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arXiv · 2512.17386

Deterministic implementation in single-item auctions

Yan Liu·Zeyu Ren·Pingzhong Tang·Zihe Wang·Yulong Zeng·Jie Zhang
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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.

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Yan Liu, Zeyu Ren, Pingzhong Tang, Zihe Wang, Yulong Zeng, Jie Zhang. 2025-12-19. Deterministic implementation in single-item auctions. https://arxiv.org/abs/2512.17386

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