Previous |  Up |  Next


optimal partitioning; nonatomic finite measure; nonadditive set function; Pareto optimality; core
This paper investigates the problem of optimal partitioning of a measurable space among a finite number of individuals. We demonstrate the sufficient conditions for the existence of weakly Pareto optimal partitions and for the equivalence between weak Pareto optimality and Pareto optimality. We demonstrate that every weakly Pareto optimal partition is a solution to the problem of maximizing a weighted sum of individual utilities. We also provide sufficient conditions for the existence of core partitions with non- transferable and transferable utility.
[1] Barbanel J. B., Zwicker W. S.: Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division. Theory and Decision 43 (1997), 203–207 DOI 10.1023/A:1004966624893 | MR 1470217
[2] Bondareva O. N.: Some applications of linear programming methods to the theory of cooperative games (in Russian). Problemy Kibernet. 10 (1963), 119–139 MR 0167335
[3] Dubins L. E., Spanier E. H.: How to cut a cake fairly. Amer. Math. Monthly 68 (1961), 1–17 DOI 10.2307/2311357 | MR 0129031 | Zbl 0108.31601
[4] Legut J.: Market games with a continuum of indivisible commodities. Internat. J. Game Theory 15 (1986), 1–7 DOI 10.1007/BF01769272 | MR 0839092 | Zbl 0651.90099
[5] Sagara N.: An Existence Result on Partitioning of a Measurable Space: Equity and Efficiency. Faculty of Economics, Hosei University 2006, mimeo
[6] Sagara N., Vlach M.: Representation of Convex Preferences in a Nonatomic Measure Space: $\varepsilon $-Pareto Optimality and $\varepsilon $-Core in Cake Division. Faculty of Economics, Hosei University 2006, mimeo
[7] Scarf H. E.: The core of an $N$ person game. Econometrica 35 (1967), 50–69 DOI 10.2307/1909383 | MR 0234735 | Zbl 0183.24003
[8] Shapley L.: On balanced sets and cores. Naval Res. Logist. 14 (1967), 453–460 DOI 10.1002/nav.3800140404
Partner of
EuDML logo