Two-Person Fair Division with Additive Valuations

In the literature, many desirable properties for allocations of indivisible goods have been proposed, including envy-freeness, Pareto optimality, and maximization of either the total welfare of all agents, the welfare of the worst-off agent, or the Nash product of agents’ welfares. In the two-person...

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Bibliographic Details
Published inGroup decision and negotiation Vol. 33; no. 4; pp. 745 - 774
Main Authors Kilgour, D. Marc, Vetschera, Rudolf
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2024
Springer Nature B.V
Subjects
Additives
Biological and Physical Anthropology
Business and Management
Diamonds
Efficiency
Envy
Indivisible goods
Pareto optimum
Preferences
Simulation
Welfare
Cardinal utilities
Envy-freeness
Fair division
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Summary:In the literature, many desirable properties for allocations of indivisible goods have been proposed, including envy-freeness, Pareto optimality, and maximization of either the total welfare of all agents, the welfare of the worst-off agent, or the Nash product of agents’ welfares. In the two-person context, we study relationships among these properties using both analytical models and simulation in a setting where individual preferences are given by additive cardinal utilities. We provide several new theorems linking these criteria and use simulation to study how their values are related to problem characteristics, assuming that utilities are assigned randomly. We draw some conclusions concerning the relation of problem characteristics to the availabilty of allocations with particular properties.
ISSN:0926-2644
1572-9907
DOI:10.1007/s10726-024-09885-x