On the Core of Markets with Co-ownerships and Indivisibilities

Following Balbuzanov and Kotowski (2019a), we study the exchange of indivisible objects among agents with unit demand, where initially each object is either privately owned or is co-owned by multiple agents. We propose a new notion of core called the effective core for these problems to address the inadequacies of conventional notions of core. We say that a coalition effectively blocks an assignment if it weakly blocks it–as in the definition of the strong core–and the blocking is credible in the sense that no agent in the coalition free-rides on other agents in it. We show that the effective core is a nonempty subset of the weak core and a superset of the strong core, and all assignments in it are Pareto efficient. We also propose an algorithm to find assignments in it. Lastly, we make detailed comparison between the effective core and Balbuzanov and Kotowski's exclusion core