Abstract
In their seminal book, von Neumann and Morgenstern (1944) introduced two theories of games: strategic and coalitional. Strategic game theory concentrates on the selection of strategies by payoff-maximizing players, coalitional game theory concentrates on coalition formation and the distribution of payoffs.
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Bibliography
Anderson, R.M. 1992. The core in perfectly competitive economies. In Aumann and Hart (1992).
Aumann, R.J. 1961. The core of a cooperative game without side payments. Transactions of the American Mathematical Society 98, 539–52.
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, 611–46.
Aumann, R.J. 1985. An axiomatization of the non-transferable utility value. Econometrica 53, 599–612.
Aumann, R.J. and Hart, S. 1992; 1994; 2002. The Handbook of Game Theory with Economic Application, vols 1, 2 and 3. Amsterdam: North-Holland.
Aumann, R.J. and Maschler, M. 1985. Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36, 195–213.
Aumann, R.J. and Maschler, M. 1964. The bargaining set for cooperative games. In Advances in Game Theory, ed. M. Dresher, L.S. Shapley and A.W. Tucker. Princeton: Princeton University Press.
Aumann, R.J. and Myerson, R.B. 1988. Endogenous formation of links between players and coalitions: an application of the Shapley value. In The Shapley Value, ed. A. Roth. Cambridge: Cambridge University Press.
Aumann, R.J. and Peleg, B. 1960. Von Neumann-Morgenstern solutions to cooperative games without side payments. Bulletin of the American Mathematical Society 66, 173–9.
Aumann, R.J. and Shapley, L.S. 1974. Values of Non-Atomic Games. Princeton: Princeton University Press.
Bhaskar, D. and Kar, A. 2004. Cost monotonicity, consistency and minimum cost spanning tree games. Games and Econ Behavior 48, 223–48.
Bikhchandani, S. and Ostroy, J.M. 2006. Ascending price Vickrey auctions. Games and Econ Behavior 55, 215–11.
Billera, L.J. 1970a. Existence of general bargaining sets for cooperative games without side payments. Bulletin of the American Mathematical Society 76, 375–9.
Billera, L.J. 1970b. Some theorems on the core of an n-person game without side payments. SIAM Journal of Applied Mathematics 18, 567–79.
Billera, L.J. and Bixby, R. 1973. A characterization of polyhedral market games. International Journal of Game Theory2, 253–61.
Billera, L.J., Heath, D.C. and Raanan, J. 1978. Internal telephone billing rates: a novel application of non-atomic game theory. Operations Research 26, 956–65.
Binmore, K. 1987. Nash bargaining theory III. In The Economics of Bargaining, ed. K. Binmore and P. Dasgupta. Oxford: Blackwell.
Binmore, K., Rubinstein, A. and Wolinsky, A. 1986. The Nash bargaining solution in economic modelling. Rand Journal of Economics 17, 176–88.
Bird, C.G. 1976. On cost allocation for a spanning tree: a game theoretic approach. Networks 6, 335–60.
Bondareva, O.N. 1963. Some applications of linear programming methods to the theory of cooperative games. Problemy kibernetiki 10, 119–39 [in Russian].
Brams, S.J., Lucas, W.F. and Straffin, P.D., Jr. 1983. Political and Related Models. New York: Springer.
Chun, Y. and Thomson, W. 1990. Nash solution and uncertain disagreement points. Games and Economic Behavior 2, 213–23.
Davis, M. and Maschler, M. 1965. The kernel of a cooperative game. Naval Research Logistics Quarterly 12, 223–59.
Day, R. and Milgrom, P. 2007. Core selecting package auctions. International Journal of Game Theory (forthcoming).
Debreu, G. and Scarf, H. 1963. A limit theorem on the core of an economy. International Economic Review 4, 236–16.
De Clippel, G., Peters, H. and Zank, H. 2004. Axiomatizing the Harsanyi solution, the symmetric egalitarian solution, and the consistent solution for NTU-games. International Journal of Game Theory 33, 145–58.
Deng, X. and Papadimitriou, C. 1994. On the complexity of cooperative game solution concepts. Mathematics of Operations Research 19, 257–66.
De Vries, S., Schummer, J. and Vohra, R.V. 2007. On ascending Vickrey auctions for heterogeneous objects. Journal of Economic Theory 132, 95–118.
Dubey, P. and Shapley, L.S. 1979. Some properties of the Banzhaf power index. Mathematics of Operations Research 4, 99–131.
Dubey, P. and Shapley, L.S. 1984. Totally balanced games arising from controlled programming problems. Mathematical Programming 29, 245–67.
Gale, D. and Shapley, L.S. 1962. College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15.
Gillies, D.B. 1953. Some theorems on n-person games. Ph.D. thesis, Department of Mathematics, Princeton University.
Granot, D. and Huberman, G. 1984. On the core and nucleolus of the minimum costs spanning tree games. Mathematical Programming 29, 323–47.
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, 144–57.
Harsanyi, J.C. 1959. A bargaining model for the cooperative n-person game. In Contributions to the Theory of Games, vol. 4, ed. A.W. Tucker and R.W. Luce. Princeton: Princeton University Press.
Harsanyi, J.C. 1963. A simplified bargaining model for the «-persons cooperative game. International Economic Review 4, 194–220.
Harsanyi, J.C. 1966. A general theory of rational behavior in game situations. Econometrica 34, 613–34.
Harsanyi, J.C. and Selten, R. 1972. A generalized Nash solution for two-person bargaining games with incomplete information. Management Science 18, 80–106.
Hart, S. 1973. Values of mixed games. International Journal of Game Theory 2, 69–86.
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, 103–16.
Hart, S. 1980. Measure-based values of market games. Mathematics of Operations Research 5, 197–228.
Hart, S. 1985. An axiomatization of Harsanyi’s nontransferable utility solution. Econometrica 53, 1295–314.
Hart, S. and Mas-Colell, A. 1989. The potential: a new approach to the value in multiperson allocation problems. Econometrica 57, 589–614.
Ichiishi, T. 1981. Supermodularity: applications to convex games and to the greedy algorithm for LP. Journal of Economic Theory 25, 283–6.
Jackson, M.O. and Wolinsky, A. 1996. A strategic model of social and economic networks. Journal of Economic Theory 71, 44–74.
Kalai, E. 1975. Excess functions for cooperative games without sidepayments. SIAM Journal of Applied Mathematics 29, 60–71.
Kalai, E. 1977a. Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45, 1623–30.
Kalai, E. 1977b. Non-symmetric Nash solutions for replications of 2-person bargaining. International Journal of Game Theory 6, 129–33.
Kalai, E., Postlewaite, A. and Roberts, J. 1979. Barriers to trade and disadvantageous middlemen: nonmonotonicity of the core. Journal of Economic Theory 19, 200–9.
Kalai, E. and Rosenthal, R.W. 1978. Arbitration of two-party disputes under ignorance.International Journal of Game Theory 7, 65–72.
Kalai, E. and Samet, D. 1985. Monotonie solutions to general cooperative games. Econometrica 53, 307–27.
Kalai, E. and Samet, D. 1987. On weighted Shapley values. International Journal of Game Theory 16, 205–22.
Kalai, E. and Smorodinsky, M. 1975. Other solutions to Nash’s bargaining problems. Econometrica 43, 513–8.
Kalai, E. and Zemel, E. 1982a. Generalized network problems yielding totally balanced games. Operations Research 5, 998–1008.
Kalai, E. and Zemel, E. 1982b. Totally balanced games and games of flow. Mathematics of Operations Research 7, 476–78.
Kannai, Y. 1992. The core and balancedness. In Handbook of Game Theory with Economic Applications, vol. 1, ed. R.J. Aumann and S. Hart. Amsterdam: North-Holland.
Kaneko, M. and Wooders, M. 1982. Cores of partitioning games. Mathematical Social Sciences 3, 313–27.
Kohlberg, E. 1972. The nucleolus as a solution to a minimization problem. SIAM Journal of Applied Mathematics 23, 34–49.
Larauelle, A. and Valenciano, F. 2001. Shapley-Shubik and Banzhaf indices revisited. Mathematics of Operations Research 26, 89–104.
Lehrer, E. 1988. An axiomatization of the Banzhaf value. International Journal of Game Theory 17(2), 89–99.
Lensberg, T. 1985. Bargaining and fair allocation. In Cost Allocation, Principles, Applications, ed. P. Young. Amsterdam: North-Holland.
Lensberg, T. 1988. Stability and the Nash solution. Journal of Economic Theory 45, 330–41.
Lensberg, T. and Thomson, W. 1989. Axiomatic Theory of Bargaining With a Variable Population. Cambridge: Cambridge University Press.
Levy, A. and McLean, R. 1991. An axiomatization of the non-symmetric NTU value. International Journal of Game Theory 19, 109–27.
Lucas, W.F. 1969. The proof that a game may not have a solution. Transactions of the American Mathematical Society 137, 219–29.
Lucas, W.F. and Thrall, R.M. 1963. n-person games in partition function forms. Naval Research Logistics Quarterly 10, 281–98.
Luce, R.D. and Raiffa, H. 1957. Games and Decisions: An Introduction and Critical Survey. New York: Wiley.
Maschler, M. 1992. The bargaining set, kernel and nucleolus. In Aumann and Hart (1992).
Maschler, M., Peleg, B. and Shapley, L.S. 1979. Geometric properties of the kernel, nucleolus, and related solution concepts. Mathematics of Operations Research 4, 303–38.
Maschler, M. and Perles, M. 1981. The superadditive solution for the Nash bargaining game. International Journal of Game Theory 10, 163–93.
Mas-Colell, A. 1975. A further result on the representation of games by markets. Journal of Economic Theory 10, 117–22.
Mas-Colell, A. 1977. Competitive and value allocations of large exchange economies. Journal of Economic Theory 14, 419–38.
Mas-Colell, A. 1989. An equivalence theorem for a bargaining set. Journal of Mathematical Economics 18, 129–39.
McLean, R.P. 2002. Values of non-transferable utility games. In Aumann and Hart (2002).
Milnor, J.W. and Shapley, L.S. 1978. Values of large games II: oceanic games. Mathematics of Operations Research 3, 290–307.
Monderer, D. and Samet, D. 2002. Variations on the Shapley value. In Aumann and Hart (2002).
Monderer, D., Samet, D. and Shapley, L.S. 1992. Weighted Shapley values and the core. International Journal of Game Theory 21, 27–39.
Moulin, H. 1988. Axioms of Cooperative Decision Making. Cambridge: Cambridge University Press.
Myerson, R.B. 1977a. Two-person bargaining problems and comparable utility, Econometrica 45, 1631–37.
Myerson, R.B. 1977b. Graphs and cooperation in games. Mathematics of Operations Research 2, 225–9.
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 Game Theory 13, 69–96.
Myerson, R.B. 1991. Game theory: Analysis of Conflict. Cambridge: Harvard University Press.
Nash, J.F. 1950. The bargaining problem. Econometrica 18, 155–62.
Nash, J.F. 1953. Two person cooperative games. Econometrica 21, 128–40.
Neyman, A. 1985. Semivalues of political economic games. Mathematics of Operations Research 10, 390–102.
Neyman, A. 1987. Weighted majority games have an asymptotic value. Mathematics of Operations Research 13, 556–80.
Neyman, A. 2002. Values of games with infinitely many players. In Aumann and Hart (2002).
Nisan, N., Roughgarden, T., Tardos, E. and Vazirani, V. 2007. Algorithmic Game Theory. Cambridge: Cambridge University Press.
O’Neil, B. 1982. A problem of rights arbitration from the Talmud. Mathematical Social Sciences 2, 345–71.
Owen, G. 1972. Multilinear extensions of games. Management Science 18, 64–79.
Owen, G. 1975. On the core of linear production games. Mathematical Programming 9, 358–70.
Osborne, M.J. and Rubinstein, A. 1994. A Course in Game Theory. Cambridge, MA: MIT Press.
Peleg, B. 1963a. Solutions to cooperative games without side payments. Transactions of the American Mathematical Society 106, 280–92.
Peleg, B. 1963b. Bargaining sets of cooperative games without side payments. Israel Journal of Mathematics 1, 197–200.
Peleg, B. 1985. An axiomatization of the core of cooperative games without side payments. Journal of Mathematical Economics 14, 203–14.
Peleg, B. 1986. On the reduced games property and its converse. International Journal of Game Theory 15, 187–200.
Peleg, B. 1992. Axiomatizations of the core. In Aumann and Hart (1992).
Peleg, B. and Sudholter, P. 2003. Introduction to the Theory of Cooperative Games. Dordrecht: Kluwer Academic Publications.
Peters, H.J.M. 1992. Axiomatic Bargaining Game Theory. Dordrecht: Kluwer Academic Publishers.
Peters, H., Tijs, S. and Zarzuelo, A. 1994. A reduced game property for the Kalai Smorodinsky and Egalitarian bargaining solution. Mathematical Social Sciences 27, 11–18.
Potters, J., Curiel, I. and Tijs, S. 1992. Traveling salesman game. Mathematical Programming 53, 199–211.
Raiffa, H. 1953. Arbitration schemes for generalized two-person games. In Contributions to the Theory of Games II, ed. H. Kuhn and A.W. Tucker. Princeton: Princeton University Press.
Riker, W.H. and Shapley, L.S. 1968. Weighted voting: a mathematical analysis for instrumental judgements. In Representation, ed. J.R. Pennock and J.W. Chapman. New York: Atherton.
Roth, A.E. 1977. The Shapley value as a von Neumann-Morgenstern utility. Econometrica 45, 657–64.
Roth, A.E. 1979. Axiomatic Models of Bargaining. Berlin and New York: Springer.
Roth, A.E. 1984. The evolution of the labor market for medical interns and residents: a case study in game theory. Journal of Political Economics 92, 991–1016.
Roth, A.E. and Verrecchia, R.E. 1979. The Shapley value as applied to cost allocation: a reinpt. Journal of Accounting Research 17, 295–303.
Rubinstein, A. 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109.
Scarf, H.E. 1967. The core of an n-person game. Econometrica 35, 50–69.
Schmeidler, D. 1969. The nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 17, 1163–70.
Schmeidler, D. 1972. Cores of exact games I. Journal of Mathematical Analysis and Application 40, 214–25.
Shapley, L.S. 1952. Notes on the n-person game Hi: some variants of the Von Neumann-Morgenstern definition of solution. Santa Monica: RAND Corporation RM 817.
Shapley, L.S. 1953. A value for n-person games. In Contributions to the Theory of Games II, ed. H. Kuhn and A.W. Tucker. Princeton: Princeton University Press.
Shapley, L.S. 1964. Values of large games, VII: a general exchange economy with money. Santa Monica: RAND Corporation RM 4248.
Shapley, L.S. 1967. On balanced sets and cores. Naval Research Logistics Quarterly 14, 453–60.
Shapley, L.S. 1969. Utility comparison and the theory of games. In La Décision. Paris: Edition du CNRS.
Shapley, L.S. 1971. Cores of convex games. International Journal of Game Theory 1, 11–26.
Shapley, L.S. 1973. Let’s block ‘block’. Econometrica 41, 1201–2.
Shapley, L.S. and Shubik, M. 1954. A method for evaluating the distribution of power in a committee system. American Political Science Review 48, 787–92.
Shapley, L.S. and Shubik, M. 1969a. On market games. Journal, of Economic Theory 1, 9–25.
Shapley, L.S. and Shubik, M. 1969b. Pure competition, coalitional power and fair division. International Economic Review 10, 337–62.
Shubik, M. 1959. Strategy and Market Structure: Competition, Oligopoly, and the Theory of Games. New York: Wiley.
Shubik, M. 1962. Incentives, decentralized control, the assignment of joint costs and internal pricing. Management Science 8, 325–43.
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.
Sprumont, Y. 1998. Ordinal cost sharing. Journal of Economic Theory 81, 26–162.
Tauman, Y. 1981. Value on a class of non-differentiable market games. International Journal of Game Theory 10, 155–62.
Tauman, Y 1988. The Aumann-Shapley prices: a survey. In The Shapley Value, ed. A. Roth. New York: Cambridge University Press.
Thomson, W. 1983. The fair division of a fixed supply among a growing population. Mathematics of Operations Research 8, 319–26.
Thomson, W. 1987. Monotonicity of bargaining solutions with respect to the disagreement point. Journal of Economic Theory 42, 50–8.
Thomson, W. 1994. Cooperative models of bargaining. Aumann and Hart 2002, 1237–84.
Valenciano, F. and Zarzuelo, J.M. 1994. On the interpretation of the nonsymmetric bargaining solutions and their extensions to nonexpected utility preferences. Games and Economic Behavior 7, 461–72.
Von Neumann, J. and Morgenstern, O. 1944. Theory of Games and Economic Behavior. Princeton: Princeton University Press.
Weber, R.J. 1988. Probabilistic values for games. In The Shapley Value, ed. A. Roth. Cambridge: Cambridge University Press.
Weber, R.J. 1994. Games in coalitional form. In Aumann and Hart (1994).
Wilson, R. 1978. Information, efficiency, and the core of an economy. Econometrica 46, 807–16.
Winter, E. 2002. The Shapley value. In Aumann and Hart (2002).
Wooders, M.H. and Zame, W.R. 1984. Approximate cores of large games. Econometrica 52, 1327–50.
Wooders, M.H. and Zame, W.R. 1987. Large games: fair and stable outcomes. Journal of Economic Theory 42, 59–63.
Young, H.P. 1985. Monotonie solutions of cooperative games. International Journal of Game Theory 14, 65–72.
Young, H.P. 1994. Cost allocation. In Aumann and Hart (1994).
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Durlauf, S.N., Blume, L.E. (2010). Games in Coalitional Form. In: Durlauf, S.N., Blume, L.E. (eds) Game Theory. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280847_13
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