Comparative review of allowances types for dividing a benefit with indivisible items
https://doi.org/10.26425/1816-4277-2024-10-92-99
Abstract
The article studies the issues related to the problem of sharing by two beneficiaries of a resource with a set of indivisible components. Several types of sharing that consider “envy” and realize it, including through compensatory payments to the beneficiary who does not get the corresponding indivisible component of the resource, have been noted. The difference between the values of possible bonuses at different types of sharing, which are received in addition to the values declared by the beneficiaries, and indivisible components when they are evaluated, has been determined. It has been found in which case it is more favorable for the beneficiary if “envy” is not considered, and vice versa. The method of setting the degree of preference of considering “envy” in the course of distribution of resource components has been proposed, assuming a preliminary agreement of beneficiaries on the use of this method. The result of using it has been analyzed, based on which recommendations to the beneficiaries are formulated, implying additional awareness not covered in the present study. In order to circumvent the issue of uninformedness, indications of one option of its solution have been presented, which can be considered also as possible future directions of research of stochastic nature.
About the Author
V. V. Egorov
State University of Management
Russian Federation
Russian Federation
Vladislav V. Egorov - Cand. Sci. (Phys. and Math.), Assoc.Prof. at the Mathematical Methods in Economics and Management Department
Moscow
References
1. Fromm E. The Anatomy of Human Destructiveness. New York: Henry Holt; 1973. 576 p.
2. Moulin H. Axioms of cooperative decision making. New York: Cambridge University Press; 1988. 332 p. https://doi.org/10.1017/CCOL0521360552
3. Ledyard J. The insolvency (failures) of the market. In: Eatwell J., Milgate M., Newman P. Economic theory. Moscow: Infra-M; 2004. Pp. 501–508. (In Russian).
4. Brams S.J., Taylor A.D. Fair division. From cake-cutting to dispute resolution. New York: Cambridge University Press; 1996. 272 p. https://doi.org/10.1017/S0892679400008017
5. Brams S.J., Taylor A.D. The Win–Win Solution. New York: W.W. Norton; 1999. 192 p.
6. Aleskerov F.T., Khabina E.L., Schwartz D.A. Binary relations, graphs and collective solutions. Moscow: Fizmatlit; 2012. 344 p. (In Russian).
7. Brams S., Kilgour D.M., Klamler C. Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm. SSRN (Social Science Research Network); 2013.
8. Rubchinsky A. Fair Division with Divisible and Indivisible Items. Moscow: HSE Laboratory of Decision Choice and Analysis as proxy; 2016. https://doi.org/10.48550/arXiv.1607.02423
9. Egorov V.V. On one modification of the method of dividing the indivisible inheritance. In: Bogachkova L.Yu., Davnis V.V. (ed.) Analysis, modeling and forecasting of economic processes – 2010: Proceedings of the II International Scientific & Practical Internet Conference, Volgograd, December 15, 2010. Voronezh: Tsentr nauchno-tekhnicheskoy informatsii; 2010. Pp. 127–132. (In Russian).
10. Egorov V.V. Comparative analysis of the methods of distribution of compensation for the division of indivisible goods between several persons. In: Bogachkova L.Yu., Davnis V.V. (ed.) Analysis, modeling and forecasting of economic processes – 2012: Proceedings of the IV International Scientific & Practical Internet Conference, Volgograd, December 15, 2012. Voronezh: Tsentr nauchno-tekhnicheskoy informatsii; 2012. Pp. 83–86. (In Russian).
11. Egorov V.V. On the consideration of envy in the distribution of compensation for the division of indivisible goods between several persons. In: Bogachkova L.Yu., Davnis V.V. (ed.) Analysis, modeling and forecasting of economic processes – 2013: Proceedings of the V International Scientific & Practical Internet Conference, Volgograd, December 15, 2013. Volgograd: Konsaltingovoe agentstvo; 2013. Pp. 133–135. (In Russian).
12. Rosner S., Tamir T. Cost-Sharing Games with Rank-Based Utilities. Algorithmic Game Theory. SAGT 2022. Lecture Notes in Computer Science. Springer, Cham. 2022;13584:275–292. https://doi.org/10.1007/978-3-031-15714-1_16
13. Winter E., Mendez-Naya L., Garcia-Jurado I. Mental Equilibrium and Strategic Emotions. Management Science. 2016;5(63):1302–1317. https://doi.org/10.1287/mnsc.2015.2398
14. Heinen T., Nguyen N.T., Rothe J. Fairness and Rank-Weighted Utilitarianism in Resource Allocation. Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science. Springer, Cham. 2015;9346:521–536. https://doi.org/10.1007/978-3-319-23114-3_31
15. Heinen T., Nguyen N.T., Nguyen T.T. Approximation and complexity of the optimization and existence problems for maximin share, proportional share, and minimax share allocation of indivisible goods. Auton Agent Multi-Agent Syst. 2018;32:741–778. https://doi.org/10.1007/s10458-018-9393-0
Review
For citations:
Egorov V.V. Comparative review of allowances types for dividing a benefit with indivisible items. Vestnik Universiteta. 2024;(10):92-99. (In Russ.) https://doi.org/10.26425/1816-4277-2024-10-92-99
Views:
97
Email this article 