On Multi-dimensional Envy-Free Mechanisms

We study the problem of fairness design . Specifically, we focus on approximation algorithms for indivisible items with supporting envy-free bundle prices. We present the first polynomial-communication envy-free profit-maximizing combinatorial auctions for general bidders. In this context, envy-free prices can be interpreted as anonymous non-discriminatory prices. Additionally, we study the canonical makespan-minimizing scheduling problem of unrelated machines, in an envy-free manner. For the special case of related machines model we show that tight algorithmic bounds can be achieved.

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