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.

翻译：我们研究在向具有独立私人估值的风险中性、单位需求投标人出售$k$个同质物品时的收益方差问题。尽管收益等价定理表明标准拍卖会产生相同的期望收益，但不同机制下的收益分布存在差异。先前的研究表明，在满足事后个体理性（IR）的单物品环境中，第一价格拍卖能够最小化收益方差。我们证明这一结论是脆弱的。在满足事中IR的条件下，第一价格拍卖的最优性在非对称单物品设定中不再成立，并且我们刻画了该环境下任何可实施分配规则对应的方差最小化机制。在满足事中IR的多物品对称正则环境中，我们构建了一种机制，该机制能够实施有效分配，在保持非负支付的同时保证收益恒定。在满足事后IR的条件下，我们证明通过引入支付中的负相关性，可以相对于赢家支付报价类拍卖降低收益方差。尽管如此，我们证明了在多单位物品设定中，赢家支付报价拍卖与统一第$(k+1)$价格拍卖之间的方差排序关系仍然成立。