CAREER: New Frontiers of Fairness in Allocation and Exchange Problems

Allocation and exchange problems have been an integral part of microeconomics since its inception. These problems involve the distribution, pricing, and exchange of items among agents. An enduring objective in all allocation and exchange involving human agents is fairness.

Although there is foundational work on fair allocation and exchange, the past decade has witnessed an explosion of new problems with the surge of several online economies that perform novel allocation and exchange. Some of these problems present intricate challenges that resist generalizations of existing techniques, while some require modeling from scratch to identify limitations and explore critical directions forward.

This project aims to answer the foregoing novel fundamental questions in fair allocation and exchange and also to lay the microeconomic foundations for these new economies. The techniques developed in the project are expected to make advances in optimization, algorithm design, and fixed-point theory. The project will involve and train graduate and undergraduate students at various levels of the project, integrate the findings with teaching, and make lecture notes and other material freely available online.

The project will also reach students from underrepresented groups through mentoring workshops and the opportunities provided by initiatives at the University of Illinois at Urbana-Champaign.

This project will investigate the foundations of fair allocation and exchange in the following new economies. (i) Allocation and Exchange of Chores: Chores are non-disposable items that incur costs during consumption. They are increasingly pertinent in today's online labor markets and freelance economies. Chore allocation exhibits major structural differences from good allocation, rendering existing techniques ineffective.

This proposal aims to develop novel methods for fair chore allocation and exchange using tools from continuous optimization, equilibrium analysis, and combinatorics. (ii) Allocation and Exchange of Indivisible Goods: Several modern platforms, such as peer-review systems, online homestays, and ridesharing apps, rely on integral allocations, motivating the study of fair allocation and exchange of indivisible items. However, proving the existence of fair solutions in the discrete setting is much more challenging-- most fixed-point theorems applicable in the continuous setting do not translate.

This proposal aims to develop a robust theory of algorithms, discrete fixed points, and topology to address key unresolved questions in discrete fair allocation. (iii) Allocation and Exchange of Data: The widespread adoption of ML systems has heightened the demand for high-quality data. The rise of collaborative machine learning (ML) paradigms like federated learning (FL) and online data marketplaces underscores the necessity for fair and efficient allocation and exchange mechanisms involving data.

However, economic processes involving data differ significantly from those involving other assets: data can be duplicated at negligible cost (so no concept of limited supply), agents may lack strong prior knowledge of a dataset's value, and the utility derived from a combination of datasets is perplex and non-well-behaved for strong guarantees. This project aims to establish axiomatic foundations for economic processes involving data and investigate the feasibility and limitations of achieving fairness in these contexts.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.