The Role of Information into Matching Markets - Form Theoretical Models to the Practical Application on the Hiring Procedure for Assistant Professors in Italy

The thesis is made up by three independent papers, logically linked by their validity for the analysis and redesigning proposal of the hiring procedure for Assistant Professors in Italy. All of them refer to the literature on matching theories and market design. The papers focus on the role played by information into the setting analyzed and their results are generalizable to similar job markets. The dissertation illustrates a complete work of market design, presented from the analysis of the current procedure to the proposal of a new structure. The research work started from formally demonstrating if the real-world market is failing, and, in the affirmative case, what is causing its failure. Then, the first paper introduces a decentralized matching model that proceeds by rounds, that formalizes this hiring procedure. The model shows what kind of assumptions and constraints are necessary for achieving stable results in this particular matching mechanism. On the reverse, it highlights which are the structure features that create unstable outcomes and allows the market designer to formally identify the causes of inefficiencies. The model is formalized in a setting of complete information, such that it makes clearer and easier its analysis and explanation. However, due to the unreality of this setting, I stressed the model into more realistic context where information is not always available. The second paper starts by removing only part of the information (the preferences’ profiles of the other agents), and ends into an “uncertainty” scenario. I recalled the model of symmetric information (Roth and Rothblum 1999) and I demonstrated that the mechanism implements a Bayesian Nash Equilibrium strategy profile characterized by multiple stable equilibria. Then, I stressed the model by removing almost all the information, such that they do not know how many institutions will offer a job positions, which of them will open the vacancy and when. I also assumed that agents do not have lists of preferences but they follow their utility function. I set the assumption that any candidate beliefs that the round she is playing will be the last. I demonstrated that up to the real preference profile, for a shared common belief on the others’ preference list, and for a shared common belief over the state of the world, a truthfully revealing strategy profile is a Bayesian Nash Equilibrium. Given the difficulty of managing a decentralized mechanism, I formalize the hiring procedure as a centralized market. I outline the advantages obtained by this redesigning policy, but I also show that there is still an aspect not addressed: the “meritocracy problem”. By the expression “meritocracy problem”, I refer to any contest whose winner is not actually better than all the others. The aim of the third paper is to transfer the meritocracy problem into the matching model. I recognize the so called “meritocracy problem” as a problem related to the decision rules and equivalent to an agency problem between the Institution and the committee. The focus is on the realization of the preference list. The meritocracy problem is given by a misalignment of interest – and preferences – between these two agents. It happens that the preferences’ lists submitted by the committees not always reflects the real preferences of the Institutions, i.e. commissioners misreport Institutions’ preferences. The results obtained after running the DA are stable up to the submitted preferences, but unstable up to what Institutions really desire. This instability is enough for stating the agency problem as a potential threat to the well-functioning of a matching market where at least one group of agents follow a semi-regulated decision process. I propose a solution focused on the control of commissioners’ actions.The thesis is made up by three independent papers, logically linked by their validity for the analysis and redesigning proposal of the hiring procedure for Assistant Professors in Italy. All of them refer to the literature on matching theories and market design. The papers focus on the role played by information into the setting analyzed and their results are generalizable to similar job markets. The dissertation illustrates a complete work of market design, presented from the analysis of the current procedure to the proposal of a new structure. The research work started from formally demonstrating if the real-world market is failing, and, in the affirmative case, what is causing its failure. Then, the first paper introduces a decentralized matching model that proceeds by rounds, that formalizes this hiring procedure. The model shows what kind of assumptions and constraints are necessary for achieving stable results in this particular matching mechanism. On the reverse, it highlights which are the structure features that create unstable outcomes and allows the market designer to formally identify the causes of inefficiencies. The model is formalized in a setting of complete information, such that it makes clearer and easier its analysis and explanation. However, due to the unreality of this setting, I stressed the model into more realistic context where information is not always available. The second paper starts by removing only part of the information (the preferences’ profiles of the other agents), and ends into an “uncertainty” scenario. I recalled the model of symmetric information (Roth and Rothblum 1999) and I demonstrated that the mechanism implements a Bayesian Nash Equilibrium strategy profile characterized by multiple stable equilibria. Then, I stressed the model by removing almost all the information, such that they do not know how many institutions will offer a job positions, which of them will open the vacancy and when. I also assumed that agents do not have lists of preferences but they follow their utility function. I set the assumption that any candidate beliefs that the round she is playing will be the last. I demonstrated that up to the real preference profile, for a shared common belief on the others’ preference list, and for a shared common belief over the state of the world, a truthfully revealing strategy profile is a Bayesian Nash Equilibrium. Given the difficulty of managing a decentralized mechanism, I formalize the hiring procedure as a centralized market. I outline the advantages obtained by this redesigning policy, but I also show that there is still an aspect not addressed: the “meritocracy problem”. By the expression “meritocracy problem”, I refer to any contest whose winner is not actually better than all the others. The aim of the third paper is to transfer the meritocracy problem into the matching model. I recognize the so called “meritocracy problem” as a problem related to the decision rules and equivalent to an agency problem between the Institution and the committee. The focus is on the realization of the preference list. The meritocracy problem is given by a misalignment of interest – and preferences – between these two agents. It happens that the preferences’ lists submitted by the committees not always reflects the real preferences of the Institutions, i.e. commissioners misreport Institutions’ preferences. The results obtained after running the DA are stable up to the submitted preferences, but unstable up to what Institutions really desire. This instability is enough for stating the agency problem as a potential threat to the well-functioning of a matching market where at least one group of agents follow a semi-regulated decision process. I propose a solution focused on the control of commissioners’ actions