Students assignments models: theory and applications – SCHOOL_CHOICE

In recent years, game theoretic ideas have been used to study the design of markets. Matching procedures have found practical applications in centralized labour markets, as well as school assignment systems in France and in many other countries (US, China, Turkey…). We aim at analysing the assignment procedure used in France both on theoretical and empirical bases. In particular, in a preliminary work by Hiller and Tercieux (2011) two important drawbacks have been identified for the French procedure. In this work, we point out that affirmative action policies may be totally counter-productive: increasing the priority at schools of a minority group may not ensure that they eventually get a better assignment. In addition to this, another major flaw has been identified: some parents have incentives to misreport their preferences, which may induce inefficiencies.
The first part of the project consists in improving our understanding of the first problem (that high priority groups can be worse-off) from a theoretical point of view. Up to now, the potential counter-productive effects of affirmative action policies have been highlighted only for a small number of students and schools. We plan to investigate how this result is affected as the number of students/schools grows. It would allow us to assess the importance of this drawback in real world, with a special focus on the French case. Second, we will try to assess the implications of the second problem in terms of fairness. In particular, we would like to study if less informed parents choose suboptimal strategies when reporting their preferences, resulting in bad assignments for their children. Experimental economics is a particularly powerful tool to analyse strategic behaviour by agents while controlling their preferences as well as the level of information they have. As a consequence, we plan to deal with this second point by running experiments in the lab. Finally, another factor that may hurt minorities, particularly salient in France, is the will from favoured families to try to have their children assigned in schools with a large majority of students from similar familial background. While the standard setting in school choice is silent on this issue, in our final task, we aim at building a new setup, which will explicitly account for the existence of social diversity in these school assignment problems. In particular, we will try to build a setting where preferences of parents are, in fine, affected by the type of students their child is associated with, i.e., we will to some extent endogenize preferences of parents.