Being argumentative in nature and referring to Oaxaca Decomposition for the purpose of defining the main drivers of rental flats and houses, be new, old, repaired, or unrepaired, together with applying the difference in difference method to evaluate the effectiveness of the policy, this paper calls into the question of how to inaugurate a country-specific two-sided matching algorithm for rental house allocation based on the empirical results. Model 3 is built on time series data to evaluate the policy implementation by the Azerbaijani government to provide households with financial aid. Based on Blinder-Oaxaca Decomposition, the main findings of the study manifest that for the repaired and unrepaired houses, the price discrimination is mainly explained by the room number while this is an area of the houses per meter square that explains the price gap between old and new flats. The Difference in Difference model signifies that the increase in the number of mortgage loans from 50.000 AZN to 150.000 AZN declined demand more than the increase in supply. Additionally, the study offers 2 Matching Algorithm and Mechanism Design for the allocation of rental houses with existing tenants and newcomers in addition to tenants and owners without initial endowments through YRMH-IGYT in two-sided matching markets.