On Balancing Fairness and Efficiency of Task Assignment in Agent Societies

Agent societies generally aim at collective provision of services (capabilities or resources) in a more efficient way than their agents could individually. In particular, some agents may be more efficient than the others in providing certain tasks. Thus, a task-agent assignment decision determines the overall performance of the society. The conventional linear sum assignment problem handles the assignment of tasks to a society of agents in a one-on-one manner. Such assignments typically only consider efficiency in terms of the overall cost or benefit for the system. However, an assignment strategy may be unfair if it does not explicitly consider fairness. Therefore, the conventional mathematical models for the task assignment problem should be rethought to explicitly consider fairness in the allocation of the tasks to the agents. In this paper, we study the utilitarian, egalitarian, and Nash social welfare in task assignment and propose two new assignment models that balance efficiency and fairness. Since fairness is a relatively abstract term that can be difficult to quantify, we propose three new fairness measures based on equity and equality and use them to compare the newly proposed models. Through functional examples, we show that a reasonable trade off between efficiency and fairness in task assignment can be found through the use of the proposed models.