Prominent Turkish economist Ahmet Alkan made a presentation on "Equitable stable matches under modular assessment"

On October 25, 2024, a lecture was held by the outstanding Turkish economist Ahmet Alkan, one of the leading experts in the field of game theory, matching and auctions. He holds the position of professor at the prestigious Turkish Sabanji University. Professor Alkan is also a member of the Turkish Academy of Sciences and a member of the European Science Foundation. For his work, he has been awarded several times by Turkish universities and scientific communities.

Theme: 
«Equitable stable matchings under modular assessment».

Annotation:

We address equitability and issues of social welfare in the one-to-one stable matching model. As well known, there exists a stable matching that is optimal for each side but which is infimal for the other side. Stable matchings all together, in fact, form a lattice under the group preferences of one side that is opposite to the group preferences of the other. In spite of this orderliness, locating “the middle” defies straightforward method. Here we first establish an equivalence between an ordinal condition and modular optimization on the lattice of stable matchings. This equivalence charts out a domain where equity or welfare criteria separate over individuals and appear as weights in optimization. We call the ordinal condition convexity and the domain modular. Convexity requires stable “mixtures” of matchings in a solution to also be in the solution. We next propose a novel class of equitability criteria called equity undominance and characterize the modular stable matching rules that are equity undominated. It follows from our results that the modular stable matching rules provide for clear testable implications and a wide range of specifications allowing efficient optimization.