Facility Location Games with Task Allocation

Facility location games have been studied extensively but most are about locating facilities given agents' profiles. However, in some real-life scenarios, the facility's location may be fixed already. When there are multiple facilities the strategic agents will always go to the closest one, resulting in the remote facilities unused. In this paper, we introduce the model that includes two facilities and n rational agents. There is one task at each facility to be done. Each agent will select one task and aims to minimize the amount of work assigned to her. Our goal is to design the allocation rules to achieve social optimality, i.e., every Nash equilibrium guarantees that every task can be completed. We show that no allocation rule can achieve social optimality without positive/negative incentives. For negative incentives, we propose a class of allocation rules with dummy work, where social optimality can be achieved, and no worker does the dummy work. For positive incentives, we first give a simple rule that achieves social optimality and propose a more complex rule to achieve the minimum subsidy.