Optimal Auction Design with Quantized Bids

TL;DR

This paper develops an optimal auction mechanism for selling to buyers who quantize their private valuations, ensuring maximum seller utility, incentive compatibility, and buyer participation, while also designing optimal quantization thresholds.

Contribution

It introduces a novel auction design framework that accounts for quantized bids and optimizes quantization thresholds for improved auction performance.

Findings

Optimal auction mechanism under quantized bids.

Design of quantization thresholds affecting auction outcomes.

Numerical analysis of threshold impacts on seller utility.

Abstract

This letter considers the design of an auction mechanism to sell the object of a seller when the buyers quantize their private value estimates regarding the object prior to communicating them to the seller. The designed auction mechanism maximizes the utility of the seller (i.e., the auction is optimal), prevents buyers from communicating falsified quantized bids (i.e., the auction is incentive-compatible), and ensures that buyers will participate in the auction (i.e., the auction is individually-rational). The letter also investigates the design of the optimal quantization thresholds using which buyers quantize their private value estimates. Numerical results provide insights regarding the influence of the quantization thresholds on the auction mechanism.