Abstract
The Shapley value is an a priori evaluation of the prospects of a player in a multi-person game. Introduced by Lloyd S. Shapley in 1953, it has become a central solution concept in cooperative game theory. The Shapley value has been applied to economic, political, and other models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Aumann, R.J. 1975. Values of markets with a continuum of traders. Econometrica 43: 611–646.
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: 667–678.
Aumann, R.J., and J.H. Drèze. 1974. Cooperative games with coalition structures. International Journal of Game Theory 3: 217–237.
Aumann, R.J., and S. Hart, eds. 1992 [HGT1], 1994 [HGT2], 2002 [HGT3]. Handbook of game theory, with economic applications, vols. 1–3. Amsterdam: North-Holland.
Aumann, R.J., and M. Kurz. 1977. Power and taxes. Econometrica 45: 1137–1161.
Aumann, R.J., and L.S. Shapley. 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: 317–343.
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.
Dubey, P., and L.S. Shapley. 1979. Mathematical properties of the Banzhaf power index. Mathematics of Operations Research 4: 99–131.
Dubey, P., A. Neyman, and R.J. Weber. 1981. Value theory without efficiency. Mathematics of Operations Research 6: 122–128.
Gul, F. 1989. Bargaining foundations of Shapley value. Econometrica 57: 81–95.
Gul, F. 1999. Efficiency and immediate agreement: A reply to Hart and Levy. Econometrica 67: 913–918.
Harsanyi, J.C. 1963. A simplified bargaining model for the n-person cooperative game. International Economic Review 4: 194–220.
Hart, S., and M. Kurz. 1983. Endogenous formation of coalitions. Econometrica 51: 1047–1064.
Hart, S., and Z. Levy. 1999. Efficiency does not imply immediate agreement. Econometrica 67: 909–912.
Hart, S., and A. Mas-Colell. 1989. Potential, value and consistency. Econometrica 57: 589–614.
Hart, S., and A. Mas-Colell. 1996. Bargaining and value. Econometrica 64: 357–380.
Littlechild, S.C., and G. Owen. 1973. A simple expression for the Shapley value in a special case. Management Science 20: 370–372.
Maschler, M., and G. Owen. 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: 225–229.
Nash, J.F. 1950. The bargaining problem. Econometrica 18: 155–162.
Owen, G. 1971. Political games. Naval Research Logistics Quarterly 18: 345–355.
Owen, G. 1977. Values of games with a priori unions. In Essays in mathematical economics and game theory, ed. R. Henn and O. Moeschlin. New York: Springer.
Penrose, L.S. 1946. The elementary statistics of majority voting. Journal of the Royal Statistical Society 109: 53–57.
Roth, A.E. 1977. The Shapley value as a von Neumann–Morgenstern utility. Econometrica 45: 657–664.
Shapley, L.S. 1953a. A value for n-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: 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: 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: American Mathematical Society.
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.
Shubik, M. 1962. Incentives, decentralized control, the assignment of joint costs and internal pricing. Management Science 8: 325–343.
Winter, E. 1994. The demand commitment bargaining and snowballing cooperation. Economic Theory 4: 255–273.
Young, H.P. 1985. Monotonic solutions of cooperative games. International Journal of Game Theory 14: 65–72.
Author information
Authors and Affiliations
Editor information
Copyright information
© 2018 Macmillan Publishers Ltd.
About this entry
Cite this entry
Hart, S. (2018). Shapley Value. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1369
Download citation
DOI: https://doi.org/10.1057/978-1-349-95189-5_1369
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences