Auction Design using Value Prediction with Hallucinations

TL;DR

This work studies revenue-maximizing auctions when the seller observes per-buyer predictions that may be true values or hallucinations, modeling each signal with a posteriors $F_{\gamma,s}$ and a known hallucination probability $\gamma$. It extends Myerson’s revenue theory to irregular posteriors via a generalized ironing framework (Monteiro) and derives a closed-form, piecewise ironed virtual value, enabling a direct mechanism that allocates to the highest nonnegative ironed virtual value. In the single-buyer setting, the optimal mechanism collapses to a three-regime posted-price rule—ignore, follow, or cap—depending on the realized signal, with precise threshold definitions. The analysis highlights how prediction structure fundamentally shapes revenue-optimal pricing and demonstrates robustness of the Bayesian design to hallucination risk, contrasting with noise-based models and informing practical adoption of ML-powered auction design.

Abstract

We investigate a Bayesian mechanism design problem where a seller seeks to maximize revenue by selling an indivisible good to one of n buyers, incorporating potentially unreliable predictions (signals) of buyers' private values derived from a machine learning model. We propose a framework where these signals are sometimes reflective of buyers' true valuations but other times are hallucinations, which are uncorrelated with the buyers' true valuations. Our main contribution is a characterization of the optimal auction under this framework. Our characterization establishes a near-decomposition of how to treat types above and below the signal. For the one buyer case, the seller's optimal strategy is to post one of three fairly intuitive prices depending on the signal, which we call the "ignore", "follow" and "cap" actions.

Figures (6)

• Figure 1: The figure illustrates the truncated ironing procedure. The distribution $F$ used is a mixture of two truncated normals on $[0,2]$ with parameters $(0.1,0.04)$ and $(1.9,1.8)$ and respective weights $0.8$ and $0.2$. (a) The figure shows the initial $J$ function (in blue) and the convex envelopes of this function on different intervals: $F^{-1}(0.2)$, $F^{-1}(0.5)$ and $F^{-1}(2)$. (b) The figure shows the induced virtual value function before ironing and by ironing on three subintervals: $0.2$, $0.5$ and $2$.
• Figure 2: Numerical counter-example to the near-decomposition property without regularity.
• Figure 3: Ironed virtual value for different priors. In each plot the unironed virtual value corresponds to the naive evaluation $\varphi_{F_{\gamma,s}}$, wherever it is well defined (i.e., everywhere but at $s$). The ironed virtual value corresponds to the virtual value characterized in \ref{['thm:main']}.
• Figure 4: Illustration of the three different regimes in the single-buyer case. The figure represents the correct virtual value functions under the three different regimes described in \ref{['cor:optimal_price']}, when $F$ is the uniform distribution and $\gamma = 0.75$. The place where the virtual value crosses zero is the optimal price.
• Figure 5: Optimal price as a function of the signal. We compare the optimal price for the value-with-noise and the hallucination-prone models, assuming a uniform prior in both cases. The value $\gamma$ is set to $0.75$ and $\sigma^2$ is chosen the match the variance of the hallucination model when $s=0.5$.

Theorems & Definitions (31)

• Theorem 1
• Example 1
• Proposition 1
• Proposition 2
• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4
• Proposition A-1
• proof : Proof of \ref{['prop:full_surplus']}