Infinite-Dimensional Fisher Markets and Tractable Fair Division

Fisher market equilibrium models have long been a central topic in economics and computation. Recently, they widely used the design implementation of Internet marketplaces. Although classical are well studied can be solved via tractable optimization characterizations, only allow finite number items thus face scalability issues when item space is huge or even continuous. In “Infinite-Dimensional Markets Tractable Fair Division,” Gao Kroer propose infinite-dimensional convex programs show that capture equilibria for infinite possibly continuous spaces, extending Eisenberg-Gale framework. Using these results, authors challenging cake-cutting problem piecewise linear agent valuations equivalent to finding admits characterization. Thus, it polynomial time theory highly efficiently by numerical software.