Skip to main content

Game Theory

  • Living reference work entry
  • Latest version View entry history
  • First Online:
The New Palgrave Dictionary of Economics

Abstract

Game theory concerns the behaviour of decision makers whose decisions affect each other. Its analysis is from a rational rather than a psychological or sociological viewpoint. It is indeed a sort of umbrella theory for the rational side of social science, where ‘social’ is interpreted broadly, to include human as well as non-human players (computers, animals, plants). Its methodologies apply in principle to all interactive situations, especially in economics, political science, evolutionary biology, and computer science. There are also important connections with accounting, statistics, the foundations of mathematics, social psychology, law, business, and branches of philosophy such as epistemology and ethics.

This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume

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

Access this chapter

Institutional subscriptions

Bibliography

  • Anderson, R.M 1986. Notions of core convergence. In Hildebrand and Mas-Colell (1986), 25–46.

    Google Scholar 

  • Arrow, K.J. 1951. Social choice and individual values. New York: Wiley.

    Google Scholar 

  • Arrow, K.J., and G. Debreu. 1954. Existence of an equilibrium for a competitive economy. Econometrica 22: 265–290.

    Article  Google Scholar 

  • Artstein, Z. 1972. Values of games with denumerable many players. International Journal of Games Theory 3: 129–140.

    Google Scholar 

  • Asscher, N. 1976. An ordinal bargaining set for games without side payments. Mathematics of Operations Research 1: 381–389.

    Article  Google Scholar 

  • Aumann, R.J. 1960. Linearity of unrestrictedly transferable utilities. Naval Research Logistics Quarterly 7: 281–284.

    Article  Google Scholar 

  • Aumann, R.J. 1961. The core of a cooperative game without sidepayments. Transactions of the American Mathematical Society 98: 539–552.

    Article  Google Scholar 

  • Aumann, R.J. 1964. Markets with a continuum of traders. Econometrica 32: 39–50.

    Article  Google Scholar 

  • Aumann, R.J. 1975. Values of markets with a continuum of traders. Econometrica 43: 611–646.

    Article  Google Scholar 

  • Aumann, R.J. 1985. On the non-transferable utility value: A comment on the Roth-Shafer examples. Econometrica 53: 667–677.

    Article  Google Scholar 

  • Aumann, R.J. 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55: 1–18.

    Article  Google Scholar 

  • Aumann, R.J., and J.H. Drèze. 1974. Cooperative games with coalition structures. International Journal of Games Theory 3: 217–238.

    Article  Google Scholar 

  • Aumann, R.J., and M. Kurz. 1977. Power and taxes. Econometrica 45: 1137–1161.

    Article  Google Scholar 

  • Aumann, R.J., and M. Maschler. 1985. Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36: 195–213.

    Article  Google Scholar 

  • Aumann, R.J., and B. Peleg. 1960. Von Neumann-Morgenstern solutions to cooperative games without side payments. Bulletin of the American Mathematical Society 66: 173–179.

    Article  Google Scholar 

  • Aumann, R.J., and L.S. Shapley. 1974. Values of non-atomic games. Princeton: Princeton University Press.

    Google Scholar 

  • Axelrod, R. 1984. The evolution of cooperation. New York: Basic Books.

    Google Scholar 

  • Balinski, M.L., and H.P. Young. 1982. Fair representation. New Haven: Yale University Press.

    Google Scholar 

  • Berbee, H. 1981. On covering single points by randomly ordered intervals. Annals of Probability 9: 520–528.

    Article  Google Scholar 

  • Bewley, T., and E. Kohlberg. 1976. The asymptotic theory of stochasticgames. Mathematics of Operations Research 1: 197–208.

    Article  Google Scholar 

  • Billera, L.J. 1970a. Existence of general bargaining sets for cooperative games without side payments. Bulletin of the American Mathematical Society 76: 375–379.

    Article  Google Scholar 

  • Billera, L.J. 1970b. Some theorems on the core of an n-person game without side payments. SIAM Journal of Applied Mathematics 18: 567–579.

    Article  Google Scholar 

  • Billera, L.J., and R. Bixby. 1973. A characterization of polyhedral market games. International Journal of Games Theory 2: 253–261.

    Article  Google Scholar 

  • Billera, L.J., and D.C. Heath. 1982. Allocation of shared costs: A set of axioms yielding a unique procedure. Mathematics of Operations Research 7: 32–39.

    Article  Google Scholar 

  • Billera, L.J., D.C. Heath, and J. Raanan. 1978. Internal telephone billing rates – A novel application of non-atomic game theory. Operations Research 26: 956–965.

    Article  Google Scholar 

  • Binmore, K. 1982. Perfect equilibria in bargaining models, ICERD discussion paper no. 58. London: London School of Economics.

    Google Scholar 

  • Blackwell, D. 1956. An analogue of the minimax theorem for vector payoffs. Pacific Journal of Mathematics 6: 1–8.

    Article  Google Scholar 

  • Blackwell, D., and T.S. Ferguson. 1968. The big match. Annals of Mathematical Statistics 39: 159–163.

    Article  Google Scholar 

  • Bogardi, I., and F. Szidarovsky. 1976. Application of game theory in water management. Applied Mathematical Modelling 1: 11–20.

    Article  Google Scholar 

  • Bondareva, O.N. 1963. Some applications of linear programming methods to the theory of cooperative games [in Russian]. Problemy Kibernetiki 10: 119–139.

    Google Scholar 

  • Borel, E. 1924. Sur les jeux où interviennent l’hasard et l’habilité des joueurs. In Eléments de la theorie des probabilités, ed. J. Hermann, 204–224. Paris: Librairie Scientifique.

    Google Scholar 

  • Braithwaite, R.B., and F.P. Ramsey, eds. 1950. The foundations of mathematics and other logical essays. New York: Humanities Press.

    Google Scholar 

  • Brams, S.J., W.F. Lucas, and P.D. Straffin Jr., eds. 1983. Political and related models. New York: Springer.

    Google Scholar 

  • Brown, D.J., and P. Loeb. 1976. The values of non-standard exchangeeconomies. Israel Journal of Mathematics 25: 71–86.

    Article  Google Scholar 

  • Brown, D.J., and A. Robinson. 1975. Non standard exchange economies. Econometrica 43: 41–55.

    Article  Google Scholar 

  • Case, J.H. 1979. Economics and the competitive process. New York: New York University Press.

    Google Scholar 

  • Champsaur, P. 1975. Cooperation vs. competition. Journal of Economic Theory 11: 394–417.

    Article  Google Scholar 

  • Dantzig, G.B. 1951a. A proof of the equivalence of the programming problem and the game problem. In Koopmans (1951), 330–338.

    Google Scholar 

  • Dantzig, G.B. 1951b. Maximization of a linear function of variables subject to linear inequalities. In Koopmans (1951), 339–347.

    Google Scholar 

  • Davis, M. 1964. Infinite games with perfect information. In Dresher, Shapley and Tucker (1964), 85–101.

    Google Scholar 

  • Davis, M. 1967. Existence of stable payoff configurations for cooperative games. In Shubik (1967), 39–62.

    Google Scholar 

  • Davis, M., and M. Maschler. 1965. The kernel of a cooperative game. Naval Research Logistics Quarterly 12: 223–259.

    Article  Google Scholar 

  • Debreu, G. 1952. A social equilibrium existence theorem. Proceedings of the National Academy of Sciences of the United States 38: 886–893.

    Article  Google Scholar 

  • Debreu, G., and H. Scarf. 1963. A limit theorem on the core of aneconomy. International Economic Review 4: 236–246.

    Article  Google Scholar 

  • Dresher, M.A., A.W. Tucker, and P. Wolfe, eds. 1957. Contributions to the theory of games III, Annals of Mathematics studies series 39. Princeton: Princeton University Press.

    Google Scholar 

  • Dresher, M.A., L.S. Shapley, and A.W. Tucker, eds. 1964. Advances in game theory, Annals of Mathematics studies series 52. Princeton: Princeton University Press.

    Google Scholar 

  • Drèze, J.H., Gabszewicz, J., and Gepts, S. 1969. On cores and competitive equilibria. In Guilbaud (1969), 91–114.

    Google Scholar 

  • Dubey, P. 1980. Asymptotic semivalues and a short proof of Kannai’s theorem. Mathematics of Operations Research 5: 267–270.

    Article  Google Scholar 

  • Dubey, P., and Shapley, L.S. 1980. Non cooperative exchange with a continuum of traders: Two models. Technical Report of the Institute for Advanced Studies, Hebrew University of Jerusalem.

    Google Scholar 

  • Edgeworth, F.Y. 1881. Mathematical psychics. London: Kegan Paul.

    Google Scholar 

  • Everett, H. 1957. Recursive games. In Dresher, Tucker and Wolfe (1957), 47–78.

    Google Scholar 

  • Fogelman, F., and M. Quinzii. 1980. Asymptotic values of mixedgames. Mathematics of Operations Research 5: 86–93.

    Article  Google Scholar 

  • Gabszewicz, J.J., and J.F. Mertens. 1971. An equivalence theorem for the core of an economy whose atoms are not ‘too’ big. Econometrica 39: 713–721.

    Article  Google Scholar 

  • Gale, D. 1974. A curious nim-type game. American Mathematical Monthly 81: 876–879.

    Article  Google Scholar 

  • Gale, D. 1979. The game of hex and the Brouwer fixed-point theorem. American Mathematical Monthly 86: 818–827.

    Article  Google Scholar 

  • Gale, D. 1986. Bargaining and competition, Part I: Characterization. Part II: Existence. Econometrica 54 (785–806): 807–818.

    Article  Google Scholar 

  • Gale, D., and L.S. Shapley. 1962. College admissions and the stability of marriage. American Mathematical Monthly 69: 9–15.

    Article  Google Scholar 

  • Gale, D., and F.H. Stewart. 1953. Infinite games with perfect information. In Kuhn and Tucker (1953), 245–266.

    Google Scholar 

  • Galil, Z. 1974. The nucleolus in games with major and minor players. International Journal of Games Theory 3: 129–140.

    Article  Google Scholar 

  • Gillies, D.B. 1959. Solutions to general non-zero-sum games. In Luce and Tucker (1959), 47–85.

    Google Scholar 

  • Guilbaud, G.T., ed. 1969. La décision: aggrégation et dynamique des orders de préférence. Paris: Editions du CNRS.

    Google Scholar 

  • Harsanyi, J.C. 1956. Approaches to the bargaining problem before and after the theory of games: A critical discussion of Zeuthen’s, Hicks’ and Nash’s theories. Econometrica 24: 144–157.

    Article  Google Scholar 

  • Harsanyi, J.C. 1959. A bargaining model for the cooperative n-person game. In Tucker and Luce (1959), 325–356.

    Google Scholar 

  • Harsanyi, J.C. 1963. A simplified bargaining model for the n-person cooperative game. International Economic Review 4: 194–220.

    Article  Google Scholar 

  • Harsanyi, J.C. 1966. A general theory of rational behavior in game situations. Econometrica 34: 613–634.

    Article  Google Scholar 

  • Harsanyi, J.C. 1967–8. Games with incomplete information played by‘Bayesian’ players, parts I, II and III. Management Science 14: 159–182, 320–334, 486–502.

    Google Scholar 

  • Harsanyi, J.C. 1973. Games with randomly disturbed payoffs: A new rationale for mixed strategy equilibrium points. International Journal of Games Theory 2: 1–23.

    Article  Google Scholar 

  • Harsanyi, J.C. 1982. Solutions for some bargaining games under the Harsanyi-Selten solution theory I: Theoretical preliminaries; II: Analysis of specific games. Mathematical Social Sciences 3 (179–91): 259–279.

    Article  Google Scholar 

  • Harsanyi, J.C., and R. Selten. 1972. A generalized Nash solution for two-person bargaining games with incomplete information. Management Science 18: 80–106.

    Article  Google Scholar 

  • Harsanyi, J.C., and R. Selten. 1987. A general theory of equilibrium selection in games. Cambridge, MA: MIT Press.

    Google Scholar 

  • Hart, S. 1973. Values of mixed games. International Journal of Games Theory 2: 69–86.

    Article  Google Scholar 

  • Hart, S. 1974. Formation of cartels in large markets. Journal of Economic Theory 7: 453–466.

    Article  Google Scholar 

  • Hart, S. 1977a. Asymptotic values of games with a continuum of players. Journal of Mathematical Economics 4: 57–80.

    Article  Google Scholar 

  • Hart, S. 1977b. Values of non-differentiable markets with a continuum of traders. Journal of Mathematical Economics 4: 103–116.

    Article  Google Scholar 

  • Hart, S. 1980. Measure-based values of market games. Mathematics of Operations Research 5: 197–228.

    Article  Google Scholar 

  • Hart, S. 1985a. An axiomatization of Harsanyi’s nontransferable utility solution. Econometrica 53: 1295–1314.

    Article  Google Scholar 

  • Hart, S. 1985b. Non zero-sum two-person repeated games with incomplete information. Mathematics of Operations Research 10: 117–153.

    Article  Google Scholar 

  • Hart, S., and A. Mas-Colell. 1986. The potential: A new approach to the value in multi-person allocation problems. Harvard University Discussion Paper No. 1157.

    Google Scholar 

  • Hart, S., and D. Schmeidler. 1988. Correlated equilibria: An elementary existence proof. Mathematics of Operations Research.

    Google Scholar 

  • Hildenbrand, W., ed. 1982. Advances in economic theory. Cambridge: Cambridge University Press.

    Google Scholar 

  • Hildenbrand, W., and A. Mas-Colell. 1986. Contributions to mathematical economics in honor of G. Debreu. Amsterdam: North-Holland.

    Google Scholar 

  • Hu, T.C., and S.M. Robinson, eds. 1973. Mathematical programming. New York: Academic.

    Google Scholar 

  • Isaacs, R. 1965. Differential games: A mathematical theory with applications to warfare and pursuit, control and optimization. New York: Wiley.

    Google Scholar 

  • Kakutani, S. 1941. A generalization of Brouwer’s fixed point theorem. Duke Mathematical Journal 8: 457–459.

    Article  Google Scholar 

  • Kalai, E., and M. Smorodinsky. 1975. Other solutions to Nash’s bargainingproblem. Econometrica 43: 513–518.

    Article  Google Scholar 

  • Kaneko, M., and M. Wooders. 1982. Cores of partitioning games. Mathematical Social Sciences 3: 313–327.

    Article  Google Scholar 

  • Kannai, Y. 1966. Values of games with a continuum of players. Israel Journal of Mathematics 4: 54–58.

    Article  Google Scholar 

  • Kohlberg, E. 1971. On the nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 20: 62–66.

    Article  Google Scholar 

  • Kohlberg, E. 1972. The nucleolus as a solution to a minimization problem. SIAM Journal of Applied Mathematics 23: 34–49.

    Article  Google Scholar 

  • Koopmans, T.C., ed. 1951. Activity analysis of production and allocation. New York: Wiley.

    Google Scholar 

  • Kuhn, H.W. 1952. Lectures on the theory of games. Issued as a report of the Logistics Research Project, Office of Naval Research, Princeton University.

    Google Scholar 

  • Kuhn, H.W. 1953. Extensive games and the problem of information. In Kuhn and Tucker (1953), 193–216.

    Google Scholar 

  • Kuhn, H.W., and A.W. Tucker, eds. 1950. Contributions to the theory of games I, Annals of Mathematics studies series 24. Princeton: Princeton University Press.

    Google Scholar 

  • Kuhn, H.W., and A.W. Tucker, eds. 1953. Contributions to the theory of games II, Annals of Mathematics studies series 28. Princeton: Princeton University Press.

    Google Scholar 

  • Lemke, L.E., and J.T. Howson. 1962. Equilibrium points of bimatrix games. SIAM Journal of Applied Mathematics 12: 413–423.

    Article  Google Scholar 

  • Lensberg, T. 1981. The stability of the Nash solution. Unpublished.

    Google Scholar 

  • Lewis, D.K. 1969. Convention. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Littlechild, S.C. 1976. A further note on the nucleolus of the ‘airportgame’. International Journal of Games Theory 5: 91–95.

    Article  Google Scholar 

  • Littlechild, S.C., and G. Owen. 1973. A simple expression for the Shapley value in a special case. Management Science 20: 370–372.

    Article  Google Scholar 

  • Lucas, W.F. 1969. The proof that a game may not have a solution. Transactions of the American Mathematical Society 137: 219–229.

    Article  Google Scholar 

  • Lucas, W.F. 1983. Measuring power in weighted voting systems. In Brams, Lucas and Straffin (1983), ch. 9.

    Google Scholar 

  • Lucas, W.F., and M. Rabie. 1982. Games with no solutions and emptycore. Mathematics of Operations Research 7: 491–500.

    Article  Google Scholar 

  • Luce, R.D., and H. Raiffa. 1957. Games and decisions, introduction and critical survey. New York: Wiley.

    Google Scholar 

  • Luce, R.D., and A.W. Tucker, eds. 1959. Contributions to the theory of games IV, Annals of Mathematics studies series 40. Princeton: Princeton University Press.

    Google Scholar 

  • Lyapounov, A.A. 1940. On completely additive vector-functions (in Russian, abstract in French). Akademiia Nauk USSR Izvestiia Seriia Mathematicheskaia 4: 465–478.

    Google Scholar 

  • Martin, D.A. 1975. Borel determinacy. Annals of Mathematics 102: 363–371.

    Article  Google Scholar 

  • Maschler, M., ed. 1962. Recent advances in game theory. Proceedings of a Conference, privately printed for members of the conference. Princeton: Princeton University Conferences.

    Google Scholar 

  • Maschler, M., and M. Perles. 1981. The superadditive solution for the Nash bargaining game. International Journal of Games Theory 10: 163–193.

    Article  Google Scholar 

  • Maschler, M., B. Peleg, and L.S. Shapley. 1979. Geometric properties of the kernel, nucleolus, and related solution concepts. Mathematics of Operations Research 4: 303–338.

    Article  Google Scholar 

  • Mas-Colell, A. 1975. A further result on the representation of games by markets. Journal of Economic Theory 10: 117–122.

    Article  Google Scholar 

  • Mas-Colell, A. 1977. Competitive and value allocations of large exchange economies. Journal of Economic Theory 14: 419–438.

    Article  Google Scholar 

  • Mas-Colell, A. 1988. An equivalence theorem for a bargaining set. Journal of Mathematical Economics.

    Google Scholar 

  • Maynard Smith, J. 1982. Evolution and the theory of games. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Mertens, J.F. 1982. Repeated games: An overview of the zero-sum case. In Hildenbrand (1982), 175–182.

    Google Scholar 

  • Mertens, J.F. 1988. The Shapley value in the non-differentiable case. International Journal of Games Theory 17: 1–65.

    Article  Google Scholar 

  • Mertens, J.F., and A. Neyman. 1981. Stochastic games. International Journal of Games Theory 10: 53–66.

    Article  Google Scholar 

  • Milnor, J.W. 1978. Values of large games II: Oceanic games. Mathematics of Operations Research 3: 290–307.

    Article  Google Scholar 

  • Milnor, J.W. and Shapley, L.S. 1957. On games of survival. In Dresher, Tucker and Wolfe (1957), 15–45.

    Google Scholar 

  • Moschovakis, Y.N. 1980. Descriptive set theory. New York: North-Holland.

    Google Scholar 

  • Moschovakis, Y.N., ed. 1983. Cabal seminar 79–81: Proceedings, Caltech-UCLA Logic Seminar 1979–81, Lecture notes in Mathematics 1019. New York: Springer-Verlag.

    Google Scholar 

  • Mycielski, J., and H. Steinhaus. 1964. On the axiom of determinateness. Fundamenta Mathematicae 53: 205–224.

    Google Scholar 

  • Myerson, R.B. 1977. Graphs and cooperation in games. Mathematics of Operations Research 2: 225–229.

    Article  Google Scholar 

  • Myerson, R.B. 1979. Incentive compatibility and the bargaining problem. Econometrica 47: 61–74.

    Article  Google Scholar 

  • Myerson, R.B. 1984. Cooperative games with incomplete information. International Journal of Games Theory 13: 69–96.

    Article  Google Scholar 

  • Nash, J.F. Jr. 1950. The bargaining problem. Econometrica 18: 155–162.

    Article  Google Scholar 

  • Nash, J.F. Jr. 1951. Non-cooperative games. Annals of Mathematics 54: 289–295.

    Article  Google Scholar 

  • Neyman, A. 1985a. Bounded complexity justifies cooperation in the finitely repeated prisoner’s dilemma. Economics Letters 19: 227–230.

    Article  Google Scholar 

  • Neyman, A. 1985b. Semivalues of political economic games. Mathematics of Operations Research 10: 390–402.

    Article  Google Scholar 

  • Neyman, A. 1987. Weighted majority games have an asymptotic value. Mathematics of Operations Research.

    Google Scholar 

  • O’Neill, B. 1987. Non-metric test of the minimax theory of two-person zero-sum games. Proceedings of the National Academy of Sciences of the United States 84: 2106–2109.

    Article  Google Scholar 

  • Owen, G. 1972. Multilinear extensions of games. Management Science 18: 64–79.

    Article  Google Scholar 

  • Peleg, B. 1963a. Solutions to cooperative games without side payments. Transactions of the American Mathematical Society 106: 280–292.

    Article  Google Scholar 

  • Peleg, B. 1963b. Bargaining sets of cooperative games without side payments. Israel Journal of Mathematics 1: 197–200.

    Article  Google Scholar 

  • Peleg, B. 1967. Existence theorem for the bargaining set M1(i). In Shubik (1967), 53–56.

    Google Scholar 

  • Peleg, B. 1968. On weights of constant-sum majority games. SIAM Journal of Applied Mathematics 16: 527–532.

    Article  Google Scholar 

  • Peleg, B. 1985. An axiomatization of the core of cooperative games without side payments. Journal of Mathematical Economics 14: 203–214.

    Article  Google Scholar 

  • Peleg, B. 1986. On the reduced game property and its converse. International Journal of Games Theory 15: 187–200.

    Article  Google Scholar 

  • Pennock, J.R., and J.W. Chapman, eds. 1968. Representation. New York: Atherton.

    Google Scholar 

  • Ramsey, F.P. 1931. Truth and probability. In Braithwaite (1950).

    Google Scholar 

  • Ransmeier, J.S. 1942. The Tennesee valley authority: A case study in the economics of multiple purpose stream planning. Nashville: Vanderbilt University Press.

    Google Scholar 

  • Regelmann, K., and E. Curio. 1986. How do great tit (Parus major) pair mates cooperate in broad defence? Behavior 97: 10–36.

    Article  Google Scholar 

  • Riker, W.H. and Shapley, L.S. 1968. Weighted voting: A mathematical analysis for instrumental judgements. In Pennock and Chapman (1968), 199–216.

    Google Scholar 

  • Robinson, A. 1974. Non-standard analysis. Amsterdam: North-Holland.

    Google Scholar 

  • Rosenthal, R.W. 1979. Sequences of games with varying opponents. Econometrica 47: 1353–1366.

    Article  Google Scholar 

  • Rosenthal, R.W., and A. Rubinstein. 1984. Repeated two player games withruin. International Journal of Games Theory 13: 155–177.

    Article  Google Scholar 

  • Roth, A.E. 1977. The Shapley value as a von Neumann-Morgenstern utility. Econometrica 45: 657–664.

    Article  Google Scholar 

  • Roth, A.E. 1984. The evolution of the labor market for medical interns and residents: A case study in game theory. Journal of Political Economy 92: 991–1016.

    Article  Google Scholar 

  • Roth, A.E., and R.E. Verrecchia. 1979. The Shapley value as applied to cost allocation: A reinterpretation. Journal of Accounting Research 17: 295–303.

    Article  Google Scholar 

  • Rubinstein, A. 1982. Perfect equilibrium in a bargaining model. Econometrica 50: 97–109.

    Article  Google Scholar 

  • Rubinstein, A. 1986. Finite automata play the repeated prisoner’s dilemma. Journal of Economic Theory 39: 83–96.

    Article  Google Scholar 

  • Savage, L.J. 1954. The foundations of statistics. New York: Wiley.

    Google Scholar 

  • Scarf, H.E. 1967. The core of an n-person game. Econometrica 35: 50–69.

    Article  Google Scholar 

  • Scarf, H.E. 1973. The computation of economic equilibria. New Haven: Yale University Press.

    Google Scholar 

  • Schelling, T.C. 1960. The strategy of conflict. Cambridge, MA: Harvard University Press.

    Google Scholar 

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

    Article  Google Scholar 

  • Selten, R.C. 1965. Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetragheit. Zeitschrift für die Gesammte Staatswissenschaft 121: 301–324; 667–689.

    Google Scholar 

  • Selten, R.C. 1975. Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Games Theory 4: 25–55.

    Article  Google Scholar 

  • Selten, R.C. 1980. A note on evolutionary stable strategies in asymmetric animal conflicts. Journal of Theoretical Biology 84: 101–101.

    Article  Google Scholar 

  • Selten, R.C. 1983. Evolutionary stability in extensive two-part games. Mathematical Social Sciences 5: 269–363.

    Article  Google Scholar 

  • Shapley, L.S. 1953a. Stochastic games. Proceedings of the National Academy of Sciences of the United States 39: 1095–1100.

    Article  Google Scholar 

  • Shapley, L.S. 1953b. A value for n-person games. In Kuhn and Tucker (1953), 305–317.

    Google Scholar 

  • Shapley, L.S. 1962. Values of games with infinitely many players. In Maschler (1962), 113–118.

    Google Scholar 

  • Shapley, L.S. 1964. Values of large games, VII: A general exchange economy with money. RAND Publication RM–4248, Santa Monica.

    Google Scholar 

  • Shapley, L.S. 1967. On balanced sets and cores. Naval Research Logistics Quarterly 14: 453–460.

    Article  Google Scholar 

  • Shapley, L.S. 1969a. Utility comparison and the theory of games. In Guilbaud (1969), 251–263.

    Google Scholar 

  • Shapley, L.S. 1969b. On market games. Journal of Economic Theory 1: 9–25.

    Article  Google Scholar 

  • Shapley, L.S. 1969c. Pure competition, coalitional power and fair division. International Economic Review 10: 337–362.

    Article  Google Scholar 

  • Shapley, L.S. 1973a. On balanced games without side payments. In Hu and Robinson (1973), 261–290.

    Google Scholar 

  • Shapley, L.S. 1973b. Let’s block ‘block’. Econometrica 41: 1201–1202.

    Article  Google Scholar 

  • Shapley, L.S. 1984. Convergence of the bargaining set for differentiable market games. Appendix B in Shubik (1984), 683–692.

    Google Scholar 

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

    Article  Google Scholar 

  • Shitovitz, B. 1973. Oligopoly in markets with a continuum of traders. Econometrica 41: 467–501.

    Article  Google Scholar 

  • Shubik, M. 1959a. Edgeworth market games. In Luce and Tucker (1959), 267–278.

    Google Scholar 

  • Shubik, M. 1959b. Strategy and market structure. New York: Wiley.

    Google Scholar 

  • Shubik, M., ed. 1967. Essays in mathematical economics in honor of Oskar Morgenstern. Princeton: Princeton University Press.

    Google Scholar 

  • Shubik, M. 1973. Commodity, money, oligopoly, credit and bankruptcy in a general equilibrium model. Western Economic Journal 11: 24–36.

    Google Scholar 

  • Shubik, M. 1982. Game theory in the social sciences, concepts and solutions. Cambridge, MA: MIT Press.

    Google Scholar 

  • Shubik, M. 1984. A game theoretic approach to political economy. Cambridge, MA: MIT Press.

    Google Scholar 

  • Sobolev, A.I. 1975. Characterization of the principle of optimality for cooperative games through functional equations (in Russian). In Vorobiev (1975), 94–151.

    Google Scholar 

  • Sorin, S. 1986a. On repeated games of complete information. Mathematics of Operations Research 11: 147–160.

    Article  Google Scholar 

  • Sorin, S. 1986b. An asymptotic property of non-zero sum stochastic games. International Journal of Games Theory 15 (2): 101–107.

    Article  Google Scholar 

  • Tauman, Y. 1981. Value on a class of non-differentiable market games. International Journal of Games Theory 10: 155–162.

    Article  Google Scholar 

  • Ville, J.A. 1938. Sur le théorie générale des jeux où intervient I’habilité des joueurs. In Traité du calcul des probabilités et de ses applications, ed. E. Borel, vol. 4, 105–113. Paris: Gauthier-Villars.

    Google Scholar 

  • Vinacke, W.E., and A. Arkoff. 1957. An experimental study of coalitions in the triad. American Sociological Review 22: 406–415.

    Article  Google Scholar 

  • Vind, K. 1965. A theorem on the core of an economy. Review of Economic Studies 32: 47–48.

    Article  Google Scholar 

  • von Neumann, J. 1928. Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100: 295–320.

    Article  Google Scholar 

  • von Neumann, J. 1949. On rings of operators. Reduction theory. Annals of Mathematics 50: 401–485.

    Article  Google Scholar 

  • von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.

    Google Scholar 

  • Vorobiev, N.N., ed. 1975. Mathematical Methods in Social Science (in Russian). Vipusk 6, Vilnius.

    Google Scholar 

  • Wilson, R. 1978. Information, efficiency, and the core of an economy. Econometrica 46: 807–816.

    Article  Google Scholar 

  • Wolfe, P. 1955. The strict determinateness of certain infinite games. Pacific Journal of Mathematics 5: 841–847.

    Article  Google Scholar 

  • Wooders, M.H. 1983. The epsilon core of a large replica game. Journal of Mathematical Economics 11: 277–300.

    Article  Google Scholar 

  • Wooders, M.H., and W.R. Zame. 1984. Approximate cores of largegames. Econometrica 52: 1327–1350.

    Article  Google Scholar 

  • Young, H.P. 1985. Monotonic solutions of cooperative games. International Journal of Games Theory 14: 65–72.

    Article  Google Scholar 

  • Zermelo, E. 1913. Über eine Anwendung der Mengenlehre auf die theorie des Schachspiels. Proceedings of the Fifth International Congress of Mathematicians 2: 501–504.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Copyright information

© 2008 The Author(s)

About this entry

Cite this entry

Aumann, R. (2008). Game Theory. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_942-2

Download citation

  • DOI: https://doi.org/10.1057/978-1-349-95121-5_942-2

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Palgrave Macmillan, London

  • Online ISBN: 978-1-349-95121-5

  • eBook Packages: Springer Reference Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Game Theory
    Published:
    22 March 2017

    DOI: https://doi.org/10.1057/978-1-349-95121-5_942-2

  2. Original

    Game Theory
    Published:
    10 November 2016

    DOI: https://doi.org/10.1057/978-1-349-95121-5_942-1