Infinite-Dimensional Fisher Markets and Tractable Fair Division

Abstract

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