The Role of Transparency in Repeated First-Price Auctions with Unknown Valuations

TL;DR

This paper analyzes how the level of transparency in repeated first-price auctions impacts a bidder's ability to minimize regret when valuations are unknown, providing a comprehensive characterization across various environments.

Contribution

It offers a complete characterization of minimax regret in first-price auctions based on transparency levels, applicable under stochastic, adversarial, and smoothed environments.

Findings

Minimax regret depends critically on auction transparency levels.

Results hold across different environmental assumptions.

Provides insights into optimal bidding strategies under varying information disclosures.

Abstract

We study the problem of regret minimization for a single bidder in a sequence of first-price auctions where the bidder discovers the item's value only if the auction is won. Our main contribution is a complete characterization, up to logarithmic factors, of the minimax regret in terms of the auction's \emph{transparency}, which controls the amount of information on competing bids disclosed by the auctioneer at the end of each auction. Our results hold under different assumptions (stochastic, adversarial, and their smoothed variants) on the environment generating the bidder's valuations and competing bids. These minimax rates reveal how the interplay between transparency and the nature of the environment affects how fast one can learn to bid optimally in first-price auctions.