On profit-maximizing envy-free pricing
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In this paper, we study the revenue maximization envy-free pricing in multi-item markets: there are mitems 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 the total revenue given that all buyers are envy-free. We give a polynomial time algorithm to compute a revenue maximization envy-free pricing when every buyer evaluates at most two items 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. Next we extend the model to allow buyers to demand a subset of consecutive items, motivated from TV advertising where advertisers are interested in different consecutive slots with different valuations and lengths. We show that the revenue maximization envy-free pricing in this setting can be computed in polynomial time.