Revenue Variance Minimization: Beyond First Price Auctions

TL;DR

This paper investigates revenue variance in auction mechanisms for selling multiple homogeneous items, revealing that traditional results about variance minimization are fragile and proposing new mechanisms to reduce revenue variance under different IR conditions.

Contribution

It characterizes revenue variance-minimizing mechanisms beyond first-price auctions, especially under interim IR, and introduces mechanisms that achieve constant revenue and reduce variance in multi-item settings.

Findings

First-price auction minimizes revenue variance under ex-post IR in single-item settings.

New mechanisms can implement efficient allocations with constant revenue under interim IR.

Revenue variance can be reduced by negative payment correlations, but some variance rankings remain unchanged.

Abstract

We study revenue variance in the sale of $k$ homogeneous items to risk-neutral, unit-demand bidders with independent private values. Although the Revenue Equivalence Theorem implies that standard auctions generate the same expected revenue, the distribution of revenue differs across mechanisms. Prior work shows that, in single-item environments with ex-post individual rationality (IR), the first-price auction minimizes revenue variance. We show that this result is fragile. Under interim IR, the optimality of the first-price auction breaks down in asymmetric single-item settings, and we characterize the variance-minimizing mechanisms for any implementable allocation rule in this environment. In multi-item symmetric regular environments with interim IR, we construct a mechanism that implements the efficient allocation and guarantees constant revenue while maintaining non-negative payments. Under ex-post IR, we show that revenue variance can be reduced relative to winner-pays-bid formats by introducing negative correlations in payments. Nevertheless, we show that the variance ranking between the winner-pays-bid auction and the uniform $(k+1)$-st price auction is maintained in multi-unit settings.