Abstract: We consider a division problem where agents have to be matched in pairs and each pair has to perform a task of unit value. Agents have preferences over the amount of effort they have to contribute to the task. Preferences are single-peaked and continuous. An allocation rule specifies an assignment of pairs and a division of effort levels for the task for each pair. We are interested in stable allocations, i.e. allocations where no pair of agents can block the allocation by abandoning their partners and proposing a feasible division of effort among themselves such that both agents in the pair strictly improve. We provide an algorithm which generates a stable and Pareto efficient allocation. We show that stable allocations may not exist when preferences are single-peaked but not continuous.
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