The ANPEC is an association of graduate Centers in Economics in Brazil which provides, every year, an examination that ranks the candidates who want to be admitted by these Centres. This classification is used by the Institutions to elaborate their preferences on the candidates. The allocation procedure of candidates to graduate Economic Schools in Brazil is descentralized. We describe the history of the organization of this Market along the last 30 years. We analyse the descentralized Market and explain the reasons of the failure of the centralized mechanism of 1997. Empirical observations are fundamented by the existent theory and by new theoretical results presented. A new design for this Market is proposed, aiming to correct the failures presented in the actual model.