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A Robust Multi-Item Auction Design with Statistical Learning

Jiale Han, Xiaowu Dai

TL;DR

A novel statistical learning method for multi-item auctions that incorporates credible intervals to reduce the time cost of implementing auctions and introduces two new strategies that leverage these credible intervals to reduce the time cost of implementing auctions.

Abstract

We propose a novel statistical learning method for multi-item auctions that incorporates credible intervals. Our approach employs nonparametric density estimation to estimate credible intervals for bidder types based on historical data. We introduce two new strategies that leverage these credible intervals to reduce the time cost of implementing auctions. The first strategy screens potential winners' value regions within the credible intervals, while the second strategy simplifies the type distribution when the length of the interval is below a threshold value. These strategies are easy to implement and ensure fairness, dominant-strategy incentive compatibility, and dominant-strategy individual rationality with a high probability, while simultaneously reducing implementation costs. We demonstrate the effectiveness of our strategies using the Vickrey-Clarke-Groves mechanism and evaluate their performance through simulation experiments. Our results show that the proposed strategies consistently outperform alternative methods, achieving both revenue maximization and cost reduction objectives.

A Robust Multi-Item Auction Design with Statistical Learning

TL;DR

A novel statistical learning method for multi-item auctions that incorporates credible intervals to reduce the time cost of implementing auctions and introduces two new strategies that leverage these credible intervals to reduce the time cost of implementing auctions.

Abstract

We propose a novel statistical learning method for multi-item auctions that incorporates credible intervals. Our approach employs nonparametric density estimation to estimate credible intervals for bidder types based on historical data. We introduce two new strategies that leverage these credible intervals to reduce the time cost of implementing auctions. The first strategy screens potential winners' value regions within the credible intervals, while the second strategy simplifies the type distribution when the length of the interval is below a threshold value. These strategies are easy to implement and ensure fairness, dominant-strategy incentive compatibility, and dominant-strategy individual rationality with a high probability, while simultaneously reducing implementation costs. We demonstrate the effectiveness of our strategies using the Vickrey-Clarke-Groves mechanism and evaluate their performance through simulation experiments. Our results show that the proposed strategies consistently outperform alternative methods, achieving both revenue maximization and cost reduction objectives.
Paper Structure (29 sections, 6 theorems, 52 equations, 12 figures, 3 algorithms)

This paper contains 29 sections, 6 theorems, 52 equations, 12 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results
  4. Estimation of Distribution and Credible Intervals for bidder types
  5. Winnow Down Potential Winners
  6. Lower Credible Bound Method
  7. Degenerated VCG Mechanism
  8. Numerical Experiments
  9. Conclusion
  10. Proofs
  11. Proof of Proposition \ref{['fairness']}
  12. Proof of Theorem \ref{['New1']}
  13. Proof of Theorem \ref{['T1']}
  14. Allocation Complexity Analysis
  15. Algorithm
  16. ...and 14 more sections

Key Result

Proposition 1

Let $\mathcal{B}_j$ denote the set of bidders linked to the bidder with the highest upper confidence bound for item $j$, as defined by Bb. Then for each item $j \in [N]$, considering only bidders in the set $\mathcal{B}_j$ to implement a fair mechanism results in a new mechanism that is $\alpha$-fai

Figures (12)

  • Figure 1: Comparison of the revenue and regret when $m=30$, $N=10$.
  • Figure 2: Comparison of the proportion of bidder types without queries and comparison of the confidence rate when $m=30$, $N=10$.
  • Figure 3: Flow chart of the proposed mechanism.
  • Figure 4: Comparison of the revenue and regret when $m=30$, $N=10$.
  • Figure 5: Comparison of the proportion of bidder types without queries and comparison of the confidence rate when $m=30$, $N=10$.
  • ...and 7 more figures

Theorems & Definitions (15)

  • Definition 1: DSIC
  • Definition 2: $\delta$-DSIR
  • Definition 3: $\delta$-fairness
  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Lemma 1: Bernoulli's Inequality
  • Proof A.1: Proof of Lemma \ref{['lemma1']}
  • Proof A.2
  • Proof A.3
  • ...and 5 more