Credible, Truthful, and Bounded-Round Mechanisms via Cryptographic Commitments

We consider the sale of a single item to multiple buyers by a revenue-maximizing seller. Recent work of Akbarpour and Li formalizes credibility as an auction desideratum, and prove that the only optimal, credible, strategyproof auction is the ascending price auction (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 two-round auction which is optimal, credible, and strategyproof. 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.