Envy-free pricing in multi-item markets

Abstract

In this article, we study revenue maximizing envy-free pricing in multi-item markets: There are m indivisible items with unit supply each and n potential buyers where each buyer is interested in acquiring one item. The goal is to determine allocations (a matching between buyers and items) and prices of all items to maximize total revenue given that all buyers are envy-free. We give a polynomial time algorithm to compute a revenue maximizing envy-free pricing when every buyer evaluates at most two items at a positive valuation, by reducing it to an instance of weighted independent set in a perfect graph and applying the Strong Perfect Graph Theorem. We complement our result by showing that the problem becomes NP-hard if some buyers are interested in at least three items.