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arXiv · 2610.34236

A Truthful-in-Expectation 2-Approximation for Pair-Specific Cascade Auctions in AI-Generated Content

Tao Jiang·Minbo Gao·Shaowei Cai
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Abstract

Generative AI interfaces can insert sponsored content at multiple points in an answer, where click-through rates (CTRs) depend on the advertiser-position pair. Under the cascade model, users read ads sequentially and stop after their first click, so both ad assignment and display order affect welfare. For arbitrary pair-specific CTRs, Balseiro et al. (WWW 2026) gave a $4/(1-\varepsilon)$-approximation whose monotonicity has not been established, and a monotone $O(\log m)$-approximation for $m$ candidate positions. Earlier truthful constant-factor mechanisms require factorized CTR models and do not apply. Whether monotonicity is compatible with a constant-factor approximation in this general setting was left open by that work. We give a polynomial-time mechanism for arbitrary pair-specific CTRs and any limit on displayed ads that is truthful and individually rational in expectation and achieves a 2-approximation to optimal cascade welfare. Our mechanism selects an advertiser-position matching and a designated last ad, then randomly thins earlier ads so that each selected ad's expected cascade CTR is the same fraction of its standalone CTR. This yields an exact closed-form expression for expected welfare, which we maximize over a bid-independent lottery range using linear programming. Exact optimization ensures monotonicity, while a random-prefix decomposition proves the factor-two guarantee, which is tight for this range. We also show that exactly optimizing the previous welfare surrogate can violate monotonicity, and evaluate welfare and running time on synthetic instances.

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Tao Jiang, Minbo Gao, Shaowei Cai. 2026-10-25. A Truthful-in-Expectation 2-Approximation for Pair-Specific Cascade Auctions in AI-Generated Content. https://arxiv.org/abs/2610.34236

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