Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Some notions and problems of game theory


Author: J. C. C. McKinsey
Journal: Bull. Amer. Math. Soc. 58 (1952), 591-611
DOI: https://doi.org/10.1090/S0002-9904-1952-09648-8
MathSciNet review: 0052748
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. K. J. Arrow, D. Blackwell, and M. A. Girshick, Bayes and minimax solutions of sequential decision problems, Econometrica vol. 17 (1949) pp. 213-244. MR 32173
  • 2. R. Bellman and D. Blackwell, Some two-person games involving bluffing, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 600-605. MR 31700
  • 3. H. F. Bohnenblust, S. Karlin, and L. S. Shapley, "Solutions of discrete two-person games," Contributions to the theory of games (ed. by H. W. Kuhn and A. W. Tucker), Princeton, Princeton University Press, 1950. MR 39218
  • 4. H. F. Bohnenblust, S. Karlin, and L. S. Shapley, "Games with continuous, convex pay-off," Contributions to the theory of games (ed. by H. W. Kuhn and A. W. Tucker), Princeton, Princeton University Press, 1950. MR 39226
  • 5. G. W. Brown, Iterative solutions of games by fictitious play, Activity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, New York, Wiley, 1951. MR 56265
  • 6. G. W. Brown and J. von Neumann, "Solutions of games by differential equations," Contributions to the theory of games (ed. by H. W. Kuhn and A. W. Tucker), Princeton, Princeton University Press, 1950. MR 39220
  • 7. M. Dresher, S. Karlin, and L. S. Shapley, "Polynomial games," Contributions to the theory of games (ed. by H. W. Kuhn and A. W. Tucker), Princeton, Princeton University Press, 1950. MR 39225
  • 8. D. Gale and S. Sherman, "Solutions of finite two-person games," Contributions to the theory of games (ed. H. W. Kuhn and A. W. Tucker), Princeton, Princeton University Press, 1950. MR 39217
  • 9. O. Gross, "On certain games with transcendental value," Contributions to the theory of games. II, Annals of Mathematics Studies, No. 28, in preparation.
  • 10. S. Karlin, "Operator treatment of minimax principle," Contributions to the theory of games (ed. by H. W. Kuhn and A. W. Tucker), Princeton, Princeton University Press, 1950. MR 41414
  • 11. W. D. Krentel, J. C. C. McKinsey, and W. V. Quine, A simplification of games in extensive form, Duke Math. J. vol. 18 (1951) pp. 885-900. MR 47302
  • 12. H. W. Kuhn, Extensive games, Proc. Nat. Acad. Sci. U.S.A. vol. 36 (1950) pp. 570-576. MR 39229
  • 13. H. W. Kuhn and A. W. Tucker, "Preface" to Contributions to the theory of games, Princeton, Princeton University Press, 1950.
  • 14. L. H. Loomis, On a theorem of von Neumann, Proc. Nat. Acad. Sci. U.S.A. vol. 32 (1946) pp. 213-215. MR 17258
  • 15. J. McDonald, The theory of strategy, Fortune vol. 38 (1949) pp. 100-110.
  • 16. J. McDonald, Strategy in poker, business, and war, New York, Norton, 1950.
  • 17. P. M. Morse, Mathematical problems in operations research, Bull. Amer. Math. Soc. vol. 54 (1948) pp. 602-621.
  • 18. J. F. Nash, Non-cooperative games, Ann. of Math. vol. 54 (1951) pp. 286-295. MR 43432
  • 19. J. v. Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. 100 (1928), no. 1, 295–320 (German). MR 1512486, https://doi.org/10.1007/BF01448847
  • 20. J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton, Princeton University Press, 1947. MR 21298
  • 21. J. Robinson, An iterative method of solving a game, Ann. of Math. vol. 54 (1951) pp. 296-301. MR 43430
  • 22. L. S. Shapley and R. N. Snow, "Basic solutions of discrete games," Contributions to the theory of games (ed. by H. W. Kuhn and A. W. Tucker), Princeton, Princeton University Press, 1950. MR 39216
  • 23. A. Tarski, A decision method for elementary algebra and geometry, Berkeley, University of California Press, 1951. MR 44472
  • 24. J. Ville, "Sur la théorie générale des jeux où intervient l'habilité des jeueurs," Traité du Calcul des Probabilités et ses Applications, by E. Borel and collaborators, Paris, 1938, vol. 2, pp. 105-113.
  • 25. A. Wald, Foundation of a general theory of sequential decision functions, Econometrica vol. 15 (1947) pp. 279-313. MR 24113
  • 26. A. Wald, Statistical decision functions, New York, Wiley, 1950. MR 36976


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1952-09648-8

American Mathematical Society