Skip to main content
Log in

The Coming of Game Theory

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

This is a brief historical note on game theory. We cover its historical roots (prior to its formal definition in 1944), and look at its development until the late 1960's.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Albers, D. J., and Alexanderson, G. L. (eds) (1985), Mathematical People. Boston: Birkhäuser.

    Google Scholar 

  • Arrow, K. J. and Intriligator, M. D. (eds) (1981), Handbook of Mathematical Economics. Amsterdam: North-Holland.

    Google Scholar 

  • Aumann, R. J. and Maschler M. (1963), A non-zero-sum game related to a Test Ban Treaty, in Applications of Statistical Methodology to Arms Control and Disarmament. Report to the U. S. Arms Control and Dis-armament Agency, 273–287.

  • Aumann, R. J. (1964), The bargaining set for cooperative games, in M. Dresher, L. S. Shapley and Tucker, A. W. (eds), Advances in Game Theory, Annals of Mathematics Study 52, 443–477.

  • Aumann, R. J. (1995), Repeated Games with Incomplete Information, M. I. T. Press (with the collaboration of R. Stearns).

  • Aumann, R. J. and Peleg, B. (1960), Von Neumann–Morgenstern Solution to Cooperative Games without Side Payments, Bulletin of the American Mathematical Society 66, 173–179.

    Google Scholar 

  • Baumol, W. J. and Goldfeld, S. M. (1968), Precursors in Mathematical Eco-nomics:An Anthology. Reprinted in:Scarce Works in Political Economy Vol. 19. London: London School of Economics.

    Google Scholar 

  • Bernoulli, D. (1738), Specimen theorie novae de mensura sortis, in Com-mentarii Academiae Scientiarum Imperialis Petropolitanae Vol. 5, 175–192. Translated by L. Somer in (1953) as 'Exposition of a New Theory on the Measurement of Risk', Econometrica 22, January, 23–36.

    Google Scholar 

  • Bertrand, J. (1924), Calcul des probabilités, éléments de la théorie des probabilités, 3rd edn. Paris: Gauthier-Villars.

    Google Scholar 

  • Bondareva, O. (1962), The Core of an n-Person Game, Vestnik Leningrad University 13, 141–142.

    Google Scholar 

  • Borel, E. (1921), La théorie du jeu et les équations intégrales ànoyau sy-métrique gauche, in Comptes Rendus de l' Académie des Sciences, Vol 173, 1304–1308. Translated by L. J. Savage in (1953) as 'The Theory of Play and Integral Equations with Skew–Symmetric Kernels', Econometrica 21 January, 97–100.

    Google Scholar 

  • Borel, E. (1924), 'Sur les jeux oùinterviennent le hasard et l' habiletédes joueurs', in J. Hermann (ed.), Théorie des probabilités, Paris:Librairie Scienti que. Translated by L. J. Savage in (1953) as 'On Games that In-volve Chance and the Skill of Players', Econometrica, 21 (January), 101–115.

  • Borel, E. (1927), Sur les systèmes de formes linéaires àdéterminant symé-trique gauche et la théorie générale du jeu, in Comptes Rendus de l' Aca-démie des Sciences, Vol. 184, 52–53. Translated by L. J. Savage in (1953) as 'On Systems of Linear Forms of Skew Symmetric Determinant and the General Theory of Play', Econometrica, 21 (January), 116–117.

    Google Scholar 

  • Cournot, A. (1838), Recherches sur les principes mathématiques de la théorie des richesses. M. Rivière et Cie, Paris Translated by A. M. Kelly in 1960 as Researches into the Mathematical Principles of Wealth. New York: A. M. Kelly.

    Google Scholar 

  • Davis, M. and M. Maschler (1965), The Kernel of a Coperative Game, Naval Research Log. Quarterly 12, 223–259.

    Google Scholar 

  • Doyle, A. C. (1891), The Final Solution.

  • Edgeworth, F. Y. (1881), Mathematical Psychics. London: Routledge and Kegan Paul.

    Google Scholar 

  • Everett, H. (1957), Recursive Games. Contributions to the Theory of Games III, (Princeton), 47–78.

    Google Scholar 

  • Follett, K. (1985), The Modigliani Scandal. New York: Signet.

    Google Scholar 

  • Gillies, D. 1953, Some Theorems on n-Person Games. Ph. D. Thesis, Department of Mathematics, Princeton University.

  • Harsanyi, J. (1967), Games with incomplete information played by “Baye-sian” Players, I:the basic model, Management Science 14(3), 159–182.

    Google Scholar 

  • Harsanyi, J. (1968a), Games with incomplete information played by “Bayesian” Players, II:Bayesian equilibrium points, Management Science 14(5) 320–334.

    Google Scholar 

  • Harsanyi, J. (1968b), 'Games with incomplete information played by “Bayesian” Players, III:the basic probability distribution of the game', Management Science 14, 486–502.

    Google Scholar 

  • Koopmans, T. C. et al. (1951), Activity Analysis of Production and Alloca-tion, New York: Wiley.

    Google Scholar 

  • Kuhn, H. W. (1950), Extensive Games, Proceedings of the National Academy of Sciences 36(10), 570–576.

    Google Scholar 

  • Kuhn, H. W. (1952), Lectures on the Theory of Games, Report of the Logistics Research Project, Office of Naval Research. Princeton University Press, Princeton.

    Google Scholar 

  • Kuhn, H. W. and Tucker, A. W. (eds) (1950), Contributions to the theory of games, I. Annals of Mathematical Studies, Vol. 20, Princeton: Princeton University Press.

  • Kuhn, H. W. and Tucker, A. W. (eds) (1953), Contributions to the theory of games, II, Annals of Mathematical Studies, Vol. 24, Princeton: Princeton University Press.

  • Lemke, C. E. (1965), Bimatrix equilibrium points and mathematical pro-gramming, Management Science 11(7), 681–689.

    Google Scholar 

  • Lucas, W. F. (1968), A game with no solution, Bulletin of the American Mathematical Society 74, 237–239.

    Google Scholar 

  • Lucas, W. F. (1969), The proof that a game may not have a solution, Transactions of the American Mathematical Society 136, 219–229.

    Google Scholar 

  • Luce, R. D. and Raiffa, H. (1957), Games and Decisions. New York: McGraw-Hill.

    Google Scholar 

  • Maschler, M. and Peleg, B. (1966), A characterization, existence proof, and dimension bounds for the Kernel of a game, Pacific Journal of Mathe-matics 47, 289–328.

    Google Scholar 

  • McDonald, J. (1950), Strategy in Poker, Business and War. New York: Norton.

    Google Scholar 

  • McKinsey, J. C. C. (1952), Introduction to the Theory of Games. New York: McGraw-Hill.

    Google Scholar 

  • Mirowsky, P. (1991), When games grow deadly serious:the military in. u-ence on the evolution of game theory, in C. D. Goodwin (ed.), Economics and National Security. Durham, NC: Duke University Press.

    Google Scholar 

  • Morgenstern, O. (1976), The collaboration between Oskar Morgenstern and John von Neumann on the Theory of games, Journal of Economic Lit-erature 14(3), 805–816.

    Google Scholar 

  • Morgenstern, O. and Von Neumann, J. (1944), The Theory of Games and Economic Behavior. Princeton: Princeton University Press.

    Google Scholar 

  • Nash, J. (1950a), Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, USA, 36(1) 48–49.

    Google Scholar 

  • Nash, J. (1950b), The bargaining problem, Econometrica 18, 155–162.

    Google Scholar 

  • Nash, J. (1951), Non-cooperative games, Annals of Mathematics, 54(2) 286–295.

    Google Scholar 

  • Nash, J. (1953), Two-Person Cooperative Games, Econometrica 21, 128–140.

    Google Scholar 

  • Owen, G. (1968), Game Theory, I edn. II edn. 1982, III edn, 1993. New York: Academic Press.

    Google Scholar 

  • Poe, A. (1845), The Purloined Letter.

  • Rees, M. (1980), The Mathematical Sciences and Word War II, American Mathematical Monthly 87(8) 607–621.

    Google Scholar 

  • Riker, W. H. (1953), Democracy in the United States. New York: McMillan.

    Google Scholar 

  • Riker, W. H. (1986), The first power index, Social Choice and Welfare 3, 293–295.

    Google Scholar 

  • Robinson, J. (1951), An iterative method of solving a game, Annals of Mathematics 54, 286–295.

    Google Scholar 

  • Scarf, H. E. (1967), The Core of an n-person game, Econometrica 35, 50–69.

    Google Scholar 

  • Schelling, T. (1960), The Strategy of Conflict. Cambridge, MA: Harward University Press.

    Google Scholar 

  • Schmeidler, D. (1969), The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics 17, 1163–1170.

    Google Scholar 

  • Schotter, A. (1992), 'Oskar Morgenstern 's contribution to the development of the theory of games', in E. R. Weintraub (ed.), Towards a History of Game Theory', History of Political Economy, Annual Supple-ment to Vol. 24, Durham and London: Duke University Press, pp. 95–112.

    Google Scholar 

  • Shapley, L. S. (1953a), A value for n-person games, in H. W. Kuhn and A. W. Tucker (eds), Contributions to the Theory of Games, II, Annals of Mathematical Studies, Vol. 20. Princeton: Princeton University Press, pp. 307–317.

    Google Scholar 

  • Shapley, L. S. (1953b), Stochastic games, Proceedings of the National Academy of Science USA, 39, 1095–1100.

    Google Scholar 

  • Shapley, L. S. (1965), On balanced sets and cores, Rand Memo RM-4601-PR.

  • Shapley, L. S. and Shubik, M. (1954), A method for evaluating the dis-tributions of power in a committee system, American Political Science Review 48, 787–792.

    Google Scholar 

  • Steinhaus, H. 1925, Paper in Polish, in Mysl Akademicka Lwow, (Vol. 1, pp. 13–14). Translated by E. Rzymovski in (1960) as De nitions for a Theory of Games and Pursuit, with an introduction by H. Kuhn, Naval Research Logistics Quarterly 7(2), 105–108.

    Google Scholar 

  • Szegö, G. P. (ed.) (1982), Mathematical methods for economic analysis:A biased review, New Quantitative Techniques for Economic Analysis. New York: Academic Press, 3–17.

  • Theocharis, R. D. (1983), Early Developments in Mathematical Economics, 2nd edn London: McMillan.

    Google Scholar 

  • Thompson, G. L. (1953), in H. W. Kuhn and A. W. Tucker (eds), Signalling Strategies in N-Person Games and Bridge Signalling.

  • Ville, J. (1938), Sur la théorie générale des jeux oùintervient l' habiletédes joueurs, Applications des Jeux de Hasard (E. Borel et al. eds), 4(2), 105–113.

  • von Neumann, J. (1928), Zur theorie der Gesellschaftsspiele, Mathematische Annalen 100, 295–320. Translated by S. Bargmann in (1959) in R. D. Luce and A. W. Tucker (eds), as On the Theory of Games of Strategy.

    Google Scholar 

  • von Neumann, J. (1937), 'Über ein Ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes', in K. Menger (ed.), Ergebnisse eines Mathematischen Seminars. Vienna. Translated by G. Morton in (1945) as A model of general economic equilibrium, Review of Economic Studies 13(1), 1–9.

    Google Scholar 

  • Weintraub, E. R. (ed.) (1992), Towards a History of Game Theory, History of Political Economy, Annual Supplement to Vol 24. Durham and Lon-don: Duke University Press.

  • Weyl, H. (1935), Elementare Theorie der konvexen Polyeder, Commentarii Mathematici Helvetici 7, 290–306. Translated by H. W. Kuhn (1950) in H. W. Kuhn and A. W. Tucker (eds) as The Elementary Theory of Convex Polyhedra.

    Google Scholar 

  • Weyl, H. (1950), Elementary Proof of a Minimax Theorem Due to von Neumann, in H. W. Kuhn and A. W. Tucker (eds), Contributions to the Theory of Games, I, Annals of Mathematical Studies, Vol. 20. Princeton: Princeton University Press, 19–25.

    Google Scholar 

  • Williams, J. D. (1954), The Compleet Strategyst. New York: McGraw-Hill.

    Google Scholar 

  • Zermelo, E. (1913), Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings of V International Congress of Mathemati-cians 2, 501–504.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gambarelli, G., Owen, G. The Coming of Game Theory. Theory and Decision 56, 1–18 (2004). https://doi.org/10.1007/s11238-004-5629-3

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-004-5629-3

Navigation