Truthful by Omission: Click Thinning for LLM-Native Advertising

Junhua Liu; Zhicheng Liang; Zejun Zhang; Langzhou He; Feng Qian

cs.GTOct 22, 2026

Truthful by Omission: Click Thinning for LLM-Native Advertising

Authors: Junhua Liu, Zhicheng Liang, Zejun Zhang, Langzhou He, Feng Qian

Organizations: University of Southern California, Los Angeles, USA · The Chinese University of Hong Kong, Shenzhen, Shenzhen, China · University of Illinois Chicago, Chicago, USA

Abstract

Generative AI assistants are becoming an advertising medium, embedding sponsored content in their answers. This setting departs from classical position auctions in two ways: an ad's click-through rate depends on the passage that hosts it, and because users stop at their first click, earlier ads take clicks from later ones. This competition for clicks makes truthfulness delicate: a higher bid can reshape the allocation and put a competitor ahead of the bidder, reducing the bidder's clicks. Existing mechanisms either attain a constant fraction of the optimal welfare (advertisers' total click value) but are not known to be truthful, or are truthful but their welfare guarantee degrades as the number of passages grows. We achieve both even when the answer and its editorial order are fixed before bidding. Assuming each ad's click-through rate when reached is known and unaffected by omitting other ads, we give a computationally efficient mechanism that is truthful in expectation and attains at least half the optimal welfare under free reordering. Our key idea, click thinning, omits ads at random, showing earlier ads less often so that each ad's overall click probability no longer depends on the order of the ads. Welfare maximization then reduces to a tractable matching problem, and solving it exactly with VCG-style payments makes truthful bidding optimal in expectation. Characterizing the click probabilities that omission can achieve sharpens the approximation factor from $2$ to $2-(1-δ)^{K-1}$ when at most $K$ ads are shown and each click-through rate is at most $δ$ . This factor is the best possible for any order-preserving rule, even one that ignores incentives and computation, so truthfulness and computational efficiency incur no additional worst-case loss.

Figures & tables

Figure 1. Structure of the basic mechanism. Click thinning realizes order-invariant click service. Exact range optimization with click-contingent pivot payments ensures truthfulness in expectation and welfare at least $\mathrm{OPT}(v)/2$ at truthful reports.

Setting		Welfare $W/O$			Decomposition
$\delta$	$K$	Mean	Min.	Guarantee	$W/F$	$F/O$
0.1	2	0.963	0.930	0.909	0.970	0.992
	4	0.931	0.873	0.787	0.943	0.987
0.8	2	0.894	0.6427	0.556	0.908	0.985
	4	0.916	0.766	0.502	0.945	0.970

Table 1. Odds welfare ratios over 24 instances per row.

W/F

and

F/O

are means. Guarantee is

1/\alpha(K,\delta)

(Theorem 5.1 ).

Setting		Baselines			Proposed mechanisms
$\delta$	$K$	Single	Raw	Stand.	Basic	Odds	Aug.
0.1	2	0.795	0.987	0.987	0.905	0.963	0.968
	4	0.721	0.974	0.974	0.876	0.931	0.962
0.8	2	0.830	0.952	0.977	0.6431	0.894	0.909
	4	0.874	0.948	0.642	0.626	0.916	0.929

Table 2. Mean welfare/free-order OPT. All rules preserve editorial order. Raw and Stand. lack incentive guarantees.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Subset $S$	$\Pr(S)$	Click 1	Click 2	No click
$\varnothing$	$1/6$	$0$	$0$	$1$
$\{1\}$	$1/6$	$1/2$	$0$	$1/2$
$\{2\}$	$1/3$	$0$	$1/2$	$1/2$
$\{1,2\}$	$1/3$	$1/2$	$1/4$	$1/4$
Unconditional	$1$	$1/4$	$1/4$	$1/2$

Appendix

Table 3. Two-ad thinning (Section 3.1 ). Click and no-click probabilities are conditional on

S

except in the last row. Unequal retention (

1/2

2/3

) yields equal click service.

$A$ ’s report $x$	Selected matching	$q_{A}$	$u_{A}$ at $v_{A}=4$
$0\leq x<27/19$	$\{By\}$	$0$	$0$
$27/19<x<27/4$	$\{Ax,By\}$	$8/27$	$392/513$
$x>27/4$	$\{Ax\}$	$4/9$	$61/171$

Appendix

Table 4. Basic mechanism as

A

’s report

x

varies (

b_{B}=3

v_{A}=4

). Breakpoint ties use the public tie rule.

Contexts $m$	Cap $K$	Odds A/P	DP-VCG A/P	Min. $W/O$
4	2	6.1/14.2	4.6/8.9	0.924
4	4	6.7/30.5	9.0/35.8	0.914
8	2	13.6/25.3	16.6/33.3	0.918
8	4	14.6/62.4	128.1/518.0	0.937
12	2	18.1/43.6	41.2/74.4	0.924
12	4	24.2/112.1	747.2/2830.6	0.930

Appendix

Table 5. Median prototype times in ms (A/P: allocation/all pivots), six paired instances per row (

n\in\{32,128\}

). Min. is the smallest odds welfare/free-order OPT in the row.

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