Deterministic implementation in single-item auctions
Abstract
Deterministic auctions are attractive in practice due to their transparency, simplicity, and ease of implementation, motivating a sharper understanding of when they can attain the same outcomes as randomized mechanisms. We study deterministic implementation in single-item auctions under two notions of outcomes: (revenue, welfare) pairs and interim allocations. For (revenue, welfare) pairs, we show a separation in discrete settings: 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 equivalent to randomized BIC auctions in terms of achievable outcomes. For interim allocations, under a strict monotonicity condition, we establish a deterministic analogue of Border's theorem for two bidders, providing a necessary and sufficient condition for deterministic DSIC implementability. Using this characterization, we exhibit an interim allocation implementable by a randomized BIC auction but not by any deterministic DSIC auction.
Keywords
Cite
@article{arxiv.2512.17386,
title = {Deterministic implementation in single-item auctions},
author = {Yan Liu and Zeyu Ren and Pingzhong Tang and Zihe Wang and Yulong Zeng and Jie Zhang},
journal= {arXiv preprint arXiv:2512.17386},
year = {2025}
}