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 particularly focus on the case where agents can refuse their assignment and obtain the outside option instead. Without the refusal option, if the uniform rank-minimizing mechanism is used, truth-telling is not strategically dominated by any strategies. However, if agents have the option, then an outside option demotion strategy -- revealing all object types as acceptable without changing the ranking of truly acceptable ones -- strategically dominates truth-telling. Moreover, we show that adopting this strategy may lead to inefficient assignments. To counter this, we propose the modified uniform rank-minimizing mechanism, though it may lead agents to strategically reduce the number of acceptable types.