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Отсутствие зависти в задачах распределения большого числа неделимых благ
С. 36–37.
Maricheva A.
Language:
Russian
Publication based on the results of:
In book
М.: МИЭМ НИУ ВШЭ, 2016.
Moulin H., Aziz H., Sandomirskiy F., Operations Research Letters 2020 Vol. 48 No. 5 P. 573–578
We consider fair allocation of indivisible items under additive utilities. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric weights. The result does not hold if either of Pareto optimality ...
Added: August 25, 2020
Moulin H., Caragiannis I., Kurokawa D. et al., ACM Transactions on Economics and Computation 2018
The maximum Nash welfare (MNW) solution — which selects an allocation that maximizes the product of utilities — is known to provide outstanding fairness guarantees when allocating divisible goods. And while it seems to lose its luster when applied to indivisible goods, we show that, in fact, the MNW solution is unexpectedly, strikingly fair even ...
Added: October 19, 2018
Bogomolnaia A., Sandomirskiy F., Moulin H. et al., / NRU Higher School of Economics. Series EC "Economics". 2017. No. 158.
A mixed manna contains goods (that everyone likes), bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homothetic, concave (and monotone), the Competitive Equilibrium with Equal Incomes maximizes the Nash product of utilities: hence it ...
Added: March 2, 2017
Blank M., Problems of Information Transmission 2016 Vol. 52 No. 3 P. 299–307
We propose an elementary solution to the apartment rent division problem. This problem belongs to the class of problems of “fair division,” but differs from its standard setting by “heterogeneity,” i.e., the presence of both a conventional continuous component and a discrete one, a fixed set of rooms. A combinatorial-topological approach to solving this problem ...
Added: December 7, 2016
Bogomolnaia A., Moulin H., Sandomirskiy F. et al., / NRU Higher School of Economics. Series EC "Economics". 2016. No. 153.
When utilities are additive, we uncovered in our previous paper (Dividing Goods or Bads Under Additive Utilities) many similarities but also surprising di erences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads. The rule picks in both cases the critical points of the product of utilities ...
Added: November 14, 2016
Bogomolnaia A., Moulin H., Sandomirskiy F. et al., / Series arXiv:1610.03745 [cs.GT] "Computer Science". 2016.
When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads. The rule picks in both cases the critical points of the ...
Added: October 13, 2016
Moulin H., Caragiannis I., Kurokawa D. et al., , in: Proceeding of the 17th ACM Conference on Economics and Computation.: [б.и.], 2016.
The maximum Nash welfare (MNW) solution — which selects an allocation that maximizes the product of utilities — is known to provide outstanding fairness guarantees when allocating divisible goods. And while it seems to lose its luster when applied to indivisible goods, we show that, in fact, the MNW solution is unexpectedly, strikingly fair even ...
Added: June 8, 2016
Rubchinskiy A., / NRU Higher School of Economics. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2009. No. 05.
In the work the fair division problem for two participants in presence of both divisible and indivisible items is considered. The set of all the divisions is formally described; it is demonstrated that fair (in terms of Brams and Taylor) divisions, unlikely the case where all the items are divisible, not always exist. The necessary ...
Added: March 23, 2013