Abstract
In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way —giving each agent a piece with a value of at least 1∕n of the total. In many applications, such as dividing a land-estate or a time-interval, it is also important that the pieces are connected. We propose two additional requirements: resource-monotonicity (RM) and population-monotonicity (PM). When either the cake or the set of agents grows or shrinks and the cake is re-divided using the same rule, the utility of all remaining agents must change in the same direction. Classic cake-cutting protocols are neither RM nor PM. Moreover, we prove that no Pareto-optimal proportional division rule can be either RM or PM. Motivated by this negative result, we search for division rules that are weakly-Pareto-optimal — no other division is strictly better for all agents. We present two such rules. The relative-equitable rule, which assigns the maximum possible relative value equal for all agents, is proportional and PM. The so-called rightmost mark rule, which is an improved version of the Cut and Choose protocol, is proportional and RM for two agents.
| Original language | English |
|---|---|
| Pages (from-to) | 19-30 |
| Number of pages | 12 |
| Journal | Mathematical Social Sciences |
| Volume | 95 |
| DOIs | |
| State | Published - Sep 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2018 Elsevier B.V.
Funding
The idea of this paper was born in the COST Summer School on Fair Division in Grenoble , 7/2015 (FairDiv-15). We are grateful to COST and the conference organizers for the wonderful opportunity to meet with fellow researchers from around the globe. In particular, we are grateful to Ioannis Caragiannis, Ulle Endriss and Christian Klamler for sharing their insights on cake-cutting. We are also thankful to Marcus Berliant, Shiri Alon-Eron, Christian Blatter and Ilan Nehama for their very helpful comments. This research was supported by the Higher Education Institutional Excellence Program of the Ministry of Human Capacities in the framework of the ‘ Financial and Retail Services ’ research project ( 1783-3/2018/FEKUTSTRAT ) at the Corvinus University of Budapest. The authors acknowledge the support of Hungarian National Research, Development and Innovation Office , grant no. K124550 , the ISF grants 1083/13 and 1394/16 , the Doctoral Fellowships of Excellence Program, the Wolfson Chair and the Mordecai and Monique Katz Graduate Fellowship Program at Bar-Ilan University. The idea of this paper was born in the COST Summer School on Fair Division in Grenoble, 7/2015 (FairDiv-15). We are grateful to COST and the conference organizers for the wonderful opportunity to meet with fellow researchers from around the globe. In particular, we are grateful to Ioannis Caragiannis, Ulle Endriss and Christian Klamler for sharing their insights on cake-cutting. We are also thankful to Marcus Berliant, Shiri Alon-Eron, Christian Blatter and Ilan Nehama for their very helpful comments. This research was supported by the Higher Education Institutional Excellence Program of the Ministry of Human Capacities in the framework of the ‘Financial and Retail Services’ research project (1783-3/2018/FEKUTSTRAT) at the Corvinus University of Budapest. The authors acknowledge the support of Hungarian National Research, Development and Innovation Office, grant no. K124550, the ISF grants 1083/13 and 1394/16, the Doctoral Fellowships of Excellence Program, the Wolfson Chair and the Mordecai and Monique Katz Graduate Fellowship Program at Bar-Ilan University.
| Funders | Funder number |
|---|---|
| Corvinus University of Budapest | |
| Mordecai and Monique Katz Graduate Fellowship Program at Bar-Ilan University | |
| Wolfson Chair | |
| Iowa Science Foundation | |
| Israel Science Foundation | 1083/13, 1394/16 |
| Emberi Eroforrások Minisztériuma | 1783-3/2018/FEKUTSTRAT |
| National Research, Development and Innovation Office | K124550 |