Nov. 7 (14:00-15:00) room C.714
Daniela Bubboloni (Firenze)
Symmetric mechanisms for two-sided matching problems
We focus on the one-to-one two-sided matching model with two disjoint sets of agents of equal size, where each agent in a set has preferences on the agents in the other set modeled by a linear order. A mechanism associates a set of matchings to each preference profile; resoluteness, that is the capability to select a unique matching, and stability are important properties for a mechanism. The two versions of the deferred acceptance algorithm are resolute and stable mechanisms but they are unfair since they strongly favor one side of the market. We introduce a property for mechanisms that relates to fairness; such property, called symmetry, captures different levels of fairness and generalizes existing notions. We provide several possibility and impossibility results mainly involving the most general notion of symmetry, known as gender fairness, resoluteness, stability, weak Pareto optimality and minimal optimality. In particular, we prove that: resolute, gender fair mechanisms exist if and only if each side of the market consists of an odd number of agents; there exists no resolute, gender fair, minimally optimal mechanism. Those results are obtained by employing algebraic methods based on group theory, an approach not yet explored in matching theory.
The talk is based on joint work with Michele Gori and Claudia Meo.