Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms
研究了随机优先和概率序列两种分配机制，发现当市场变大时两者渐近等价，随机优先的低效率在大市场中变小，为实际应用提供了理论依据。
The random priority (random serial dictatorship) mechanism is a common method for assigning objects. The mechanism is easy to implement and strategy-proof. However, this mechanism is inefficient, because all agents may be made better off by another mechanism that increases their chances of obtaining more preferred objects. This form of inefficiency is eliminated by a mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications is an open question. We show that these mechanisms become equivalent when the market becomes large. More specifically, given a set of object types, the random assignments in these mechanisms converge to each other as the number of copies of each object type approaches infinity. Thus, the inefficiency of the random priority mechanism becomes small in large markets. Our result gives some rationale for the common use of the random priority mechanism in practical problems such as student placement in public schools.