Additive rules in bankruptcy problems and other related problems. (English) Zbl 1092.91056
There are four kinds of problems in dividing an estate among several agents. In bankruptcy problems, each agent is to receive between 0 and his claim. In allocation problems, agents can receive anything. In surplus problems, every agent must received at least 0. In loss problems, every agent must receive at most his claim. This paper characterizes the set of rules satisfying additivity on the estate along with additivity on the estate and the claims in these problems.
Reviewer: Elias Shiu (Iowa City)
MSC:
| 91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |
| 91B99 | Mathematical economics |
References:
| [1] | Aczél, J.; Dhombres, J., Functional equations in several variables, (Rota, G. C., Encyclopedia of Mathematics and its Applications, Vol. 31 (1989), Cambridge University Press) · Zbl 0685.39006 |
| [2] | Aumann, R. J.; Maschler, M., Game theoretic analysis of a bankruptcy problem from the Talmud, Journal of Economy Theory, 36, 195-213 (1985) · Zbl 0578.90100 |
| [3] | Bergantiños, G.; Méndez-Naya, L., Additivity in bankruptcy problems and in allocation problems, Spanish Economic Review, 3, 223-229 (2001) |
| [4] | Chun, Y., The proportional solution for rights problems, Mathematical Social Sciences, 15, 231-246 (1988) · Zbl 0657.92020 |
| [5] | De Frutos, M. A., Coalitional manipulation in a bankruptcy problem, Review of Economic Design, 4, 255-272 (1999) |
| [6] | Herrero, C.; Maschler, M.; Villar, A., Individual rights and collective responsibility: the rights-egalitarian solution, Mathematical Social Sciences, 37, 59-77 (1999) · Zbl 0953.91008 |
| [7] | Moulin, H., Equal or proportional division of a surplus, and other methods, International Journal of Game Theory, 16, 161-186 (1987) · Zbl 0631.90093 |
| [8] | Moulin, H., Priority rules and other inequitable rationing methods, Econometrica, 68, 643-684 (2000) · Zbl 1038.91536 |
| [9] | Moulin, H., Axiomatic cost and surplus sharing, (Arrow, K.; Sen, A.; Suzumura, K., Handbook of Social Choice and Welfare (2002), Elsevier: Elsevier Amsterdam), 289-357 |
| [10] | O’Neill, B., A problem of rights arbitration from the Talmud, Mathematical Social Sciences, 2, 345-371 (1982) · Zbl 0489.90090 |
| [11] | Thomson, W., Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey, Mathematical Social Sciences, 45, 249-297 (2003) · Zbl 1042.91014 |
| [12] | Young, P., Distributive justice in taxation, Journal of Economic Theory, 43, 321-335 (1988) · Zbl 0637.90027 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
