---
title: "Deterministic Implementation in Single-Item Auctions"
authors:
  - "Yan Liu"
  - "Zeyu Ren"
  - "Pingzhong Tang"
  - "Zihe Wang"
  - "Yulong Zeng"
  - "Jie Zhang"
doi: "10.24963/ijcai.2026/388"
url: "https://ijcai.org/proceedings/2026/388"
pdf: "https://ijcai.org/proceedings/2026/0388.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "3488-3496"
track: "Main Track"
keywords:
  - "Game Theory and Economic Paradigms: Mechanism design"
  - "Game Theory and Economic Paradigms: Auctions and market-based systems"
---

# Deterministic Implementation in Single-Item Auctions

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

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 3488-3496. DOI: [10.24963/ijcai.2026/388](https://doi.org/10.24963/ijcai.2026/388)

## 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.