PhD Internal Seminar Series with Pietro Salmaso

Title: Stable and efficient task assignment to pairs 

 

Abstract: 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. Preferences over partner-task pairs are non separable, but correlated in the following sense. Every agent has a set of tasks (possibly empty) that he likes to perform with a potential partner. This set is agent-specific and the set of tasks that agent i would like to perform with partner j may be different from the set that he likes to perform with agent k. Preferences are symmetric in the sense that the set of task that agent i likes to perform with agent j coincides with the set of tasks that agent j would like to perform with agent i. Individual preferences are such that all partner-task pairs belong to three indifference classes. In the topmost indifference class, there are the pairs in which an agent is matched with a partner and a commonly good task. The second class contains all the pairs in which the agent is matched with a partner with whom has some commonly good tasks, but the task they are assigned to does not belong to this set. Finally, the bottom class contains all pairs in which the agent is matched with someone with whom he has not any commonly good task. We propose an algorithm that identifies a stable and Pareto efficient assignment. We also show that the procedure is strategy-proof and also pairwise strategy proof, meaning that pairs of agents do not have incentive to jointly misreport the set of commonly good tasks. We conjecture that the algorithm is also group strategy-proof.