Learning to Coordinate Bidders in Non-Truthful Auctions
Hu Fu, Tao Lin
TL;DR
This paper tackles learning Bayes correlated equilibria (BCE) in non-truthful auctions by analyzing the sample complexity when bidder values are drawn from unknown, independent, bounded distributions. The authors reduce BCE learning to estimating interim utilities for monotone bidding strategies and bound the problem via the pseudo-dimension, deriving an upper bound of $ ilde{O}ig( rac{n}{oldsymbol{varepsilon}^2}ig)$ samples and a matching information-theoretic lower bound. They extend the results to Bayes Nash equilibria (BNE) as a corollary, since BNEs are also monotone in this setting, and show how to learn BCE using samples from the value distributions through an empirical product-distribution approach. A key technical ingredient is showing that utilities under monotone strategies can be learned even when only sample-based utilities are available, and that BCEs can be learned from the empirical product distribution with controlled approximation loss. The work demonstrates the statistical feasibility of learning to coordinate bidders in large-scale, data-scarce non-truthful auction environments, with implications for practical mediator-based coordination in online platforms.
Abstract
In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding Bayes-Nash equilibrium notion, are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to achieve better outcomes in non-truthful auctions is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distributions of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the set of strategic-form BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $\tilde O(\frac{n}{\varepsilon^2})$ of samples of bidders' values. This moderate number of samples demonstrates the statistical feasibility of learning to coordinate bidders. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies.