Matching with Partners and Projects

We study a model that is a hybrid of the classical roommate matching model object allocation model. We propose a model where agents are matched in pairs in order to undertake a project. Agents have preferences over both the partner and the project they are assigned to. These preferences over partners and projects are separable and dichotomous. Each agent partitions the set of partners into friends and outsiders, and the set of projects into good and bad ones. Friendship is mutual and transitive. In addition, preferences over projects among friends are correlated (homophily). We define a suitable notion of the weak core and propose an algorithm, the minimum demand priority algorithm (MDPA) that generates an assignment in the weak core. In general, the strong core does not exist but the MDPA assignment satisfies a limited version of the strong core property when only friends can be members of the blocking coalition. The MDPA is also strategy-proof. Finally we show that our assumptions on preferences are indispensable. We show that the weak core may fail to exist if any of the assumptions of homophily, separability anddichotomous preferences are relaxed.