How to fairly and efficiently assign tasks in individually rational agents’ coalitions? Models and fairness measures

An individually rational agent will participate in a multiagent coalition if the participation, given available information and knowledge, brings a payoff that is at least as high as the one achieved by not participating. Since agents' performance and skills may vary from task to task, the decisions about individual agent-task assignment will determine the overall performance of the coalition. Maximising the efficiency of the one-on-one assignment of tasks to agents corresponds to the conventional linear sum assignment problem, which considers efficiency as the sum of the costs or benefits of individual agent-task assignments obtained by the coalition as a whole. This approach may be unfair since it does not explicitly consider fairness and, thus, is unsuitable for individually rational agents' coalitions. In this paper, we propose two new assignment models that balance efficiency and fairness in task assignment and study the utilitarian, egalitarian, and Nash social welfare for task assignment in individually rational agents' coalitions. 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 is possible through the use of the proposed models.