We consider the sale of a single item to multiple buyers by a revenue-maximizing seller. Recent work of Akbarpour and Li formalizes \emph{credibility} as an auction desideratum, and prove that the only optimal, credible, strategyproof auction is the ascending price auction with reserves (Akbarpour and Li, 2019). In contrast, when buyers' valuations are MHR, we show that the mild additional assumption of a cryptographically secure commitment scheme suffices for a simple \emph{two-round} auction which is optimal, strategyproof, and credible (even when the number of bidders is only known by the auctioneer). We extend our analysis to the case when buyer valuations are $\alpha$-strongly regular for any $\alpha > 0$, up to arbitrary $\varepsilon$ in credibility. Interestingly, we also prove that this construction cannot be extended to regular distributions, nor can the $\varepsilon$ be removed with multiple bidders.

中文翻译：

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通过密码承诺进行可信、真实和两轮（最佳）拍卖

我们考虑由一个收入最大化的卖家向多个买家出售一件商品。Akbarpour 和 Li 的近期工作将 \emph {credibility} 正式化为拍卖的必要条件，并证明唯一最优、可信、具有策略性的拍卖是带有储备的上涨价格拍卖（Akbarpour 和 Li，2019）。相比之下，当买家的估值为 MHR 时，我们表明加密安全承诺方案的温和附加假设足以进行简单的\emph{两轮}拍卖，该拍卖是最优的、策略证明的和可信的（即使投标人的数量只有拍卖师知道）。我们将我们的分析扩展到以下情况：买方估值为 $\alpha$-对于任何 $\alpha > 0$ 都具有很强的规律性，直至任意 $\varepsilon$ 的可信度。有趣的是，