Improved Two Sample Revenue Guarantees via Mixed-Integer Linear Programming
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We study the performance of the Empirical Revenue Maximizing (ERM) mechanism in a single-item, single-seller, single-buyer setting. We assume the buyer's valuation is drawn from a regular distribution F and that the seller has access to two independently drawn samples from F. By solving a family of mixed-integer linear programs (MILPs), the ERM mechanism is proven to guarantee at least .5914 times the optimal revenue in expectation. Using solutions to these MILPs, we also show that the worst-case efficiency of the ERM mechanism is at most .61035 times the optimal revenue. These guarantees improve upon the best known lower and upper bounds of .558 and .642, respectively, of [Daskalakis Zampetakis, '20].
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