. I., Game-Theoretical Control Problems, Nauka, Moscow, Russia, 1974 (in Russian); see also Springer, New York, NY, 1988 (in English).
107. BERKOVITZ, L.D., The Existence of Value and Saddle Point in Games of Fixed Duration, SIAM Journal on Control and Optimization, Vol. 23, pp. 172-196, 1985.
108. BERKOVITZ, L. D., A Survey of Recent Results in Differential Games, Lecture Notes in Control and Information Sciences, Vol. 119, pp. 35-50, 1989.
109. BERKOVITZ, L. D., Thirty Years of Differential Games, Lecture Notes in Pure and Applied Mathematics, Vol. 119, pp. 1-11, 1989.
110. BERKOVITZ, L. D., A Theory of Differential Games, Annals of the International Society of Dynamic Games, Vol. 1, pp. 3-22, 1994 (it includes a brief review of Isaacs' early work).
111. VALENTINE, F. A., The Problem of Lagrange with Differential Inequalities as Added Side Conditions, PhD Thesis, University of Chicago, 1937; see also Contributions to the Calculus of Variations 1933-1937, University of Chicago Libraries, Chicago, Illinois, pp. 403-447, 1937.
112. CRANDALL, M. G., and LIONS, P. L., Condition d'Unicité pour les Solutions Generaliseés des Equations de Hamilton-Jacobi du Premier Ordre, Comptes Rendus des Seances de l'Academie des Sciences, Vol. 292 (First Series, Mathematics), pp. 183-186, 1981 (in French);
113. see also Two Approximations of Solutions of Hamilton-Jacobi Equations, Mathematics of Computation, Vol. 43, pp. 1-19, 1984 (in English).
114. CARATHEODORY, C., Variationsrechnung und partielle Differentialgleichungen erster Ordnung, B. G. Teubner, Leipzig, Germany, 1935 (in German);
115. see also Calculus of Variations and Partial Differential Equations of the First Order, Holden-Day, San Francisco, California, 1965/67 (in English).
116. PESCH, H. J., and BULIRSCH, R., The Maximum Principle, Bellman's Equation, and Caratheodory's Work, Journal of Optimization Theory and Applications, Vol. 80, pp. 199-225, 1994.
117. BOLTYANSKIJ, V. G., GAMKRELIDZE, R. V., and PONTRYAGIN, L. S., On Theory of Optimal Processes, Doklady Akademii Nauk SSSR, Vol. 110, pp. 7-10, 1956 (in Russian).
118. PONTRYAGIN, L. S., Optimal Control Processes, Proceedings of the International Congress of Mathematicians, Edinburg, Scotland, 1958; Edited by J. A. Todd, Cambridge University Press, Cambridge, UK, pp. 182-202, 1960;
119. see also Uspekhi Matematicheskikh Nauk, Rossijskaya Akademiya Nauk, Vol. 14, pp. 1-20, 1959 (in Russian).
120. MISHCHENKO, E. F., and PONTRYAGIN, L. S., A Statistical Problem on Optimal Control, Doklady Akademii Nauk SSSR, Vol. 128, pp. 890-892, 1959 (in Russian).
121. BOLTYANSKIJ, V. G., GAMKRELIDZE, R. V., and PONTRYAGIN, L. S., Theory of Optimal Processes, I: The Maximum Principle, Izvestiya Rossijskoj Akademii Nauk, Seriya Matematicheskaya, Vol. 24, pp. 3-42, 1960 (in Russian).
122. PETROSYAN, L. A., Discussion with the Author of This Paper at the Tenth International Symposium on Dynamic Games and Applications, St. Petersburg, Russia, July 8-11, 2002; see www.hut.fi/Units/SAL/isdg and www.isdgrus.ru/ISDG2002.
123. See also Breitner, M. H., Rufus P. Isaacs and the Early Years of Differential Games: A Survey and Discussion Paper, Proceedings of this Symposium, Edited by L. A. Petrosyan and N. A. Zenkevich, Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, St, Petersburg, Russia, pp, 113-128, 2002.
124. DRESHER, M., TUCKER, A. W., and WOLFE, P., Editors, Contributions to the Theory of Games, Vol. 3, Annals of Mathematics Studies, Princeton University Press, Princeton, New Jersey, Vol. 39, 1957.
125. VAVILOV, S. I., The Problem of Diffuse Reflection of Light by a Turbid Medium, 1943;
126. see also R. V. Ambartsumian, Editor, A Life in Astrophysics: Selected Papers of V. A. Ambartsumian, Allerton Press, New York, NY, 1998.
127. ISAACS, R. P., The Optimal Distribution of Widgets Released by Bombers Penetrating a Chain of Defense Zones, Memorandum 4M46/403, Hughes Aircraft Company, Culver City/Los Angeles, California, 1956.
128. ISAACS, R. P., Game Theory Applied to Tactics Problems in General and to the Long-Range Interceptor Problem in Particular, Memorandum 4M46/420, Hughes Aircraft Company, Culver City/Los Angeles, California, 1956.
129. ISAACS, R. P., The Expected Number of Targets Hit by a Large Number of Missiles, Memorandum 4M46/436, Hughes Aircraft Company, Culver City/Los Angeles, California, 1956.
130. ISAACS, R. P., Decoy Attacks, Report SRS10-300, Hughes Aircraft Company, Culver City/Los Angeles, California, 1958.
131. ISAACS, R. P., The Best Release Time for a Missile under: Prelaunch Attack, Internal Memorandum 7, Institute for Defense Analyses (IDA), Weapons Systems Evaluation Group, Washington, DC, 1959.
132. ISAACS, R. P., A Ring of Satellites, Internal Memorandum 10, Institute for Defense Analyses (IDA), Weapons Systems Evaluation Group, Washington, DC, 1961.
133. ISAACS, R. P., Aircraft Carriers in Future Wars: A Broad Glimpse, Document NWG-V-30/NWG 48-63, Center for Naval Analyses (CNA), Project Strike, Washington, DC, 1963.
134. ISAACS, R. P., Probability Formulas for the Destruction of CVA Catapults or Other Multiple Targets by a Succession of Bombs, Document EVAL-V-43, Center for Naval Analyses (CNA), Project Strike, Washington, DC, 1963.
135. ISAACS, R. P., Calculation of the Expected Deck Area Destruction of a Bombarded Carrier, Document EVAL-V-46, Center for Naval Analyses (CNA), Project Strike, Washington, DC, 1963.
136. ISAACS, R. P., Some Results on Carrier Aircraft Availability, Document EVALV-49, Center for Naval Analyses (CNA), Project Strike, Washington, DC, 1963.
137. ISAACS, R. P., The Best Deployment of a Naval Force in the Vicinity of Potential Trouble Spots, Internal Memorandum 31-64, Center for Naval Analyses (CNA), Operations Research and Mathematical Sciences Division, Washington, DC, 1964.
138. ISAACS, R. P., Many Weapons Fired at Many Targets, Internal Memorandum 107-65, Center for Naval Analyses (CNA), Operations Research and Mathematical Sciences Division, Washington, DC, 1965.
139. ISAACS, R. P., Maintaining Surveillance with Moving Craft, Internal Memorandum 110-65, Center for Naval Analyses (CNA), Operations Research and Mathematical Sciences Division, Washington, DC, 1965.
140. ISAACS, R. P., Bombing Separate and Vulnerable Targets, Report OEG 95-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
141. ISAACS, R. P., Nuclear or Conventional Missiles - An Optimal Firing Sequence, Report OEG 163-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
142. ISAACS, R. P., Some Episodes During the International Congress of Mathematicians, Report OEG 498-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
143. ISAACS, R. P., Estimating Probabilities from Samples with Values either Specified or Bounded, Report OEG 527-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
144. ISAACS, R. P., The Expected Number of Observations Needed to Distinguish Two Types of Radar Signals, Report OEG 651-66, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1966.
145. ISAACS, R. P., The Distribution of Gap Size in a Line of Bombers, Report OEG 71-67, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1967.
146. ISAACS, R. P., The Probability of a Carrier's Being Undetected by a Line of Advancing Bombers, Report OEG 97-67, Center for Naval Analyses (CNA), Operations Evaluation Group, Washington, DC, 1967.
147. ISAACS, R. P., Iterates of Fractional Order, Canadian Journal of Mathematics, Vol. 2, pp. 409-416, 1950.
148. ISAACS, R. P., The Evaluation of a Definite Integral, Research Memorandum RM-482, RAND Corporation, Santa Monica, California, 1950.
149. ISAACS, R. P., Differential Games: Their Scope, Nature, and Future, Journal of Optimization Theory and Applications, Vol. 3, pp. 283-295, 1969.
150. ISAACS, R. P., Differential Games with Incomplete Information - Introductory Remarks, Differential Games and Control Theory Proceedings of a National Science Foundation-Conference Board of the Mathematical Sciences Regional Research Conference, University of Rhode Island, Kingston, Rhode Island, 1973; Edited by E. O. Roxin, P. T. Liu, and R. L. Sternberg, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, NY, Vol. 10, pp. 179-180, 1974.
151. ISAACS, R. P., Infinite Families of Nontrivial Trivalent Graphs Which Are Not Tait Colorable, American Mathematical Monthly, Vol. 82, pp. 221 - 239, 1975.
152. ISAACS, R. P., The Past and Some Bits of the Future, The Theory and Application of Differential Games, Proceedings of a NATO Advanced Study Institute Meeting, University of Warwick, Coventry, England, 1974; Edited by J. D. Grote, NATO Advanced Study Institute Series, Reidel, Dordrecht, Holland, Vol. 13 (Series C), pp. 1-11, 1975.
153. ISAACS, R. P., Loupekhine's Snarks: A Bifamily of Non-Tait-Colorable Graphs, Technical Report 263, Department of Mathematical Sciences, Johns Hopkins University, Baltimore, Maryland, 1976.
154. ISAACS, R. P., The Distribution of Primes in a Special Ring of Integers, Mathematics Magazine, Vol. 52, pp. 31-36, 1979.
155. ISAACS, R. P., On Applied Mathematics, Journal of Optimization Theory and Applications, Vol. 27, pp. 31-50, 1979.
156. YU, P. L., Transition Surfaces of a Class of Differential Games, PhD Thesis, Department of Operations Research and Industrial Engineering, Johns Hopkins University, Baltimore, Maryland, 1969.
157. Yu, P. L., An Appreciation of Professor Rufus Isaacs, Journal of Optimization Theory and Applications, Special Issue on the Occasion of the 65th Birthday of Professor Rufus Isaacs, Vol. 27, pp. 1-6, 1979.
158. WILSON, R. J., In Memoriam: Rufus P. Isaacs (1914-1981), IEEE Transactions on Automatic Control, Vol. 26, p. 809, 1981.
159. PEISAKOFF, M. P., More on Games of Survival, Research Memorandum RM-884, RAND Corporation, Santa Monica, California, 1952.
160. GADZHIEV, M. Y., Application of the Theory of Games to Some Problems of Automatic Control, I, Avktomatika i Telemekhanika, Rossijskaya Akademiya Nauk, Vol. 23, pp. 1023-1036, 1962 (in Russian);
161. see also Automation and Remote Control, Vol. 23, pp. 957-971, 1963 (in English).
162. GADZHIEV, M. Y., Application of the Theory of Games to Some Problems of Automatic Control, II, Avtomatika i Telemekhanika, Rossijskaya Akademiya Nauk, Vol. 23, pp. 1144-1153, 1962 (in Russian);
163. see also Automation and Remote Control, Vol. 23, pp. 1074-1083, 1963 (in English).
164. GNOENSKU, L. S., On the Tracking Problem, Prikladnaya Matematika i Mekhanika, Rossijskaya Akademiya Nauk, Vol. 26, pp. 960-965, 1962 (in Russian);
165. see also Journal of Applied Mathematics and Mechanics, Vol. 26, pp. 1451-1460, 1963 (in English).
166. KELENDZERIDZE, D. L., Theory of an Optimal Pursuit Strategy, Doklady Akademii Nauk SSSR, Vol. 138, pp. 529-532, 1961 (in Russian);
167. see also Soviet Doklady Mathematics/Physics, Vol. 2, pp. 654-656, 1961 (in English).
168. KRASOVSKIJ, N. N., On a Problem of Tracking, Prikladnaya Matematika i Mekhanika, Rossijskaya Akademiya Nauk, Vol. 27, pp. 244-254, 1963 (in Russian);
169. see also Journal of Applied Mathematics and Mechanics, Vol. 27, pp. 363-377, 1963 (in English).
170. KRASOVSKIJ, N. N., On the Problem of Pursuit in the Case of Linear Monotype Objects, Prikladnaya Matematika i Mekhanika, Rossijskaya Akademiya Nauk, Vol. 30, pp. 209-225, 1966 (in Russian);
171. see also Journal of Applied Mathematics and Mechanics, Vol. 30, pp. 263-281, 1967 (in English).
172. KRASOVSKIJ, N. N., REPIN, Y. M., and TRETYAKOV, V. E., On Game Scenarios in the Theory of Controllable Systems, Izvestiya Rossijskaya Akademii Nauk SSSR, Tekhnicheskaya Kibernetika, Vol. 4, pp. 3-13, 1965 (in Russian).
173. KRASOVSKIJ, N. N., and TRETYAKOV, V. E., On a Pursuit Problem in the Case of Restrictions on the Impulses of Control Forces, Differentsial Uravneniya, Vol. 2, pp. 587-599, 1966 (in Russian);
174. see also The Pursuit Problem in the Case of Constraints on Impulses in the Controls, Differential Equations, Vol. 2, pp. 301-309, 1969 (in English).
175. PETROSYAN, L. A., On a Class of Pursuit-Evasion Games, PhD Thesis, St. Petersburg/Leningrad University, Leningrad, Russia, 1985 (in Russian).
176. PONTRYAGIN, L. S., On Some Diflerential Games, Doklady Akademii Nauk SSSR, Vol. 156, pp. 738-741, 1964 (in Russian);
177. see also Soviet Doklady Mathematics, Vol. 5, pp. 712-716, 1964 (in English).
178. PONTRYAGIN, L. S., On the Theory of Differential Games, Uspekhi Matematicheskikh Nauk, Rossijskaya Akademiya Nauk, Vol. 21, pp. 219-274, 1966 (in Russian);
179. see also Russian Mathematical Surveys, Vol. 21, pp. 193-246, 1966 (in English).
180. POZHARITSKIJ, G. K., Impulsive Tracking in the Case of Second-Order Monotype Linear Objects, Prikladnaya Matematika i Mekhanika, Rossijskaya Akademiya Nauk, Vol. 30, pp. 897-907, 1966 (in Russian);
181. see also Journal of Applied Mathematics and Mechanics, Vol. 30, pp. 1061-1073, 1966 (in English).
182. SUBBOTIN, A. I., On the Problem of the Game-Interception of Motions, Prikladnaya Matematika i Mekhanika, Rossijskaya Akademiya Nauk, Vol. 31, pp. 834-840, 1967 (in Russian);
183. see also Journal of Applied Mathematics and Mechanics, Vol. 31, pp. 842-848, 1967 (in English).
184. TRETYAKOV, V. E., Regularization of a Certain Pursuit Problem, Differentsial Uravneniya, Vol. 3, pp. 2108-2121, 1967 (in Russian);
185. see also Regularization of a Pursuit Problem, Differential Equations, Vol. 3, pp. 1085-1102, 1972 (in English).
186. ZELIKIN M. I., and TYNYANSKIJ, N. T., Deterministic Differential Games, Uspekhi Matematicheskikh Nauk, Rossijskaya Akademiya Nauk, Vol. 20, pp. 151-157, 1965 (in Russian).
187. LEITMANN, G., A Simple Differential Game, Journal of Optimization Theory and Applications, Vol. 2, pp. 220-225, 1968.
188. CHATTOPADHYAY, R., Functional Analytic Analysis of a Pursuit Problem, Journal of Optimization Theory and Applications, Vol. 2, pp. 230 - 239, 1968.
189. GUINN, T., Boundary Arcs for a Class of Differential Games, Journal of Optimization Theory and Applications, Vol. 2, pp. 293-315, 1968.
190. BLAQUIER̀E, A., GERARD, F., and LEITMANN, G., Quantitative and Qualitative Games, Academic Press, New York, NY, 1969 (in English);
191. see also BLAQUIER̀E, A., and LEITMANN, G., Jeux Quantitatifs, Gauthier-Villars, Paris, France, 1969 (in French).
192. BERKOVITZ, L. D., Variational Methods in Problems of Control and Programming, Journal of Mathematical Analysis and Applications, Vol. 3, pp. 145-169, 1961;
193. see also Research Memorandum RM-2888-PR, RAND Corporation, Santa Monica, California, 1961.
194. BERKOVITZ, L. D., A Survey of Certain Aspects of the Mathematics of Control Problems, Research Memorandum RM-3309-PR, RAND Corporation, Santa Monica, California, 1962.