Optimal mechanism design of weak preference orders one-sided matching

The DA algorithm requires that both the preference orders and priority orders should be strict. However,there are often weak preference orders in matching.In this situation,any algorithm can't be stable,strategy-proof and Pareto efficient at the same time in two-side matching.This paper studies the matching mechanism with weak preference orders in one-side matching based on the applications of matching theory in China.Extruding mechanism is not only stable,strategy-proof and Pareto efficient, but also most efficient for one-side matching.We also use simulation method to prove that extruding mechanism promotes the efficiency of the total matching,and it mainly promotes the efficiency of students in the latter part of the priority orders;in the simulation of college admission,using extruding mechanism ensure the largest total utilities of all the students and the lowest rejection rate of high quality students.