This is a list of questions and topics I would like to research. If you find any of them interesting and would like to collaborate, drop me an email.

Working papers

These papers need co-authors in order to realize their full potential:

  1. Fair cake-cutting among groups: Mostly related to economics but contains some algorithmic content. It is about fair division of resources that are enjoyed by a whole group, such as a family or a country, rather than by a single individual. A collaborator could help to improve and add new results.

  2. How to re-divide a cake fairly?: Combines computational geometry, combinatoris, economics and social choice. I am looking for experts in any of these fields in order to help verify and improve the results.

  3. A Tradeoff Between Fairness and Efficiency in Cake-Cutting: Motivated by economics, but the techniques are mostly combinatorial. A collaborator who is proficient in combinatorics will surely find new results easily.

Reasearch projects

  1. Experiments in fair division. I have some simulation results on fair division of land, and an online game for experiments with humans on fair cake-cutting. I need partners to advance.

  2. Implementing fair division algorithms in real-estate projects. Currently, apartments are divided by lottery and/or protection… There are better ways and I would like to check how they can be implemented.

Open Questions

I would very much like to know the answer to the following questions.

  1. When value-densities can be both positive and negative, does there always exist a connected envy-free division for 4 or more agents? Mainly a question in algebraic topology. May be related to combinatorics. My working paper has a solution for 3 agents.

  2. How many cuts are required for cake-cutting when the agents have different entitlements? Mainly a combinatorics question. May be related to measure theory and topology. My MathOverflow question has some preliminary results.

  3. Does there always exist a Pareto-efficient envy-free allocation of “family goods”? Mainly an economics question. My economics.SE question has some more details. Our group cake-cutting paper solves a related but easier problem.

  4. Is it possible to find in bounded time an envy-free and proportional cake-division with connected pieces? Mainly an algorithmic question. The Wikipedia page I wrote on envy-free cake-cutting gives some background. Our waste-makes-haste paper presents the current status.

  5. Given a collection of points in the plane, what is the largest possible collection of pairwise-disjoint wet-squares? Mainly a geometric question. This draft presents the question formally and gives some directions. Our fair-and-square papers (extended abstract and full preprint) present the economic motivation.