Pairwise efficiency and monotonicity imply Pareto efficiency in (probabilistic) object allocation We consider object allocation problems with capacities (see, e.g., Abdulkadiroglu and Sonmez, 1998; Basteck, 2025) where objects have to be assigned to agents. We show that if a lottery rule satisfies...

Everyone is assigned one object, and you know that no pair of agents wants to swap their objects.

When can you be sure that there will also not exist a group of any size (larger than two) who want to exchange their objects?

Find the answer in our WP (with Bettina Klaus): arxiv.org/abs/2508.05340

A theory of fair random allocation under priorities You have to enable JavaScript in your browser's settings in order to use the eReader.

Just read a fantastic paper by Xiang Han.

For everyone interested in matching problems, I highly recommend sitting down and reading his work, it's a fresh and unifying perspective on such a well-studied topic.

onlinelibrary.wiley.com/share/MYZZFH...

Quantifying Core Stability Relaxations in Hedonic Games We study relationships between different relaxed notions of core stability in hedonic games, which are a class of coalition formation games. Our unified approach applies to a newly introduced family o...

The core can be empty in many variants of coalition formation games. In our new working paper, we quantify the relationship between two intuitive concepts of core relaxation in hedonic games.

Find out why larger blocking coalitions might sometimes be worse off in: arxiv.org/abs/2412.01666.