Study On Housing Match Problem Based On Weak Preference

Matching is a market mechanism for allocation and exchange of indivisible discrete trading resources. Matching theoretical research scope is very broad. Trading kidney problems, housing and other aspects are categories of matching theory. The results of which influence the future of a person to a great degree. thus the research on matching theory has great theoretical significance and practical value.This paper first analyze Extended Top Trading Cycle(ETTC) algorithm in house allocation problem with private endowments under weak preference domain, which satisfies many good axioms, such as individual rationality, pareto efficiency and strategy-proofness. However, ETTC requires public housing priority order, which could hardly be obtained in reality. At the same time people are out of consideration for the Housing size, geographical location, floors, etc., may be unable to distinguish the two houses which is good, that gives Housing Priority which may be weak preference ordering.To solve this problem, this paper presents the top trading cycle algorithm without public housing priority sequence top trading cycle algorithm(ETTAS) based on ETTC. ETTAS is applicable for allocation with private endowments in which no public housing priority order exists. ETTAS maintains good properties of ETTC, such as individual rationality,pareto efficiency and strategy-proofness. Secondly, the paper analyze Top Trading Cycle Absorbing Sets(TTAS) mechanisms in house market under weak preference domain,TTAS requires public housing priority order, which could hardly be obtained in reality.This paper presents the top trading absorbing sets mechanisms without public housing priority sequence(NTTAS) based on TTAS.In the end, the paper expounds the idea of low rent housing allocation problem in real life. It also presents a proved allocating method on the basis of “waiting Yaohao”used in many provinces. This paper put forward a new method to the low rent housing allocation problem based on NTTAS. An example is used to compare both original and improvedmethod. The results prove that the improved method is better than the original method.