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Advances and Challenges in Fair Division: Quantiles, Subsidies, and Randomization

Series: Bangalore Theory Seminars

Speaker: Vishnu Narayan, Tel-Aviv University, Israel

Date/Time: Aug 27 11:00:00

Location: CSA auditorium [Room No. 104], ground floor

Abstract:
The question of how to fairly divide a collection of indivisible items amongst a set of agents has remained of central importance to humanity since antiquity. In this fundamental problem, the agents have varied preferences, and an allocator seeks to find a single allocation such that every agent perceives its bundle as fair. This problem arises in various applications, ranging from classical examples like the division of inherited estates and international borders to modern applications such as assigning seats in college courses and allocating computational resources fairly. Recent decades have witnessed significant progress, transforming this problem into a fascinating mathematical landscape with surprising results and intriguing new challenges. The broad goal is to devise natural definitions of fairness, and then study questions such as: does a fair allocation always exist?; can one be (efficiently) computed?; what are the precise limits to the degree of fairness one can guarantee? In this talk, I will focus on selected recent papers, highlighting three techniques (Quantiles, Subsidies, and Randomization) we use to extend the study of fair allocations to general valuation classes and resolve some conjectures and open problems.

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Hosts: Rameesh Paul, KVN Sreenivas, Rahul Madhavan, Debajyoti Kar