Efficiency and fairness in team search with self-interested agents

We consider team-work settings where individual agents incur costs on behalf of the team. In such settings it is frequently the custom to reimburse agents for the costs they incur (at least in part) in order to promote fairness. We show, however, that when agents are self-interested such reimbursement can result in degradation in efficiency - at times severe degradation. We thus study the relationship between efficiency and fairness in such settings, distinguishing between ex-ante and ex-post fairness. First, we analyze reimbursement policies that reimburse solely based on purchase receipts (as is customary), and show that with such policies the degradation in both efficiency and fairness can be unbounded. We thus introduce two other families of reimbursement policies. The first family guarantees optimal efficiency and ex-ante fairness, but not ex-post fairness. The second family improves (at times) on ex-post fairness, but at the expense of efficiency, thus providing a tradeoff between the two.