Simple and Effective: A Deterministic Auction with Support Information
Abstract:
Problem definition: We study an auction design problem, where a seller aims to sell an item to multiple bidders. Bidders’ willingness to pay (values) are independent random variables, and the seller only knows an upper bound on these values, lacking specific distribution knowledge. The objective is to devise a deterministic auction mechanism effective across various plausible distributions.
Methodology/results: We propose a second price auction with a reserve price set to half of the upper bound. Even though no deterministic mechanism can achieve a positive fraction of the maximum achievable expected revenue across all distributions, we define a distribution class G, which is extensive and contains several distributions of practical importance with diverse structural properties, and we demonstrate that our mechanism achieves at least 1/4 (1/2 under i.i.d. values) of the maximum expected revenue for distributions within G. We conduct numerical experiments to evaluate our mechanism’s performance beyond G, under randomly generated distributions, demonstrating its superior performance in approximately 95% of the generated instances compared to benchmark mechanisms from the literature. Additionally, we illustrate numerically that our mechanism exhibits greater robustness against different correlations than the benchmarks when considering two non-independent bidders. We also consider the scenario where the estimated upper bound is subject to errors and show that appropriately lowering the reserve price based on estimation confidence ensures a constant positive fraction of the maximum expected revenue across G.
Managerial implications:
Traditional auction design strategies, under distributional ambiguity, often propose randomized mechanisms that lack interpretability and transparency, potentially leading to trust issues among bidders and implementation challenges. Our deterministic mechanism is simple, requires minimal information, and is provably effective in various practical scenarios.
Language: English
This is a free Seminar. Registration is mandatory.