Abstract
The value of an uncertain outcome (a ‘lottery’) is an a priori measure, in the participant’s utility scale, of what he expects to obtain (this is the subject of ‘utility theory’). The question is, how would one evaluate the prospects of a player in a multiperson interaction, that is, in a game?
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Bibliography
Aumann, R.J. 1975. Values of markets with a continuum of traders. Econometrica 43, 611–46.
Aumann, R.J. 1978. Recent developments in the theory of the Shapley Value. Proceedings of the International Congress of Mathematicians, Helsinki.
Aumann, R.J. 1985. On the non-transferable utility value: a comment on the Roth-Shafer examples. Econometrica 53, 667–78.
Aumann, R.J. and Drèze, J.H. 1974. Cooperative games with coalition structures. International Journal of Game Theory 3, 217–37.
Aumann, R.J. and Hart, S., eds. 1992 [HGT1], 1994 [HGT2], 2002 [HGT3]. Handbook of Game Theory, with Economic Applications, vols 1–3. Amsterdam: North-Holland.
Aumann, R.J. and Kurz, M. 1977. Power and taxes. Econometrica 45, 1137–61.
Aumann, R.J. and Shapley, L.S. 1974. Values of Non-atomic Games. Princeton: Princeton University Press.
Banzhaf, J.F. 1965. Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Review 19, 317–13.
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.
Dubey, P., Neyman, A. and Weber, R.J. 1981. Value theory without efficiency. Mathematics of Operations Research 6, 122–8.
Dubey, P. and Shapley, L.S. 1979. Mathematical properties of the Banzhaf Power Index. Mathematics of Operations Research 4, 99–131.
Gui, F. 1989. Bargaining foundations of Shapley value. Econometrica 57, 81–95.
Gui, F. 1999. Efficiency and immediate agreement: a reply to Hart and Levy. Econometrica 67, 913–18.
Harsanyi, J.C. 1963. A simplified bargaining model for the «-person cooperative game. International Economic Review 4, 194–220.
Hart, S. and Kurz, M. 1983. Endogenous formation of coalitions. Econometrica 51, 1047–64.
Hart, S. and Levy, Z. 1999. Efficiency does not imply immediate agreement. Econometrica 67, 909–12.
Hart, S. and Mas-Colell, A. 1989. Potential, value and consistency. Econometrica 57, 589–614.
Hart, S. and Mas-Colell, A. 1996. Bargaining and value. Econometrica 64, 357–80.
Littlechild, S.C. and Owen, G. 1973. A simple expression for the Shapley value in a special case. Management Science 20, 370–72.
Maschler, M. and Owen, G. 1992. The consistent Shapley value for games without side payments. In Rational Interaction: Essays in Honor of John Harsanyi, ed. R. Selten. New York: Springer.
Myerson, R.B. 1977. Graphs and cooperation in games. Mathematics of Operations Research 2, 225–29.
Nash, J.F. 1950. The bargaining problem. Econometrica 18, 155–62.
Owen, G. 1971. Political games. Naval Research Logistics Quarterly 18, 345–55.
Owen, G. 1977. Values of games with a priori unions. In Essays in Mathematical Economics and Game Theory, ed. R. Herrn and O. Moeschlin. New York: Springer.
Penrose, L.S. 1946. The elementary statistics of majority voting. Journal of the Royal Statistical Society 109, 53–7.
Roth, A.E. 1977. The Shapley value as a von Neumann-Morgenstern utility. Econometrica 45, 657–64.
Shapley, L.S. 1953a. A value for «-person games. In Contributions to the Theory of Games, II, ed. H.W. Kuhn and A.W. Tucker. Princeton: Princeton University Press.
Shapley, L.S. 1953b. Additive and non-additive set functions. Ph.D. thesis, Princeton University.
Shapley, L.S. 1964. Values of large games VII: a general exchange economy with money. Research Memorandum 4248-PR. Santa Monica, CA: RAND Corp.
Shapley, L.S. 1969. Utility comparison and the theory of games. In La Décision: agrégation et dynamique des ordres de préférence. Paris: Editions du CNRS.
Shapley, L.S. 1977. A comparison of power indices and a nonsymmetric generalization. Paper No. P-5872. Santa Monica, CA: RAND Corp.
Shapley, L.S. 1981. Measurement of power in political systems. Game Theory and its Applications, Proceedings of Symposia in Applied Mathematics, vol. 24. Providence, RI: American Mathematical Society.
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.
Shubik, M. 1962. Incentives, decentralized control, the assignment of joint costs and internal pricing. Management Science 8, 325–43.
Winter, E. 1994. The demand commitment bargaining and snowballing cooperation. Economic Theory 4, 255–73.
Young, H.P. 1985. Monotonie solutions of cooperative games. International Journal of Game Theory 14, 65–72.
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Durlauf, S.N., Blume, L.E. (2010). Shapley value. In: Durlauf, S.N., Blume, L.E. (eds) Game Theory. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280847_33
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DOI: https://doi.org/10.1057/9780230280847_33
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