A planner-optimal matching mechanism and its incentive compatibility in a restricted domain
证明在逆有界无差异域中，满足交换单调性、下不变性和内上方差三个公理的机制可实现贝叶斯激励相容，并分析了约束随机串行独裁机制的激励性质。
In many random assignment problems, the central planner pursues their own policy objective, such as matching size and minimum quota fulfillment. Several practically important policy objectives do not align with agents' preferences and are known to be incompatible with strategy-proofness. This paper demonstrates that such policy objectives can be attained using mechanisms that satisfy Bayesian incentive compatibility within a restricted domain of von Neumann Morgenstern utilities. We establish that a mechanism satisfies Bayesian incentive compatibility in an inverse-bounded-indifference domain if and only if the mechanism satisfies the three axioms of swap monotonicity, lower invariance, and interior upper variance. We apply this axiomatic characterization to analyze the incentive property of the constrained random serial dictatorship mechanism (CRSD). CRSD is designed to generate an individually rational assignment that optimizes the central planner's policy objective function. Since CRSD satisfies these axioms, it is Bayesian incentive compatible within an IBI domain.