Abstract
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group receives a single contiguous piece and every player is envy-free. For two groups, we characterize the group sizes for which such an assignment can be computed by a finite algorithm, showing that the task is possible exactly when one of the groups is a singleton. We also establish an analogous existence result for chore division, and show that the result does not hold for a mixed cake.
| Original language | English |
|---|---|
| Pages (from-to) | 203-213 |
| Number of pages | 11 |
| Journal | American Mathematical Monthly |
| Volume | 130 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.
Funding
This work was partially supported by the Israel Science Foundation under grant number 712/20, by the Singapore Ministry of Education under grant number MOE-T2EP20221-0001, and by an NUS Start-up Grant. The authors wish to thank the editor and the anonymous reviewers for several constructive comments.
| Funders | Funder number |
|---|---|
| National University of Singapore | |
| Ministry of Education - Singapore | MOE-T2EP20221-0001 |
| Israel Science Foundation | 712/20 |