Estate division problem: In search of a fair mechanism

F. Zak
Additional contact information
F. Zak: Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia

Journal of the New Economic Association, 2026, vol. 70, issue 1, 12-46

Abstract: . In the Nash Divide-the-Dollar (DD) game, n agents simultaneously submit claims on an estate of size E. If the total claim does not exceed E, each agent receives the amount requested; otherwise, all agents receive zero. The set of Nash equilibria coincides with the simplex of n-tuples of non-negative numbers summing to E. However, it is intuitively clear - and confirmed by experiments - that an equal division of the estate among the participants is the most reasonable and fair outcome. A large body of literature is devoted to resolving this tension by considering various mathematical models. Owing to its simplicity, the DD game serves as a prototype for many problems in which the question arises whether the standard tools of mathematical economics - such as different notions of equilibrium - can be modified to explain empirical data re?ecting the idea of fairness. In this survey article we review various modifications of the DD game, including those based on non-selfish preferences and bankruptcy rules. We discuss Nash and Kant equilibria (multiplicative and additive), models with restricted demands and penalties, as well as utility functions re?ecting different degrees of morality and inequality aversion.

Keywords: divide-the-dollar (DD) game; bankruptcy problem; bankruptcy rule; Nash equilibrium; Kant equilibrium; inequality aversion; homo moralis (search for similar items in EconPapers)
JEL-codes: C02 C62 C65 C78 D61 D62 D63 (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.econorus.org/repec/journl/2026-70-12-46r.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nea:journl:y:2026:i:70:p:12-46

DOI: 10.31737/22212264_2026_1_12-46

Access Statistics for this article

Journal of the New Economic Association is currently edited by Victor Polterovich and Aleksandr Rubinshtein

More articles in Journal of the New Economic Association from New Economic Association Contact information at EDIRC.
Bibliographic data for series maintained by Alexey Tcharykov ().