Abstract
Cooperative game theory begins with descriptions of coalitional behavior. For every permissible coalition, a subset of the players of the game, there is a given set of feasible outcomes for its members. Each outcome is presupposed to arise from cooperative behavior by the members of the coalition; specific individual actions are secondary.1 Cooperative games take several forms—games with side payments, games without side payments, partition function form games, and others, including, for example, bargaining games. In this paper we focus on games with and without side payments.
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References
Aumann, R. J. (1959). Acceptable Points in General Cooperative N-Person Games. In Tucker, A. W. and Luce, R. D., editors, Contributions to the Theory of Games, vol. 4, Annals of Math. Studies 40, pages 287–324. Princeton University Press, Princeton.
Aumann, R. J. (1960). Linearity of Unrestricted Transferable Utilities. Naval Research Logistics Quarterly, 7:281–284.
Aumann, R. J. (1961). The Core of a Cooperative Game Without Side Payments. Transactions AMS, 9(8):539–552.
Aumann, R. J. (1981). Survey of Repeated Games. In Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern, pages 11-42. Bibliographishes Institut.
Aumann, R. J. (1985a). An Axiomatization of the Non-Transferable Utility value. Econometrica, 53:599–612.
Aumann, R. J. (1985b). On the Non-Transferable Utility Value: A Comment on the Roth-Shafer Examples. Econometrica, 53:667–677.
Aumann, R. J. (1986). Rejoinder. Econometrica, 54:985–989.
Aumann, R. J. (1987). Value, Symmetry, and Equal Treatment: A Comment on Scafuri and Yannelis. Econometrica, 55:1461–1464.
Aumann, R. J. and Maschler, M. (1964). The Bargaining Set for Cooperative Games. In Dresher, M., Shapley, L. S., and Tucker, A. W., editors, Advances in Game Theory, pages 443–476. Princeton University Press, Princeton.
Davis, M. Maschler, M. (1965). The Kernel of a Cooperative Game. Naval Research Logistics Quarterly, 12:223–259.
Debreu, G. (1959). Theory of Value. John Wiley and Sons, New York.
Hammond, P. J. (1998). Objectively Expected Utility. In Barberà , S., Hammond, P. J., and Seidl, C., editors, Handbook of Utility Theory, volume 1, pages 143–211. Kluwer, Dordrecht.
Herstein, I. N. and Milnor, J. (1953). An Axiomatic Approach to Measurable Utility. Econometrica, 21:291–297.
Hicks, J. R. (1956). A Revision of Demand Theory. Oxford University Press, Oxford.
Kaneko, M. (1975). Necessary and Sufficient Conditions for the Nonemptiness of the Core of a Voting Game. International Journal of Game Theory, 4:215–219.
Kaneko, M. (1976). On Transferable Utility. International Journal of Game Theory, 5:183–185.
Kaneko, M. (1983). Housing Markets with Indivisibilities. Journal of Urban Economics, 13:22–50.
Moulin, H. (1988). Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge.
Nakamura, K. (1975). The Core of a Simple Game Without Ordinal Preferences. International Journal of Game Theory, 4:95–104.
Negishi, T. (1960). Welfare Economics and Existence of an Equilibrium for a Competitive Economy. Metroeconomica, 12:92–97.
Rawls, J. (1970). A Theory of Justice. Harvard University Press, Boston.
Roth, A. E. (1980). Values for Games Without Sidepayments; Some Difficulties With Current Concepts. Econometrica, 48:457–465.
Roth, A. E. (1986). On the Non-Transferable Utility Value: A Reply to Aumann. Econometrica, 54:981–984.
Scafuri, A. J. and Yannelis, N. (1984). Non-Symmetric Cardinal Value Allocations. Econometrica, 52:1365–1368.
Scarf, H. E. (1967). The Core of an N-Person Game. Econometrica, 35:50–69.
Scarf, H. E. (1971). On the Existence of a Cooperative Solution for a General Class of N-Person Games. Journal of Economic Theory, 3:169–181.
Schmeidler, D. (1969). The Nucleolus of a Characteristic Function Game. SIAM Journal of Applied Mathematics, 17:1163–1170.
Shapley, L. S. (1953). A Value for N-Person Games. In Kuhn, H. and Tucker, A. W., editors, Contributions to the Theory of Games, vol. 1, Annals of Mathematical Studies No. 24, pages 307–317. Princeton University Press, Princeton.
Shapley, L. S. (1969). Utility Comparisons and the Theory of Games. In La Decision: Agregation et Dynamique des Ordres de Preference, pages 251–261, Paris. Editions du Centre National de la Recherche Scientifique.
Shapley, L. S. and Shubik, M. (1966). On Market Games. Journal of Economic Theory, 1:9–25.
Shapley, L. S. and Shubik, M. (1971). The Assignment Game I: The Core. International Journal of Game Theory, 1:11–30.
Shubik, M. (1984). Game Theory in the Social Sciences. MIT Press.
Uzawa, H. (1958). The Kuhn-Tucker Theorem in Concave Programming. In Arrow, K. J., Hurwicz, L., and Uzawa, H., editors, Studies in Linear and Nonlinear Programming, pages 32–37. Stanford University Press, Stanford.
von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press, Princeton.
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Kaneko, M., Wooders, M.H. (2004). Utility Theories in Cooperative Games. In: BarberĂ , S., Hammond, P.J., Seidl, C. (eds) Handbook of Utility Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4020-7964-1_6
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DOI: https://doi.org/10.1007/978-1-4020-7964-1_6
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