We study a model in which agents are matched in pairs in order to undertake a task and have preferences over both the partner and the task they are assigned to. Every possible pair of agents have a set of tasks (possibly empty) that they like to perform together. This set is pair-specific because an agent may prefer to perform different tasks with different partners. Agent i is an acquaintance of agent j if there is a task they like to perform together.
Individual preferences are such that all partner-task pairs belong to three indifference classes. The topmost indifference class consists of the pairs in which an agent is matched with an acquaintance and a task they like to perform together. The second class contains all the pairs in which the agent is matched with an acquaintance but the task assigned to the pair does not belong to the set they like. Finally, the bottom class contains all pairs in which the agent is not matched with an acquaintance. We propose a group strategy-proof algorithm that identifies a Pareto efficient assignment in the weak core.
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