Matching with Minimum Quotas

In this paper, I consider a matching model with minimum quotas for one side of the market.The main objective is to find algorithms which respect minimum quo tas and find matchings which are both nonwasteful and fair if there exists such a matching. Otherwise, the algorithms find either fair or nonwasteful matchings. My algorithms, CNWF and FCNW (constrained nonwasteful fair and fair constrained nonwasteful), start with finding the range of pos sible matchings when there are minimum quotas. Then, using an innova tive graph, they select the matchings which are both fair and nonwasteful, and if there do not exist such matchings, CNWF selects a constrained non-wasteful matching with a maximum degree of fairness, and FCNW selects a fair matching with a maximum degree of nonwastefulness.Furthermore, I show that my algorithms are applicable to the case where there are different types of agents, which is a key factor for match ing markets that are concerned with diversity. In addition, I study the incentive properties of my algorithms when there are minimum quotas that need to be filled.Compared to the existing algorithms my algorithms are unified and more intuitive