Abstract
The ancient problems of bankruptcy, contested garment, and rights arbitration have generated many studies, debates, and controversy. The objective of this paper is to show that the Shapley value from game theory, measuring the power of each player in a game, may be consistently applied for getting the general one-step solution of all these three problems viewed as n-person games. The decision making is based on the same tool, namely the game theory logic based on the use of the Shapley value, but the specific games involved are slightly different in each problem. The kind of claims of the players, the relationship between the given claims and the given resources available, and the particular way of calculating the generalized characteristic function of the game determine the specific type of game which has to be solved in each of the three ancient problems mentioned. The iterative use of the Shapley value may also justify the well-known Aumann–Maschler step-by-step procedure for solving the bankruptcy problem.
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References
Alcade J., Marco M. del C., Silva J. A. (2005) Bankruptcy games and the Ezra’s proposal. Economic Theory 26: 103–114
Aumann R. J., Maschler M. (1985) Game-theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36: 195–213
De Mesnard, L. (2008). On the Talmud division: Equity and robustness. Congrès AFSE (Social Science Research Network SSRN), 1–27.
Gura, E.-Y. (2009). Insights into the game theory: An alternative mathematical experience. In Quaderni di Ricerca Didattica. G.R.I.M. (Department of Mathematics, University of Palermo, Italy), n. 19, pp. 172–183.
Moulin H. J. (1992) An application of the Shapley value to fair division with money. Econometrics 60: 1331–1349
Moulin H. J. (2003) Fair division and collective welfare. MIT Press, Cambridge, MA
O’Neill B. (1982) A problem of rights arbitration from the Talmud. Mathematical Social Sciences 2: 345–371
Shapley L. S. (1953) A value for n-person games. Annals of Mathematical Studies 28: 307–317
Thomson W. (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: A survey. Mathematical Social Sciences 45: 249–297
Winston W. L. (1994) Operations research. Applications and algorithms (3rd ed.). Duxbury Press, Wadsworth Publishing Co, Belmont CA
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Guiasu, S. Three ancient problems solved by using the game theory logic based on the Shapley value. Synthese 181 (Suppl 1), 65–79 (2011). https://doi.org/10.1007/s11229-010-9818-z
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DOI: https://doi.org/10.1007/s11229-010-9818-z