Reassignment-based strategy-proof mechanisms for interdependent task allocation

Classical mechanism design assumes that an agent's value of any determined outcome depends only on its private information. However in many situations, an agent's value of an outcome depends on the private information of other agents in addition to its private information (i.e., interdependent valuations). We consider the interdependent task allocation (ITA) problem, where a set of tasks with predefined dependencies is to be assigned to self-interested agents based on what they report about their privately known capabilities and costs. We consider the possibility that tasks may fail during their execution, which imposes interdependencies between the agents' valuations. For such ITA problem where agents have private costs, strategy-proof mechanisms have not been proposed yet. In this study, we prove that it is impossible to achieve strategy-proofness if the mechanism uses a single allocation round. Then, we design reassignment-based mechanisms that reassign failing tasks, and prove their strategy-proofness along with investigating the conditions under which center rationality is maintained.