Optimal Bi-Valued Auctions

TL;DR

This paper introduces an optimal deterministic auction for bi-valued digital goods, establishing tight lower bounds and emphasizing the importance of general competitiveness which accounts for additive and multiplicative losses.

Contribution

It constructs a polynomial-time deterministic auction for bi-valued settings and proves a tight lower bound, highlighting the significance of general competitiveness in auction analysis.

Findings

Optimal auction is uncompetitive under traditional measures.

Established tight lower bounds for auction performance.

Highlighted the importance of additive losses in competitiveness.

Abstract

We investigate \emph{bi-valued} auctions in the digital good setting and construct an explicit polynomial time deterministic auction. We prove an unconditional tight lower bound which holds even for random superpolynomial auctions. The analysis of the construction uses the adoption of the finer lens of \emph{general competitiveness} which considers additive losses on top of multiplicative ones. The result implies that general competitiveness is the right notion to use in this setting, as this optimal auction is uncompetitive with respect to competitive measures which do not consider additive losses.