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Mechanism Design for Correlated Valuations: Efficient Methods for Revenue Maximization.
Michael
Albert, Vincent Conitzer, Giuseppe Lopomo, and Peter Stone.
Operations
Research, March 2021.
Traditionally, much of the focus of the mechanism/auction design community has been on revenue optimal mechanisms for settings where bidders' valuations are independent. However, in settings where valuations are correlated, much stronger results are possible. For example, the entire surplus of efficient allocations can be extracted as revenue. These stronger results are true, in theory, under generic conditions on parameter values. However, in practice, they are rarely, if ever, implementable because of the stringent requirement that the mechanism designer knows the distribution of the bidders types exactly. In this work, we provide a computationally efficient and sample efficient method for designing mechanisms that can robustly handle imprecise estimates of the distribution over bidder valuations. This method guarantees that the selected mechanism will perform at least as well as any ex post mechanism with high probability. The mechanism also performs nearly optimally with sufficient information and correlation. Furthermore, we show that when the distribution is not known and must be estimated from samples from the true distribution, a sufficiently high degree of correlation is essential to implement optimal mechanisms. Finally, we demonstrate through simulations that this new mechanism design paradigm generates mechanisms that perform significantly better than traditional mechanism design techniques given sufficient samples.
@article{OR21-Albert,
author={Michael Albert and Vincent Conitzer and Giuseppe Lopomo and Peter Stone},
title={Mechanism Design for Correlated Valuations: Efficient Methods for Revenue Maximization},
journal={Operations Research},
doi={10.1287/opre.2020.2092},
month="March",
year="2021",
abstract={Traditionally, much of the focus of the mechanism/auction design community has been on revenue optimal mechanisms for settings where bidders' valuations are independent. However, in settings where valuations are correlated, much stronger results are possible. For example, the entire surplus of efficient allocations can be extracted as revenue. These stronger results are true, in theory, under generic conditions on parameter values. However, in practice, they are rarely, if ever, implementable because of the stringent requirement that the mechanism designer knows the distribution of the bidders types exactly. In this work, we provide a computationally efficient and sample efficient method for designing mechanisms that can robustly handle imprecise estimates of the distribution over bidder valuations. This method guarantees that the selected mechanism will perform at least as well as any ex post mechanism with high probability. The mechanism also performs nearly optimally with sufficient information and correlation. Furthermore, we show that when the distribution is not known and must be estimated from samples from the true distribution, a sufficiently high degree of correlation is essential to implement optimal mechanisms. Finally, we demonstrate through simulations that this new mechanism design paradigm generates mechanisms that perform significantly better than traditional mechanism design techniques given sufficient samples.},
}
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