Strategic Analysis of Fair Rank-Minimizing Mechanisms with Agent Refusal Option

This study examines strategic issues in fair rank-minimizing mechanisms, which choose an assignment that minimizes the average rank of object types to which agents are assigned and satisfy a fairness property called equal treatment of equals. As one of these fair mechanisms, the uniform rank-minimizing mechanism is considered. We focus on the case where agents can refuse their assignment and obtain the outside option instead. Without the refusal option, truth-telling is not strategically dominated by any strategies if a fair rank-minimizing mechanism is used. However, if agents have the option and the uniform rank-minimizing mechanism is used, then a strategy called an outside option demotion strategy strategically dominates truth-telling. Moreover, we show that adopting this strategy may lead to inefficient assignments. To counter this, we propose a modification of the uniform rank-minimizing mechanism, though it may lead agents to strategically reduce the number of acceptable types.