Deterministic auctions are attractive in practice due to their transparency, simplicity, and ease of implementation, motivating a sharp understanding of when they match randomized designs. We study deterministic implementation in single-item auctions under two outcome notions: (revenue, welfare) pairs and interim allocations. For (revenue, welfare) pairs, we show a discrete separation: there exists a pair implementable by a deterministic Bayesian incentive-compatible (BIC) auction but not by any deterministic dominant-strategy incentive-compatible (DSIC) auction. For continuous atomless priors, we identify conditions under which deterministic DSIC auctions are implementationally equivalent to randomized BIC auctions in terms of achievable outcomes. For interim allocations, we establish a deterministic analogue of Border's theorem for two bidders, providing a necessary and sufficient condition for deterministic DSIC implementability, and use it to exhibit an interim allocation implementable by a deterministic BIC auction but not by any deterministic DSIC auction.

翻译：确定性拍卖因其透明度高、结构简单且易于实施而在实践中备受青睐，这促使我们深入探究其在何种条件下能与随机化设计相匹敌。本文研究单物品拍卖中基于两种结果概念（收益与福利组合、事前分配）的确定性实现。针对收益与福利组合，我们揭示了一种离散分离现象：存在某些组合可通过确定性贝叶斯激励相容拍卖实现，但无法通过任何确定性占优策略激励相容拍卖实现。对于连续无原子先验分布，我们确定了使确定性占优策略激励相容拍卖在可达结果集上与随机化贝叶斯激励相容拍卖实现等价的充分条件。针对事前分配，我们为双竞拍者情形建立了确定性版本的Border定理，给出了事前分配可通过确定性占优策略激励相容拍卖实现的充要条件，并借此构造出可通过确定性贝叶斯激励相容拍卖实现、但无法通过任何确定性占优策略激励相容拍卖实现的事前分配实例。