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.
Keywords
- Asymmetric information
- Aumann, R. J.
- Axelrod, R.
- Axiomatics
- Bargaining
- Bounded rationality
- Brouwer’s fixed-point theorem
- Coalitional games
- Coalitions
- Common knowledge assumption
- Competitive equilibrium
- Consistency
- Continuous games
- Cooperative game theory
- Cooperative games
- Cores
- Correlated equilibria
- Cost allocation
- Differential games
- Distributed computing
- Duality theorems
- Dynamic games
- Ethics
- Evolutionary economics
- Expected utility theory
- Extensive form games
- Fixed threats
- Folk theorem
- Game theory
- Games of incomplete information
- General equilibrium
- Gillies, D.
- Harsanyi, J.
- Impossibility theorem
- Imputations
- Individual rationality
- Kakutani’s fixed point theorem
- Kernel
- Kuhn, H.
- Lemke-Howson algorithm
- Linear inequalities
- Linear programming
- Luce, R.
- Market games
- Mathematical economics
- Mathematical programming
- Milnor, J.
- Minimax theorem
- Mixed strategy game
- Monopoly
- Monopsony
- Morgenstern, O.
- Nash equilibrium
- Nash program
- Nash, J.
- Net worth
- Non-cooperative games
- Nucleolus
- Oligopoly
- Perfect information
- Prisoner’s dilemma
- Probability distributions
- Raiffa, H.
- Ramsey, F.
- Randomization
- Refinements of Nash equilibrium
- Repeated games
- Savage, L.
- Selten, R.
- Shadow pricing
- Shapley value
- Shapley, L.
- Shubik, M.
- Small worlds
- Maynard Smith, J.
- Solution concepts
- Stable set theory
- Statistical decision theory
- Stochastic games
- Strategic equilibrium
- Strategic games
- Strictly competitive games
- Strictly determined games
- Subgame perfection
- Subgames
- Super additivity
- Testing
- Tit for tat
- Transferable utility
- Tucker, A.
- Uncertainty
- Utility functions
- Value equivalence principle
- von Neumann, J.
- Voting games
- Weighted voting game
- Zermelo’s theorem
- Zero-sum games
JEL Classifications
This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume
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Bibliography
Anderson, R.M 1986. Notions of core convergence. In Hildebrand and Mas-Colell (1986), 25–46.
Arrow, K.J. 1951. Social choice and individual values. New York: Wiley.
Arrow, K.J., and G. Debreu. 1954. Existence of an equilibrium for a competitive economy. Econometrica 22: 265–290.
Artstein, Z. 1972. Values of games with denumerable many players. International Journal of Games Theory 3: 129–140.
Asscher, N. 1976. An ordinal bargaining set for games without side payments. Mathematics of Operations Research 1: 381–389.
Aumann, R.J. 1960. Linearity of unrestrictedly transferable utilities. Naval Research Logistics Quarterly 7: 281–284.
Aumann, R.J. 1961. The core of a cooperative game without sidepayments. Transactions of the American Mathematical Society 98: 539–552.
Aumann, R.J. 1964. Markets with a continuum of traders. Econometrica 32: 39–50.
Aumann, R.J. 1975. Values of markets with a continuum of traders. Econometrica 43: 611–646.
Aumann, R.J. 1985. On the non-transferable utility value: A comment on the Roth-Shafer examples. Econometrica 53: 667–677.
Aumann, R.J. 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55: 1–18.
Aumann, R.J., and J.H. Drèze. 1974. Cooperative games with coalition structures. International Journal of Games Theory 3: 217–238.
Aumann, R.J., and M. Kurz. 1977. Power and taxes. Econometrica 45: 1137–1161.
Aumann, R.J., and M. Maschler. 1985. Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36: 195–213.
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.
Aumann, R.J., and L.S. Shapley. 1974. Values of non-atomic games. Princeton: Princeton University Press.
Axelrod, R. 1984. The evolution of cooperation. New York: Basic Books.
Balinski, M.L., and H.P. Young. 1982. Fair representation. New Haven: Yale University Press.
Berbee, H. 1981. On covering single points by randomly ordered intervals. Annals of Probability 9: 520–528.
Bewley, T., and E. Kohlberg. 1976. The asymptotic theory of stochasticgames. Mathematics of Operations Research 1: 197–208.
Billera, L.J. 1970a. Existence of general bargaining sets for cooperative games without side payments. Bulletin of the American Mathematical Society 76: 375–379.
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.
Billera, L.J., and R. Bixby. 1973. A characterization of polyhedral market games. International Journal of Games Theory 2: 253–261.
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.
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.
Binmore, K. 1982. Perfect equilibria in bargaining models, ICERD discussion paper no. 58. London: London School of Economics.
Blackwell, D. 1956. An analogue of the minimax theorem for vector payoffs. Pacific Journal of Mathematics 6: 1–8.
Blackwell, D., and T.S. Ferguson. 1968. The big match. Annals of Mathematical Statistics 39: 159–163.
Bogardi, I., and F. Szidarovsky. 1976. Application of game theory in water management. Applied Mathematical Modelling 1: 11–20.
Bondareva, O.N. 1963. Some applications of linear programming methods to the theory of cooperative games [in Russian]. Problemy Kibernetiki 10: 119–139.
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.
Braithwaite, R.B., and F.P. Ramsey, eds. 1950. The foundations of mathematics and other logical essays. New York: Humanities Press.
Brams, S.J., W.F. Lucas, and P.D. Straffin Jr., eds. 1983. Political and related models. New York: Springer.
Brown, D.J., and P. Loeb. 1976. The values of non-standard exchangeeconomies. Israel Journal of Mathematics 25: 71–86.
Brown, D.J., and A. Robinson. 1975. Non standard exchange economies. Econometrica 43: 41–55.
Case, J.H. 1979. Economics and the competitive process. New York: New York University Press.
Champsaur, P. 1975. Cooperation vs. competition. Journal of Economic Theory 11: 394–417.
Dantzig, G.B. 1951a. A proof of the equivalence of the programming problem and the game problem. In Koopmans (1951), 330–338.
Dantzig, G.B. 1951b. Maximization of a linear function of variables subject to linear inequalities. In Koopmans (1951), 339–347.
Davis, M. 1964. Infinite games with perfect information. In Dresher, Shapley and Tucker (1964), 85–101.
Davis, M. 1967. Existence of stable payoff configurations for cooperative games. In Shubik (1967), 39–62.
Davis, M., and M. Maschler. 1965. The kernel of a cooperative game. Naval Research Logistics Quarterly 12: 223–259.
Debreu, G. 1952. A social equilibrium existence theorem. Proceedings of the National Academy of Sciences of the United States 38: 886–893.
Debreu, G., and H. Scarf. 1963. A limit theorem on the core of aneconomy. International Economic Review 4: 236–246.
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.
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.
Drèze, J.H., Gabszewicz, J., and Gepts, S. 1969. On cores and competitive equilibria. In Guilbaud (1969), 91–114.
Dubey, P. 1980. Asymptotic semivalues and a short proof of Kannai’s theorem. Mathematics of Operations Research 5: 267–270.
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.
Edgeworth, F.Y. 1881. Mathematical psychics. London: Kegan Paul.
Everett, H. 1957. Recursive games. In Dresher, Tucker and Wolfe (1957), 47–78.
Fogelman, F., and M. Quinzii. 1980. Asymptotic values of mixedgames. Mathematics of Operations Research 5: 86–93.
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.
Gale, D. 1974. A curious nim-type game. American Mathematical Monthly 81: 876–879.
Gale, D. 1979. The game of hex and the Brouwer fixed-point theorem. American Mathematical Monthly 86: 818–827.
Gale, D. 1986. Bargaining and competition, Part I: Characterization. Part II: Existence. Econometrica 54 (785–806): 807–818.
Gale, D., and L.S. Shapley. 1962. College admissions and the stability of marriage. American Mathematical Monthly 69: 9–15.
Gale, D., and F.H. Stewart. 1953. Infinite games with perfect information. In Kuhn and Tucker (1953), 245–266.
Galil, Z. 1974. The nucleolus in games with major and minor players. International Journal of Games Theory 3: 129–140.
Gillies, D.B. 1959. Solutions to general non-zero-sum games. In Luce and Tucker (1959), 47–85.
Guilbaud, G.T., ed. 1969. La décision: aggrégation et dynamique des orders de préférence. Paris: Editions du CNRS.
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.
Harsanyi, J.C. 1959. A bargaining model for the cooperative n-person game. In Tucker and Luce (1959), 325–356.
Harsanyi, J.C. 1963. A simplified bargaining model for the n-person cooperative game. International Economic Review 4: 194–220.
Harsanyi, J.C. 1966. A general theory of rational behavior in game situations. Econometrica 34: 613–634.
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.
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.
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.
Harsanyi, J.C., and R. Selten. 1972. A generalized Nash solution for two-person bargaining games with incomplete information. Management Science 18: 80–106.
Harsanyi, J.C., and R. Selten. 1987. A general theory of equilibrium selection in games. Cambridge, MA: MIT Press.
Hart, S. 1973. Values of mixed games. International Journal of Games Theory 2: 69–86.
Hart, S. 1974. Formation of cartels in large markets. Journal of Economic Theory 7: 453–466.
Hart, S. 1977a. Asymptotic values of games with a continuum of players. Journal of Mathematical Economics 4: 57–80.
Hart, S. 1977b. Values of non-differentiable markets with a continuum of traders. Journal of Mathematical Economics 4: 103–116.
Hart, S. 1980. Measure-based values of market games. Mathematics of Operations Research 5: 197–228.
Hart, S. 1985a. An axiomatization of Harsanyi’s nontransferable utility solution. Econometrica 53: 1295–1314.
Hart, S. 1985b. Non zero-sum two-person repeated games with incomplete information. Mathematics of Operations Research 10: 117–153.
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.
Hart, S., and D. Schmeidler. 1988. Correlated equilibria: An elementary existence proof. Mathematics of Operations Research.
Hildenbrand, W., ed. 1982. Advances in economic theory. Cambridge: Cambridge University Press.
Hildenbrand, W., and A. Mas-Colell. 1986. Contributions to mathematical economics in honor of G. Debreu. Amsterdam: North-Holland.
Hu, T.C., and S.M. Robinson, eds. 1973. Mathematical programming. New York: Academic.
Isaacs, R. 1965. Differential games: A mathematical theory with applications to warfare and pursuit, control and optimization. New York: Wiley.
Kakutani, S. 1941. A generalization of Brouwer’s fixed point theorem. Duke Mathematical Journal 8: 457–459.
Kalai, E., and M. Smorodinsky. 1975. Other solutions to Nash’s bargainingproblem. Econometrica 43: 513–518.
Kaneko, M., and M. Wooders. 1982. Cores of partitioning games. Mathematical Social Sciences 3: 313–327.
Kannai, Y. 1966. Values of games with a continuum of players. Israel Journal of Mathematics 4: 54–58.
Kohlberg, E. 1971. On the nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 20: 62–66.
Kohlberg, E. 1972. The nucleolus as a solution to a minimization problem. SIAM Journal of Applied Mathematics 23: 34–49.
Koopmans, T.C., ed. 1951. Activity analysis of production and allocation. New York: Wiley.
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.
Kuhn, H.W. 1953. Extensive games and the problem of information. In Kuhn and Tucker (1953), 193–216.
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.
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.
Lemke, L.E., and J.T. Howson. 1962. Equilibrium points of bimatrix games. SIAM Journal of Applied Mathematics 12: 413–423.
Lensberg, T. 1981. The stability of the Nash solution. Unpublished.
Lewis, D.K. 1969. Convention. Cambridge, MA: Harvard University Press.
Littlechild, S.C. 1976. A further note on the nucleolus of the ‘airportgame’. International Journal of Games Theory 5: 91–95.
Littlechild, S.C., and G. Owen. 1973. A simple expression for the Shapley value in a special case. Management Science 20: 370–372.
Lucas, W.F. 1969. The proof that a game may not have a solution. Transactions of the American Mathematical Society 137: 219–229.
Lucas, W.F. 1983. Measuring power in weighted voting systems. In Brams, Lucas and Straffin (1983), ch. 9.
Lucas, W.F., and M. Rabie. 1982. Games with no solutions and emptycore. Mathematics of Operations Research 7: 491–500.
Luce, R.D., and H. Raiffa. 1957. Games and decisions, introduction and critical survey. New York: Wiley.
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.
Lyapounov, A.A. 1940. On completely additive vector-functions (in Russian, abstract in French). Akademiia Nauk USSR Izvestiia Seriia Mathematicheskaia 4: 465–478.
Martin, D.A. 1975. Borel determinacy. Annals of Mathematics 102: 363–371.
Maschler, M., ed. 1962. Recent advances in game theory. Proceedings of a Conference, privately printed for members of the conference. Princeton: Princeton University Conferences.
Maschler, M., and M. Perles. 1981. The superadditive solution for the Nash bargaining game. International Journal of Games Theory 10: 163–193.
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.
Mas-Colell, A. 1975. A further result on the representation of games by markets. Journal of Economic Theory 10: 117–122.
Mas-Colell, A. 1977. Competitive and value allocations of large exchange economies. Journal of Economic Theory 14: 419–438.
Mas-Colell, A. 1988. An equivalence theorem for a bargaining set. Journal of Mathematical Economics.
Maynard Smith, J. 1982. Evolution and the theory of games. Cambridge: Cambridge University Press.
Mertens, J.F. 1982. Repeated games: An overview of the zero-sum case. In Hildenbrand (1982), 175–182.
Mertens, J.F. 1988. The Shapley value in the non-differentiable case. International Journal of Games Theory 17: 1–65.
Mertens, J.F., and A. Neyman. 1981. Stochastic games. International Journal of Games Theory 10: 53–66.
Milnor, J.W. 1978. Values of large games II: Oceanic games. Mathematics of Operations Research 3: 290–307.
Milnor, J.W. and Shapley, L.S. 1957. On games of survival. In Dresher, Tucker and Wolfe (1957), 15–45.
Moschovakis, Y.N. 1980. Descriptive set theory. New York: North-Holland.
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.
Mycielski, J., and H. Steinhaus. 1964. On the axiom of determinateness. Fundamenta Mathematicae 53: 205–224.
Myerson, R.B. 1977. Graphs and cooperation in games. Mathematics of Operations Research 2: 225–229.
Myerson, R.B. 1979. Incentive compatibility and the bargaining problem. Econometrica 47: 61–74.
Myerson, R.B. 1984. Cooperative games with incomplete information. International Journal of Games Theory 13: 69–96.
Nash, J.F. Jr. 1950. The bargaining problem. Econometrica 18: 155–162.
Nash, J.F. Jr. 1951. Non-cooperative games. Annals of Mathematics 54: 289–295.
Neyman, A. 1985a. Bounded complexity justifies cooperation in the finitely repeated prisoner’s dilemma. Economics Letters 19: 227–230.
Neyman, A. 1985b. Semivalues of political economic games. Mathematics of Operations Research 10: 390–402.
Neyman, A. 1987. Weighted majority games have an asymptotic value. Mathematics of Operations Research.
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.
Owen, G. 1972. Multilinear extensions of games. Management Science 18: 64–79.
Peleg, B. 1963a. Solutions to cooperative games without side payments. Transactions of the American Mathematical Society 106: 280–292.
Peleg, B. 1963b. Bargaining sets of cooperative games without side payments. Israel Journal of Mathematics 1: 197–200.
Peleg, B. 1967. Existence theorem for the bargaining set M1(i). In Shubik (1967), 53–56.
Peleg, B. 1968. On weights of constant-sum majority games. SIAM Journal of Applied Mathematics 16: 527–532.
Peleg, B. 1985. An axiomatization of the core of cooperative games without side payments. Journal of Mathematical Economics 14: 203–214.
Peleg, B. 1986. On the reduced game property and its converse. International Journal of Games Theory 15: 187–200.
Pennock, J.R., and J.W. Chapman, eds. 1968. Representation. New York: Atherton.
Ramsey, F.P. 1931. Truth and probability. In Braithwaite (1950).
Ransmeier, J.S. 1942. The Tennesee valley authority: A case study in the economics of multiple purpose stream planning. Nashville: Vanderbilt University Press.
Regelmann, K., and E. Curio. 1986. How do great tit (Parus major) pair mates cooperate in broad defence? Behavior 97: 10–36.
Riker, W.H. and Shapley, L.S. 1968. Weighted voting: A mathematical analysis for instrumental judgements. In Pennock and Chapman (1968), 199–216.
Robinson, A. 1974. Non-standard analysis. Amsterdam: North-Holland.
Rosenthal, R.W. 1979. Sequences of games with varying opponents. Econometrica 47: 1353–1366.
Rosenthal, R.W., and A. Rubinstein. 1984. Repeated two player games withruin. International Journal of Games Theory 13: 155–177.
Roth, A.E. 1977. The Shapley value as a von Neumann-Morgenstern utility. Econometrica 45: 657–664.
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.
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.
Rubinstein, A. 1982. Perfect equilibrium in a bargaining model. Econometrica 50: 97–109.
Rubinstein, A. 1986. Finite automata play the repeated prisoner’s dilemma. Journal of Economic Theory 39: 83–96.
Savage, L.J. 1954. The foundations of statistics. New York: Wiley.
Scarf, H.E. 1967. The core of an n-person game. Econometrica 35: 50–69.
Scarf, H.E. 1973. The computation of economic equilibria. New Haven: Yale University Press.
Schelling, T.C. 1960. The strategy of conflict. Cambridge, MA: Harvard University Press.
Schmeidler, D. 1969. The nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 17: 1163–1170.
Selten, R.C. 1965. Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetragheit. Zeitschrift für die Gesammte Staatswissenschaft 121: 301–324; 667–689.
Selten, R.C. 1975. Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Games Theory 4: 25–55.
Selten, R.C. 1980. A note on evolutionary stable strategies in asymmetric animal conflicts. Journal of Theoretical Biology 84: 101–101.
Selten, R.C. 1983. Evolutionary stability in extensive two-part games. Mathematical Social Sciences 5: 269–363.
Shapley, L.S. 1953a. Stochastic games. Proceedings of the National Academy of Sciences of the United States 39: 1095–1100.
Shapley, L.S. 1953b. A value for n-person games. In Kuhn and Tucker (1953), 305–317.
Shapley, L.S. 1962. Values of games with infinitely many players. In Maschler (1962), 113–118.
Shapley, L.S. 1964. Values of large games, VII: A general exchange economy with money. RAND Publication RM–4248, Santa Monica.
Shapley, L.S. 1967. On balanced sets and cores. Naval Research Logistics Quarterly 14: 453–460.
Shapley, L.S. 1969a. Utility comparison and the theory of games. In Guilbaud (1969), 251–263.
Shapley, L.S. 1969b. On market games. Journal of Economic Theory 1: 9–25.
Shapley, L.S. 1969c. Pure competition, coalitional power and fair division. International Economic Review 10: 337–362.
Shapley, L.S. 1973a. On balanced games without side payments. In Hu and Robinson (1973), 261–290.
Shapley, L.S. 1973b. Let’s block ‘block’. Econometrica 41: 1201–1202.
Shapley, L.S. 1984. Convergence of the bargaining set for differentiable market games. Appendix B in Shubik (1984), 683–692.
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.
Shitovitz, B. 1973. Oligopoly in markets with a continuum of traders. Econometrica 41: 467–501.
Shubik, M. 1959a. Edgeworth market games. In Luce and Tucker (1959), 267–278.
Shubik, M. 1959b. Strategy and market structure. New York: Wiley.
Shubik, M., ed. 1967. Essays in mathematical economics in honor of Oskar Morgenstern. Princeton: Princeton University Press.
Shubik, M. 1973. Commodity, money, oligopoly, credit and bankruptcy in a general equilibrium model. Western Economic Journal 11: 24–36.
Shubik, M. 1982. Game theory in the social sciences, concepts and solutions. Cambridge, MA: MIT Press.
Shubik, M. 1984. A game theoretic approach to political economy. Cambridge, MA: MIT Press.
Sobolev, A.I. 1975. Characterization of the principle of optimality for cooperative games through functional equations (in Russian). In Vorobiev (1975), 94–151.
Sorin, S. 1986a. On repeated games of complete information. Mathematics of Operations Research 11: 147–160.
Sorin, S. 1986b. An asymptotic property of non-zero sum stochastic games. International Journal of Games Theory 15 (2): 101–107.
Tauman, Y. 1981. Value on a class of non-differentiable market games. International Journal of Games Theory 10: 155–162.
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.
Vinacke, W.E., and A. Arkoff. 1957. An experimental study of coalitions in the triad. American Sociological Review 22: 406–415.
Vind, K. 1965. A theorem on the core of an economy. Review of Economic Studies 32: 47–48.
von Neumann, J. 1928. Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100: 295–320.
von Neumann, J. 1949. On rings of operators. Reduction theory. Annals of Mathematics 50: 401–485.
von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.
Vorobiev, N.N., ed. 1975. Mathematical Methods in Social Science (in Russian). Vipusk 6, Vilnius.
Wilson, R. 1978. Information, efficiency, and the core of an economy. Econometrica 46: 807–816.
Wolfe, P. 1955. The strict determinateness of certain infinite games. Pacific Journal of Mathematics 5: 841–847.
Wooders, M.H. 1983. The epsilon core of a large replica game. Journal of Mathematical Economics 11: 277–300.
Wooders, M.H., and W.R. Zame. 1984. Approximate cores of largegames. Econometrica 52: 1327–1350.
Young, H.P. 1985. Monotonic solutions of cooperative games. International Journal of Games Theory 14: 65–72.
Zermelo, E. 1913. Über eine Anwendung der Mengenlehre auf die theorie des Schachspiels. Proceedings of the Fifth International Congress of Mathematicians 2: 501–504.
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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
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