Freitag, 12. Mai 2023, 10:00 - 11:30 iCal

Two-person fair allocation of indivisible items

D. Marc Kilgour,

Rudolf Vetschera,


presented by D. Marc Kilgour

Hörsaal 9
Oskar-Morgenstern-Platz 1, 1090 Wien

Antrittsvorlesung, Public Lecture

Whether independent agents can share a resource fairly is an important and easily understood social choice problem. Can each agent be assigned a satisfactory portion of the total, or is it impossible to reconcile their conflicting interests? Among the criteria that have been proposed for a good allocation are maximum total utility, identified with utilitarianism, and maximum Nash utility, which has been called “unreasonably effective.” The Rawlsian idea of maximizing the minimum utility of any agent is also applicable. Yet another criterion is envy-freeness: one agent envies another if it prefers the other’s assignment to its own; in an envy-free allocation, no agent envies any other.


This presentation assumes a finite set of indivisible items, over which each of two players has known preferences. Preference is measured on a cardinal scale and is additive in that each player’s utility for any bundle of items is the sum of its utilities for the specific items in the bundle.


Even in the two-player case, it is possible that no envy-free allocation exists. A recent discovery is that the key to envy-freeness is maximinality – an envy-free allocation exists if and only if a maximin allocation gives each player at least half of the total utility in its own measure. Moreover, when this condition fails – so that no envy-free allocation exists – there is always an allocation with the related property called EFx. The focus here is on the existence of envy-freeness and its relation with desirable properties including efficiency, maximum utility sum, and maximum Nash product. After a formal study of what is possible, a comprehensive simulation is conducted to measure the frequencies of the various possibilities.


The objective of this study is to identify properties of allocation problems that can potentially simplify the task of fair allocation, demonstrate their existence and relationships, and assess how difficult they are to use in simulations.





Brams, Steven J., D. Marc Kilgour, Christian Klamler, and Fan Wei, “Two-Person Fair Division of Indivisible Items: Bentham vs. Rawls on Envy.” To appear, Journal of Philosophy, 2023.

Kilgour, D. Marc and Rudolf Vetschera, “Two-person fair division with additive cardinal valuations,” to be presented at GDN 2023, Tokyo, Japan, June 2023.



Institut für Business Decisions and Analytics


Elitsa Nestorova
Fakultät für Wirtschaftswissenschaften
Institut für Business Decision and Analytics