The project aims to settle the computational complexity of finding stable solutions in fundamental economic settings, specifically in the settings of competitive markets including settings of fair division. Complexity classes such as PPAD and FIXP have been introduced with the goal of capturing the computational complexity of such problems and seminal work have achieved this for the problem of finding Nash equilibrium in strategic form games.

Yet, many fundamental questions about computing stable solutions in competitive markets and fair division remain widely unresolved. The project will tackle these questions by developing new complexity theoretic frameworks from a viewpoint of mathematical optimization.