Beyond Last-Click: An Optimal Mechanism for Ad Attribution
Authors: Nan An
Weian Li
Qi Qi
Changyuan Yu
Liang Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Ad Attribution
Mechanism Design
Accuracy
Dominant Strategy Incentive Compatible
Primary area: theory

Abstract: Accurate attribution for multiple platforms is critical for evaluating performance-based advertising. However, existing attribution methods rely heavily on the heuristic methods, e.g., Last-Click Mechanism (LCM) which always allocates the attribution to the platform with the latest report, lacking theoretical guarantees for attribution accuracy. In this work, we propose a novel theoretical model for the advertising attribution problem, in which we aim to design the optimal dominant strategy incentive compatible (DSIC) mechanisms and evaluate their performance. We first show that LCM is not DSIC and performs poorly in terms of accuracy and fairness. To address this limitation, we introduce the Peer-Validated Mechanism (PVM), a DSIC mechanism in which a platform's attribution depends solely on the reports of other platforms. We then examine the accuracy of PVM across both homogeneous and heterogeneous settings, and provide provable accuracy bounds for each case. Notably, we show that PVM is the optimal DSIC mechanism in the homogeneous setting. Finally, numerical experiments are conducted to show that PVM consistently outperforms LCM in terms of attribution accuracy and fairness.

Beyond Last-Click: An Optimal Mechanism for Ad Attribution
Nan An
Weian Li School of Software Shandong University Jinan, China weian. li@sdu. edu, cn
Gaoling School of Artificial Intelligence
Renmin University of China
Beijing, China annan0425@ruc. edu. en
Qi Qi
Changyuan Yu
Gaoling School of Artificial Intelligence
Baidu Inc.
Renmin University of China
Beijing, China
Beijing, China qi qit.uiiruucuuu cn
yuchangyuan@baiduu.omm com
Liang Zhang
Gaoling School of Artificial Intelligence
Renmin University of China
Beijing, China
zhang lianggruc..c..... edu. on
Abstract
Accurate attribution for multiple platforms is critical for evaluating performance- based advertising. However, existing attribution methods rely heavily on the heuristic methods, e.g., Last-Click Mechanism (LCM) which always allocates the attribution to platform with the latest report, lacking theoretical guarantees for attribution accuracy. In this work, we propose novel theoretical model for the advertising attribution problem, in which we aim design the optimal dominant strategy incentive compatible (DSIC) mechanisms and evaluate their performance. We first show that LCM is not DSIC and performs poorly in terms of accuracy and fairness. To address this limitation, (PVM), DSIC mechanism in which platform's 's attribution depends solely on the reports of other platforms. We then examine the accuracy of PVM across both homogeneous and heterogeneous settings, and provide provable accuracy bounds for each case. Notably, show that PVM is the optimal DSIC mechanism in the homogeneous setting. Finally, numerical experiments are conducted to show that PVM consistently outperforms L.M in terms of attribution accuracy and fairness.
introduce the Peer- Validtedd Mechanism
Introduction
Online advertising has become the dominant force in the global advertising landscape, with expen- ditures projected exceed $790 billion in acco-accoun for over 72% of total ad spend-an continuing to grow at consistent rate of more than 10% annually. This substantial and growing capital investment calls for the development and application of robust methodologies optimize budget allocation across diverse digital platforms.
"Corresponinng author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Advertising attribution, the process of assigning credit for user conversions (such as app downloads or product purchases) to the platforms that contributed them, plays a central role in guiding these allocation decisions and has consequently garnered significant attention. In practice, attribution reflects a variety of design principles and business objectives. Methods range from simple heuristics such as first-click and time-decay attribution to data-driven approaches based on machine learning and causal inference. Among these, last-click attribution has become the industry default due to its simplicity and its practical relevance for measuring revenue-driven, bottom-of-funme conversions.
Under last-click attribution, the platform that most recently interacted with the user receives full conversion credit. Because these credits directly determine performance metrics and future budget allocation, platforms have a strong incentive to manipulate the timing of their reports to appear last in the user's s interaction sequence. Such strategic behavior can distort attribution outcomes, overstating the influence of certain platforms even on its own terms.
This manipulation has become increasingly feasible in modern advertising ecosystems, especially when the advertiser does not control the landing page-such as app installations through app stores or purchases on major e-commerce platforms-where click events cannot be directly measured. In the past, advertisers relied on redirect-based tracking flows, where an intermediary measurement partner (MMP) logged the click before redirecting the user to the final landing page, thus providing an independent, verifiable timestamp. However, the industry has since shifted toward redirect-less tracking paradigm, in which user navigation and click reporting are decoupled to improve latency and privacy. Without an intermediary verifier, advertisers now depend entirely on platform' reporred timestamps, making strategically timed reports both feasible and practically undetectable[
Nevertheless, such strategic behavior has received limited attention in the academic literature. Most prior work on advertising attribution instead focuses on modeling platform contributions to conver- sions using increasingly sophisticated statistical or machine learning methods, under the assumption that platforms passively and truthfully report user interaction data. In this paper, we initiate the study of advertising attribution from mechanism design perspective, treating platforms as strategic agents that may misreport in order to maximize their assigned credit. Rather than proposing a new attribution philosophy, we work within the prevailing logic of last-click attribution and ask: How can we design an attribution mechanism such that platforms have no incentive to misreport, while still assigning credit to the platform with the true last click?
Main Contribution
To address the above question, we first model the advertising attribution scenario game- theorehe model in which multiple platforms strategically submit user interaction logs to compete for conversion credit. The advertiser then allocates credit according to a predefined attribution rule. In this model, our analysis focuses on characterizing dominant strategy incentive compatible (DSIC) mechanisms, and evaluating the performance of different attribution mechanisms, using two key metrics: accuracy and fairness. Accuracy measures the alignment between the assigned and true contributors, while fairness assesses whether each platform receives its deserved share of credit in expectation. Detailed results are presented in Table I with proofs in the full version.
Table 1: Mechanism performance under different settings
DSIC
Fair
Accuracy (Homogenewus)
Accuracy (Heterogeneouss)
(2 //2/ 0.3431
x
(Theorem
LCM
(Proposition
(Proposition
n 2 ((1 L
""'""
Theorem
(Theorem
3/4 = 0.75
19/27 0.7037 (Theorem
(Theorem 6
PVM
(Proposition
(Proposition
2 3: 1- (1 1)
3:
[log, (Theorem
()))
(Theorem 0
6
We begin by analyzing the commonly used Last- -lick Mechanism (LCM) and theoretically demon- strate that it is not DSIC. For LCM's performance, our findings reveal that, in the worst-case scenario,
"This shift has been driven by privacy regulations such as the European Union's 's General Data Protection Regulation and Apple's 's App Tracking Transparency framework [8 [6]. and the adoption of redirect-less systems including Google's 's and Microsoft's 's parallel tracking and Apple's SKAdVetwork 100 19 B).
2

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LCM can perform remarkably poorly. Even with just two heterogeneous platforms, both accuracy and fairness can approach arbitrarily low values.
To ensure DSIC, we propose a novel attribution mechanism called the Peer- Validated Mechanism (PVM). The mechanism operates as follows: only platforms reporting before the conversion eligible for attribution, and the credit platform receives depends solely on peer reports and prior of its own report. Since platform's 's report does not influence its own outcome, PVM is DSIC by design. We then theoretically demonstrate that PVM consistently outperforms the LCM in terms of both attribution accuracy and fairnsss. We further prove that is the optimal DSIC mechanism in the homogeneous setting (Theorem (5). Mutiple simulations using distributions fitted from real-world ad-conversion data further validate the superiority of PVM.
To the best of our knowledge, this is the first work to formally model the advertising attribution problem within a theoretical framework, and to rigorously analyze the incentive and efficiency properties of the widely adopted Last-Click Mechanism. By shifting attention from empirical heuristics and estimation to mechanism design, our work offers foundational insights for developing attribution systems that are robust, fair, and incentive-compatibe in digital advertising markets.
All missing proofs can be found in full version.
Related Work Recent research on advertising attribution has primarily focused on multi-touch attribution, which distributes conversion credit across multiple platforms based on observed user interactions data. A wide range of modeling approaches have been explored, including probabilistic models such as survival analysis [ [4
23
28 [29], Shapley value-based methods for fair allocation
14 [4]] and Markov models for channel transition influence 15]. Furthermore, causal inference 6
27 and deep learning [2] 18, 17 26 27 have been applied to better capture temporal and interaction complexity. Despite their sophistication, these approaches generally assume that the user interactions data reported by platforms are accurate and complete.
However, this assumption often fails in practice, as platforms may strategically misreport to gain greater attribution. In contrast, mechanism design offers a principled framework for addressing
strategic behavior, with incentive compatibility (IC) as a central design goal [12 20 25
5
While IC-based techniques have been widely applied in domains such as auctions 77. voting p and
resource allocation [22], their application to attribution remains underexplored. Attribution presents
new challenges: the strategic behavior of platforms is often ill-defined, and their utility depends on
uncertain conversion outcomes, making standard mechanism design tools difficult to apply directly.
2 Model and Preliminaries
This section develops formal model to study advertising attribution under strategic platform behavior. We first describe a typical real-world scenario, then formalize the model components, define the attribution mechanism, analyze strategic behavior, and finally define the advertiser's objective.
Throughout, we adopt the last-click attribution standard, treating the final platform a user's interaction sequence the one that deserves credit. We focus settings with at least two platforms, the minimal case where attribution ambiguity and manipulation arise. In practice, the number of platforms involved in conversion is typically small-often no more than five.
2.1 Real-Worls Advertising Scenario
Consider the real-world online advertising scenario where user interacts with ads from multiple platforms (n 2 2) before a conversion event. When the user converts, the advertiser seeks to allocate credit based on the click logs reported by the platforms.
The process unfolds as follows. Each platform E [n]] first detects a user click and records log at the corresponding absolute click time rahs, It then selects an absolute reported time rabs 2 1abs at which it submits the log to the advertiser. At some time to 2 max (t }. the user converts, and the advertiser performs credit attribution based on reports received by lo-that is the set {v=ghs rnghs < lo). Crucially, while the advertiser observes the conversion time lg. platforms must decide when to report without knowing when the conversion will occur.
3

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This scenario highlights the fundamental challenge in attribution: the advertiser must infer the true sequence of events based on potentially delayed reports from strategically acting platforms. The discrepancy between true click times and reported times necessitates careful mechanism design.
2.2 Advertising Attribution Model
We now present game-theoretic model of the attribution process, capturing strategic platform behavior and informing mechanism design. To simplify analysis, we adopt conversion-aligned timeline, setting the conversion time ly = 0 without loss of generality, Under this transformation, all click times are expressed relative to the conversion and lie in (-oc, 0]. Specifically, we define
: gabs to S 0, Vi [m]]
where & denotes the relative click time of platform Figure [T] illustrraes this transformation: two platforms record clicks 10:40 a.m. and 10:50 a.m., and the conversion occurs at 11:00 a.m., their relative click times become t = 20 and t = 10, with the conversion time 0. Under the
Alignment
10: 40 am
10: am
11: 00 am
-20
-10
Time
Comveriion-alinnes
Figure 1: Conversion-alignee time transformation
conversion-aligee aligned timeline, the relative click time = (tx))e(x)- wwhcc depends on the unknown conversion time-is is therefore unobservable to platforms. To capture this uncertainty, model t, as a random variable drawn independently from a commonly known distribution, with cumulative distribution function (CDF) (t( and probability density function (PDF) fi(t), supported on (-oo, 0]. This distribution may be interpreted as prior belief based on platform-level statistics. Let (E)) denote the joint distribution from which the click time vector is drawn.
To model strategic reporting, we assume each platform E [n] selects non non-negative reporting delay T 2 0, resulting reported time r; t4 + т on the conversion-aligee aliigned timeline"). Since t, is unobservable when the platform commits to its strategy, the chosen delay is applied uniformly across all realizations 4, We denote the delay profile as = (Ti) and the resulting reported time profile by r (ri)se[n) t +++ T. Unless stated otherwise, all subsequent analysis is conducted on the conversion-aligne aliigned timeline.
2.3 Attribution Mechanism
We define an attribution mechanism M by its assignment rule M(r) = (=xx(r)) {rx(())ee())) where x; (r)r) denotes the credit assigned to platform i given the reported time profile r A mechanism is said to be feasible if it satisfies the following constraints:
0
0 (r) < 1,
Vi E [n].
2 r- 0,
Vi [n].r; > 0,r-;
(2)
x
E F
Σ x.((++T)) < VF,T
Constraints I and ( bound individual credit and exclude post-conversie reports. Constraint
limits the expected credit, ensuring that the advertiser's overall budget respected
'We focus on strategic delay in reporting rather than repeated or fraudulent submissions. Each platform reports its click once, possibly after strategic delay, to maximize its attribution credit. This setting differs from click spamming and click injection, which involve multiple fabricated reports.
'In practice, reports submitted after the conversion time (i.c., > 0) are typically not received or used by the advertiser. However. for modeling generality, allow such values inputs to the mechanism. Their exclusion from attribution is later enforced through explicit feasibility constraints (see Constraint (2).
'Constraint 3 normalizes total credit in expectation rather than per conversion. This design reflects advertisers' long- term budget control: it maintains the average expenditure over many conversions while allowing more flexibility for designing decettve-compatioe mechanisms than strict per- per-instance normalization.

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Given an attribution mechanism M, we define platform i E [ni]'s instantaneous utility under report profile as the credit assigned by the mechanism: u,(r) (r)).. Given the distribution profile F and others' strategy T -is platform selects its delay T; to maximize its expected utility:
U. UT T-)) E [u, T)] E [x. + T)]
From the advertiser's perspective, ideal attribution mechanism M should achieve two primary goals: (i) incentivize truthful reporting to ensure reliable interaction data; and (ii) accurately assign credit to the platform responsible for the conversion.
We first use dominant strategy incentive compatibility (DSIC) to capture truthful reporting:
Definition 1 (DSIC). A mechanism M is DSIC if for every platform i, truthful reporting (T, = 0) maximizes utility ur(r) regardless of the realized true click times T-i chosen by other platforms That is. for all platforms E [m], all true times tę S 0 and t.;, all others' strategies T-i, and any deviation delay T 0:
(tat-i) or the strategies
u,(t,, t- + + 2 (t + T f/,t,,---)
easy to verify that DSIC is equivalent to non-increasing allocation rule with respect to platform's 's own report.
Theorem 1. An attribution mechanism M satisfies DSIC if and only if. for every platform i and any fixed reports from other platforms r-s. the credit [r,r,, r-1) is non-increasing in its own report TG-
Second, we formalize attribution accuracy as the mechanism's ability to assign credit to the true last-click platform. Specifically, we defined the accuracy of mechanism M. given F as
ACC(M; F) = EN-F Σ Cx(t+++he NE) I[[i arg max max
(4)]
3
where NN is the Nash equilibrium induced by and M. Note that NE for a DSIC mechanism. Thus, given known distribution F, the advertiser's optimization problem is formulated
max M
ACC(M;F)
(4)
s.t. Feasible and DSIC.
Beyond defining accuracy with respect a fixed F, we define the accuracy of mechanism M as ACC(M) = inf ACC(M; F),
capturing worst-case performance across F, serving evaluation for mechanism's performance.
3 The Last-Click Mechanism
In this section, we conduct a rigorous analysis the Last-Click Mechanism (LCM). We begin by formally defining LCM and then demonstrate that it fails to satisfy DSIC. We further evaluate its accuracy at equilibrium and derive accuracy bounds both homogeneous and heterogeneous platform settings. Formally, the Last-Click Mechanism is defined MLCM:
Definition (Last-Click Mechanism). Given the report profile = (ri)se(n) the Last-Click Mecha- nism defined as MLCM = (2,(r) Specifically,
{
i E S and r: r:= maxjes(fs). otherwise,
x.(r)=
S <0) is the set of platforms with effective reports. Ties are broken uniformly at random among the tied platforms.
where S =
'Note that, in the absolute-time model, the platform must take expectation over the unknown conversion time and other click times. In the conversion-alee alligned model, the conversion time fixed at 0. and the same uncertainty is reflected the distribution
'DSIC benefits cold-start scenarios by ensuring truthful reporting without requiring prior knowledge, enabling reliable attribution from the outset and facilitating the learning of the true distribution.
5

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Due to its simplicity and its intuitive principle of crediting the platform associated with the user's s final click before secersionn LCM is widely adopted in practice. However, it is easy to see that platforms may benefit from Therefore: LCM does not satisfy DSIC.
it
strateeiiacaa strategically delaying their reports, making truthful reporting suboptimal
Proposition 1. The Last-Click Mechanism not a DSIC mechanism.
Accuracy Analysis
3.1
Since LCM is not DSIC, it may assign credit to a platform that wasn't 't truly last, leading to inaccurate attriffiom
attribution. We therefore analyze its equilibrium accuracy in both homogeneous and heterogeneous
platform settings, and derive accuracy bounds for both two- two-platform and n-platform cases
We first consider the case with two homogeneous platforms and present result in Theorem 2 Theorem 2. When there are two homogeneous hmmogeneous platforms with identical distribution F((), supported on (-o0,0 0j, (), the accuracy of MLCM is exactly (2 (2- and this bound is tight.
v2)²,
To prove Theorem d we first analyze the incentive constraint at a symmetric strategy profile (To: vo)- By requiring that no platform benefits by unilaterally deviating from To to truthful reporting, derive the necessary condition F(-r)) 2 2 - V2. Since LCM can only attribute correctly when both true click times are before -oo, this yield a lower bound accuracy of (2 v2)². We then construct a family of distributions fxr (t) = Cas (e - 1), supported on M, 0]. where car is a normalization constant. We show that this game admits unique symmetric Nash equilibrium, and as n
M + oo, the accuracy converges exactly (2 2
homogeneous
We now extend our analysis to the general case with n homogeneous platforms.
Theorem 3. When there are n homogeneous platforms with identical distribution F(I), supported on (-ox, Oj. the accuracy of MLeM is bounded as follows:
a
1 1
( < ACC(MioN) S 1-
(1-11
2 V6
2 - v6
4
4
The lower bound derived using an argument similar to the two-platform case, by examining the condition required for a symmetric equilibrium. For the upper bound, we analyze the symmetric equilibrium under a specific distribution with a linear probability density function f(t) = 22t
equiliiin
supported supported on [-1, 0j.
Finally, we consider the heterogeneous case, where each platform may follow a different distribution (t). Surprisingly. we show that the accuracy. of the LCM can be arbitrarily low, even in a simple setting with just two heterogeneous heterogeneous platforms.
Theoren 4. When there are n heterogeneous platforms with distributions Fe(l), all supported on (-o0, 0). the accuracy of MLLM can be arbitrarily small and approach to 0.
The proof relies on key insight: a platform with a highly concentrated distribution (e.g., supported on (C e, C' + <)) can easily manipulate its report to secure attribution credit. We construct an instance where one platform has such a ieceenraated distribution, while the others have click time supports strictly greater than it. In this scenario, we show that in equilibrium, the concentrated aoroocchiiia 1, causing overall accuracy to approach O.
supple
platform receives attribution with probability a
4 The Peer- Validated Mechanism
in addressing
In this section, we introduce the Peer- Validated Mechanism (PVM), novel mechanism the non-DSIC issue of LCM. Intuitively, if the credit assigned to platform is independent of its own report, the mechanism is DSIC. Based on this idea, we propose the PVM as follows:
*Since our focus is on DSIC mechanisms, we restrict our evaluation of LCM to instances where equilibrium is guaranteed, without analyzing its existence in general. Even within this limited scope, the results clearly demonstrate LCM's poor performmacc in setting.

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Definition 3 (Peer- Validated Mechanism). Consider n platforms with the CDF {Fi)sen and PDF (fi)ien supported on (-oc, 0]. Let (re)) be the reported time profile from n platforms. The Peer- validtedd Mechanism assigns credit based on mutual validation among platforms, and is defined as MrvM = (n.(r))etv)) with
I[r S 0] -mma I [lfr s 0] &
ifS otherwise.
x,(r))
where S {j [m] Ir 0f denotes platforms with eligible reports. B, P(i arg max, (ty)) S fi(t)[l, Ft(t) dt is the probability that platform is the true last-click platform based on the prior. The validation threshold ag)) is defined as the solution to [ (3 = B
Roughly speaking, PVM assigns credit to platform s's credit based on cligible reports from other platforms. When such peer reports exist, the mechanism compares them to a threshold a which chosen so that the probability of peers' true click times being no later than ag matches the prior B3 that platform is the true last. This validation process leverages instance-level information to make attribution decisions while preserving incentive compatibility. If no eligible peer reports available, PVM falls back to allocating 84 based on the prior. The reason only eligible reports are used for validation is that the mechanism assumes no overt misreporting among them, while ineligible reports (ry 0) are definitely misreports and thus excluded due unmodeled behavior. Finally, the indicator T[r; & Oj ensures that attribution only goes to pre-conversion reports.
Since any reporting delay either disqualifies the platform itself or prevents others from being at- tributed, it is straightforward to verify that PVM satisfies feasibility and DSIC 10 as formalized in Proposition 2
Proposition 2. The Peer- vee--Vadddeed Mechanism is a DSIC mechanism.
As PVM is DSIC, we focus on truthful reports (r = t). In this case, S = [n]. and we let a denote the threshold used in x; (+), defined by 1 (a:) = B3.. The allocation rule then simplifies to
(t) [[max [ty} ax] Vi [n].
We adopt this reduced form throughout the remainder of our analysis of PVM.
4.1 Optimality of PVM for Homogeneous Platforms
We surprisingly find that PVM is the optimal DSIC mechanism in the homogeneous platform setting. Theorem S. When the platforms are homogeneous, the Peer-Validated Mechanism (PVM) is the optimal DSIC mechanism with respect to the accuracy.
To show this optimality, we aim to identify the DSIC attribution rule (x, that maximizes accuracy. This is challenging task, as it involves optimizing over set of functions simultancously. However, for any fixed expected attribution E = Eg [z,(t)], we can characterize the most accurate DSIC rule that achieves it, then the problem reduces optimizing over the expected attribution vector e = (c)).E(M. The following lemma shows that such a characterization indeed exists.
Lemma 1. For platform and fixed expected attribution ei, there exists optimal DSIC attribution rule for platform w.r.t. accuracy, satisfying & = EE, (t)),, that can be written as
[1, if max;4i(t,} S A,,
(11,
o, otherwise,
where G,(t) - 11g;;F(() is the CDF of the random variable maxizi(t,)) (ty) and Gz(O,) C₁.
"hhe existence and uniqueness of as and & under standard regularity conditions, along with handling edge cases (e.g.. flat or discontinuous CDFs), are detailed in full version.
10 simple variant of PVM also preserves DSIC under the click spamming problem, where platform may repeatedly report the same click at later timestamps. Specifically, the modified mechanism takes the first valid report (if' any) from each platform as input while keeping the rest of the allocation rule unchanged. Under this setting, the platform's 's own reporting time remains decoupled from its expected number of attributions.
7

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Herein, we give a proof sketch of Lemma] ! First, as any DSIC rule must be non-increasing in t (Theorem []. we claim that, maximize accuracy, the optimal DSIC rule z,(t,, should be constant when given f-j, so that larger values of 44, which more better indicate that platform is last, are not penalized. Second, given a fixed expected attribution e, the eeff-independent rule x; should prioritize instances with smaller n {t, ), where platform i is more likely to be last. This greedy strategy yields the threshold- form optimal DSIC rule in the lemma. When G, is somewhere flat, multiple thresholds may achieve e,, and combining them may yield non-threshold variants. Still, at least one such optimal rule exists.
Based on Lemma I the task reduces to finding the optimal iei)innn in)- Since G,,),) = e,, the original optimization problem (4) can therefore be reformulated in terms of (0:).e(m) as follows:
max 0
Σ
(1) Fi(u)) du
im1
s.t. Σ G,(0.)=1
In particular, for homogeneous platforms, the thresholds defined within the PVM precisely align with the solution to the optimization problem outlined above, establishing its optimality as stated in Theorem
4.2 Accuracy Analysis
We now analyze the accuracy of PVM. For the homogeneous setting, we give a tight bound on the accuracy. Since PVM is the optimal DSIC mechanism, this accuracy is the maximum value DSIC mechanism can achieve.
Theorem 6, When there are n homogeneous platforms with identical distribution F(t), supported on (-oo, 0), the accuracy of MPYM is exactly equal to
ACC(MPvM) =1 -1-1111 (1-1)
In the homogeneous case, symmetry implies that all thresholds a; are equal, denoted by a, and satisfy F(a)"-1= = 1/n. Therefore, PVM makes correct attribution if either all reports no greater than a, which occurs with probability (1/n)*/(m-1) 1), or exactly report exceeds a, which occurs with probability 1 (1/n) 1/(n11(())) These probabilities depend only n,
the specific distribution.
Summing them gives the accuracy in Theorem 6
In practice, the number of platforms n typically does not exceed 5. We therefore conduct comparison
with the Last-Click mechanism (presented in Table to show that PVM is strictly superior.
Table 2: The accuracy comparison between PVM and LCM (Upper bound).
MpvM
Upper bound of MLLM
Ratio (MPrM / /MEM UB)
0.75
(2 2 Rd 0.3431 (tight bound)
285877
0.6151
0.3336
1,8437
0.5275
0,2314
2.2799
0.4650
0.1605
2.8977
In the rest, we consider the general wwwpoggennnos-lllafffrr setting. We show a tight bound on accuracy for two-platform case (Theorem 7 and lower bound for n-platform case (Theorem 8). Theorem 7. When there are two helerogeneous platforms, the accuracy of MpyM exactly equal to ACC(MPvM) = 19/27 Re 0.7037.
To establish the result, we first formulate optimization problem that characterizes the worst-case accuracy by maximizing the misattribution probability. In the two-platform setting, all attribution outcomes can be explicitly enumerated, making this optimization analytically tractable. To show tightness, we then construct a concrete instance that satisfies the optimality conditions, thereby achieving the accuracy value of 19/27.

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Theorem 8. When there are n. heterogeneous platforms, the lower bound on the accuracy of MPvM MCC(M)vr) = (19/27) llog
For heterogeneous platforms, we design a binary-tree- based mechanism to derive lower bound for PVM. Starting from the root node, which represents all n platforms, we recursively partition them into two disjoint subsets I. and R of sizes In/2] and [n/2]]. respectively. Each subset is treated as a virtual platform, represented by the distribution of max,eL (4: or max,eR [4.. At each internal node, the attribution reduces [log2 n levels yields an overall accuracy lower bound of (19/27) [owg (Tow) "1, Since PVM is guaranteed to perform least as well as this mechanism, the same expression serves as lower bound for its accuracy.
problem between two heterogeneous platforms. Repeating this over
4.3 Fairness of PVM
Besides the DSIC and accuracy, PVM also satisfies a strong fairness property: the expected attri- bution E [j]] for each platform i exactly matches its true probability of contributing the last click, P(i arg max, {4))). This alignment offers a principled basis for evaluating long-term platform effectiveness and simultaneously promotes trust in the mechanism's 's equity. To quantify this alignment and enable comparisons across mechanisms, define the following metric:
Definition 4. The fairness score of mechanism M under the joint distribution F is defined
Eir, (t)
FAIR(M: F)
min (ii max, (4)120)
{
P(i arg max; (G))
Definition 5. A mechanism M is Fair if. for any joint distribution F, holds that
F) 1.
The fairness score FAIR(M; F) quantifies how closely a mechanism' 's expected attribution matches the true last-click probabilities, with a score of 1 indicates perfect alignment. A Fair mechanism ensures that attribution faithfully reflects contribution probabilities across all distributions. PVM is a fair mechanism directly from the choice of (as)<e(m) under DSIC:
Eg Jx. (t) = E, (m) a.] III P(i arg max(t,]) })
371
871
Proposition The Pelr-Validated Mechanism is Fair.
In contrast, the Last-Click Mechanism fails to meet this property. Proposition 4. The Last-Click Mechanism not Fair.
LCM fails the Fair property due its fairness score being highly sensitive to distributional differences and strategic delays, especially under heterogeneity. As shown in Table 3 the fairness score can degrade to in such settings.
Table Worst-Cass Fairness Score of LCM under Equilibrium.
Scenario
Worst-Case Fairness (inf F FARR F))
Homogeneous, =
1 (V2 - 1)2 0.828
Homogeneous, n 2 3 (1- (1/n)m/(a-1), 2+vl
2- jan]
Heterogeneous, n 2 2
5 Numerical Experiments
We empirically evaluate PVM against LCM using simulations based on click time distributions fitted from real-world ad conversion logs from four advertising platforms. Experiments cover two settings: homogeneous and heterogeneous. In the homogeneous case, we simulate (2,3, 4, 5) identical platforms, all following the click time same distribution, repeated across four distributions derived

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from real data, In the heterogeneous case with n 2, we simulate all six platform pairs formed by different combinations of the four distributions. Under LCM, platforms play in equilibrium; under PVM, they report truthfully by DSIC. Each configuration was evaluated using 5 x 10t simulated user paths, repeated over 10 independent runs.
PVM consistently outperforms LCM in both accuracy and fairess across all settings, Table reports the improvements as mean = standard deviation over platforms (homogeneous) or platform pairs (heterogeneous), Specifically, accuracy gains grew with n (up to 0.3041 when n = 5) and remains notable under heterogeneity (0.0655). Fairness improvements are small in homogeneous cases but substantial in heterogeneous ones (0.1320).
Table 4: Aggregate summary of PVM's improvements over LCM, (mean + standard deviation)
Homo Setting
Hetero Setting
Metric
2
4
5
(over pairs)
Acc.
0.0404 + 0.0396
0.1583 + 0.0439
0.2444 + 0.0580
0.3041 + 0.0490
0.0655 + 0.0283 0.1320 + 0.0598
Fair.
0.0248 + 0.0089
0.0157 = 0.0034
0.0107 = 0.0047
0.0111 + 0.0040
Conclusion and Discussion
This paper introduces a formal game-theoretic framework for advertising attribution under strategic platform behavior. We show that the widely used Last-Click Mechanism fails to be dominant strategy incentive-compatible (DSIC) and performs poorly in both accuracy and fairness. To address these limitations, we propose the Peer-Validant Validated Mechanism (PVM), novel DSIC mechanism that allocates credit based peer reports. We prove that PVM achieves optimal accuracy in homogeneous settings, offers provable guarantces in heterogencous ones, and satisfics a strong faireess property. Our theoretical analysis is further validated by numerical experiments using real-world data, where PVM consistently outperforms LCM.
In practice, peer-validation principle offers a concrete design guideline for trrentive-compatinee attribution systems. For instance, machine learning-bai based models, excluding a platform's 's own report as an input feature ensures truthfulness, shifting the focus from detection to design.
Besides, PVM framework can be extended settings with correlated click-time distributions while preserving the core peer-validation principle and the DSIC property. The validation rule generalizes from scalar threshold (a,) to multi-dimensional acceptance region D; over peer reports t-s, constructed greedily by including outcomes with the highest posterior probability that platform i was the true last click until P(t_, D₂) B,. A platform receives credit if and only if its peers' reports fall within D: Under this modification, the homogeneous-can results remain unchanged, since our proofs for those theorems do not rely on the independence assumption; the results for the last-click mechanism also remain the same, as its accuracy and fairness are already zero; while in heterogeneous settings, PVM retains a weaker but still meaningful 1/n lower bound on accuracy. We focus on the independence assumption in this paper to present the mechanism's 's core insight in the clearest setting, which is sufficient to capture the essential strategic structure, leaving correlated extensions for future work.
Several directions remain open. First, while PVM aligns the expected attribution with true last- click probability, future work may explore mechanisms that further improve instance-level accuracy, Second, investigating correlated click-tima distributions could enhance mechanism's 's applicability in realistic scenarios. Next, joint optimization framework modeling both advertiser and platform utilities, integrating attribution with budget allocation, represents a compelling direction. Finally, investigating repeated games with externalities-wheee platforms may strategically harm peers or misreport distributions to manipulate learned priors-could address dynamic interactions, potentially incorporating bidding strategies for more comprehensive ecosystem model.
Acknowledgment
This work was supported by National Natural Science Foundation of China NN.66242242), Public Computing Cloud, Renmin University of China, the fund for building world-class universities (disciplines) of Renmin University of China.
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Reviews:
[{"review_id": "4fHT2z6SgK", "reviewer": "Reviewer_Fr9B", "summary": "This paper studies attribution in multi-platform advertising where platforms may strategically delay impression timestamps to game credit assignment. It introduces the Peer-Validated Mechanism (PVM), which is dominant-strategy incentive compatible (DSIC), provably fair, and optimal among threshold-based mechanisms. Theoretical results are thorough and correct, and extensive experiments using real-world click data demonstrate PVM’s superiority in accuracy and fairness over Last-Click attribution.", "questions": "1. Strategic Feasibility in Practice: How common is timestamp manipulation in practice? Can you clarify when platforms are able (and willing) to delay impression timestamps, especially given common audit mechanisms or advertiser-side control?\n2. Learning Dynamics: Would LCM perform better if platforms adaptively learned their best delay strategies over time (e.g., via regret minimization)? Could PVM be robust in a repeated-game setting?\n3. PVM Threshold Implementation: How complex is threshold computation in PVM for large n? Can you comment on runtime or whether thresholds can be precomputed in practice?\n4. Advertiser Utility: Would incorporating advertiser-side objectives (e.g., conversion accuracy or ROI) affect the relative performance of LCM and PVM? Have you considered joint optimization over platform and advertiser utilities?\n5. Noise Robustness: Your simulations assume precise timestamps. How would PVM’s performance change under real-world noise: jittered impressions, delayed reports, or soft conversions?\n\nIf you address (1), (3), and (5), it would strengthen my score — especially if you can show that PVM remains practical and truthful even under noisy, partial, or delayed observations.", "limitations": "* Assumption Realism: The core setting assumes platforms can delay timestamp reports (but not report earlier). This is valid for theoretical modeling, but in practice, such manipulation is often restricted. The paper should explicitly discuss whether such strategic timing is realistic under ad industry audit standards, MMPs, or advertiser-enforced attribution windows.\n* Limited Economic Impact Discussion: The paper proves fairness in attribution, but doesn’t discuss whether that leads to better advertiser outcomes (e.g., campaign optimization) or negative impacts (e.g., over-crediting fast-reporting platforms).", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths: \n* (S1) The paper presents a rigorous and well-structured treatment of attribution in multi-platform ad settings, modeling strategic timestamp misreporting and proposing the Peer-Validated Mechanism (PVM) as a dominant-strategy alternative to the commonly used Last-Click Mechanism (LCM).\n* (S2) The experimental section (Sections 5 and Appendix D) is a major strength. It uses real-world click-timing data from four anonymized platforms, and validates PVM’s superiority in both accuracy and fairness across homogeneous and heterogeneous settings,\n\n### Weaknesses: \n* (W1) Timestamp Manipulability:  Platforms don’t usually control the raw timestamp of an impression — those are logged by an ad server or measurement pixel. Misreporting impression times could violate platform policies or audit trails. Thus, the assumption that platforms can delay reporting of impression times to strategically influence attribution (without audit consequences) is theoretically coherent but may be limited in practice. I recommend clarifying the conditions under which such misreporting is feasible, and discussing how this maps to real-world ad attribution ecosystems.\n* (W2) Unsupported claims: Readers unfamiliar with the domain lack guidance on where to look for background, as introduction does not contain any reference (apart from the related work section) and has a number of unsupported claims.  For example, “Advertisers interact with a small number of platforms”, “platforms may strategically misreport to gain greater attribution”, etc.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the positive feedback and constructive suggestions. We appreciate that you found the **rigor** and **well-structured theoretical results** valuable, as well as the **experiments using real-world data** that demonstrated PVM's superiority in accuracy and fairness. For the concerns you raised, we have summarized our overall responses below, with detailed replies provided further on.\n\n## Summary of Responses and Planned Revisions\n\n| **Question**| **Summarized Response**| **Revision**|\n|-|-|-|\n| Strategic Feasibility in Practice | Strategic feasibility arises because advertisers are often blind in funnels they don't control (e.g., direct-to-app-store installs), forcing a near-total reliance on platform-reported data as privacy regulations (like ATT) have dismantled traditional audits. | We will update the **Introduction** to highlight the recent attribution paradigm shift and the resulting platform misreporting challenges. |\n| Learning Dynamics| LCM's performance does not improve with adaptive learning. PVM is robust in repeated games due to its DSIC property. |-|\n| PVM Implementation| PVM's thresholds can be **precomputed offline**, and an online runtime complexity of $\\mathcal{O}(n^2)$ per conversion. But ad attribution is typically an offline batch process without stringent latency requirement| We will update the **PVM section** to include an analysis of its computational complexity.|\n| Advertiser Utility| A full, joint-optimization game that models both advertiser and platform utilities while integrating the attribution and budget allocation processes represents **a compelling direction for future research**. This convinces us that the field of ad attribution is rich with open questions, and we hope our foundational work can serve as a catalyst for such studies. | We will update the **Conclusion** to point towards joint optimization as a compelling direction for future work.|\n| Noise Robustness| **PVM is robust to real-world noise.** The DSIC property eliminates strategic manipulation, and operational noise (e.g., jitter) can be managed with standard data-cleaning techniques. | We will expand the **Conclusion** to include a discussion on PVM's robustness to real-world noise. |\n\n## Q1: Strategic Feasibility in Practice\nThis issue is not only feasible but increasingly prevalent, particularly in common advertising funnels where advertisers, lacking  third-party audit capabilities, must rely on the self-reported data from the platforms. **As a leading platform in the industry, we have direct insights into this challenge.**\n\n### A Prime Scenario: Direct-to-App-Store Advertising\nA prime and highly common example is the direct-to-app-store advertising funnel. In this scenario:\n- A user clicks an ad on a major platform (e.g., Meta, Google, TikTok).\n- The user is taken directly to the Apple App Store or Google Play Store, with no intermediate redirection.\n- The user installs the app. The advertiser (e.g., a game developer) receives a notification of the install from Apple/Google, but has no independent way to know which specific ad click led to it.\n\n**According to unpublished research data from our company, this method of attribution through platform-reported click data is the dominant approach, accounting for at least 70% of app download ads.**\n\nIn these cases, the platform becomes the sole source of truth for the click timestamp. This dependency creates a clear and widespread opportunity for the strategic manipulation our paper addresses. \n\n### Why Traditional Audits Are Becoming Infeasible?\n\nThe prevalence of these \"blind-reliance\" scenarios has been exacerbated by the very industry shifts, which have dismantled traditional verification methods:\n\n **(1) The Decline of Third-Party Redirection**: Prior to 2020, Mobile Measurement Partners (MMPs) could use redirects for verification. However, this is now heavily restricted. New privacy regulations (e.g., China's Personal Information Protection Law (PIPL) and Apple's App Tracking Transparency (ATT) )  prohibit or penalize such redirects to protect user data and experience. Major app stores and ad platforms now require a direct path to landing page, eliminating the crucial touchpoint for independent, real-time auditing.\n\n **(2) Advertiser-Side Constraints** \nEven when technically possible, advertisers themselves are moving away from complex tracking for key business reasons:\n- **Protection of Proprietary Data:** Advertisers are increasingly reluctant to share their user data with external parties.\n- **Degraded User Experience:** Redirects often introduce disruptive pop-up warnings (e.g., \"Are you sure you want to visit this link?\"), increasing user drop-off.\n- **High Cost:** Implementing and maintaining robust redirect solutions is expensive.\n\nThese changes have created a widespread environment where platforms have the unilateral ability to report timestamps without facing easy, real-time detection from advertisers. The willingness to exploit this reporting ability is driven by the powerful financial incentives of the LCM.\n\nTherefore, while some forms of historical or sample-based auditing might exist, they represent a costly and imperfect **\"cat-and-mouse game\"**. Our work proposes a more fundamental solution. By introducing the PVM, we leverage mechanism design to create an incentive-compatible system where truthful reporting becomes the dominant, most profitable strategy. **This obviates the need for external audits by fixing the problem at its source.**\n\n## Q2: Learning Dynamics\n\n**For LCM, adaptive learning dynamics would not improve its performance.** While learning processes, such as regret minimization, are known to converge to an equilibrium (Reference: Regret Minimization in Games with Incomplete Information. NeurIPS 2007), our analysis proves that the Nash Equilibrium in the LCM setting yields poor performance. Thus, learning provides no escape from this inefficient outcome.\n\n**In contrast, PVM is inherently robust in a repeated-game setting.** Its DSIC property makes truthful reporting a dominant strategy—the optimal action for any platform regardless of other platforms' strategies. Since this strategy is unconditionally optimal in each round, its optimality extends directly to the repeated game, eliminating any incentive for long-term strategic deviation.\n\n## Q3: PVM Threshold Implementation\n\nThe PVM mechanism is designed to be highly efficient, with threshold computation handled offline to ensure low-latency online performance.\n\n**(1) Offline Precomputation:**   While a general implementation could theoretically require precomputing an exponential number of thresholds ( $O(2^n)$ ), the equilibrium analysis central to our paper simplifies this significantly. For our use case, **only $n$ thresholds are needed**---one for each platform. This makes the offline precomputation step fast and practical for any realistic number of advertising platforms.\n\n**(2) Online Runtime Complexity:**  The online attribution process is also very efficient. To make a decision for a single conversion, the mechanism performs a check for each of the $n$ platforms. Each individual check requires finding the maximum timestamp among the other $n-1$ platforms (an $\\mathcal{O}(n)$ operation) and a single comparison. Therefore, the **total online runtime complexity per conversion event is $\\mathcal{O}(n^2)$**.\n\nBut ad attribution is typically an offline batch process without stringent latency requirement.\n\n## Q4: Advertiser Utility\nOur current objective is to maximize accuracy and fairness, assuming that a truthful signal is the most valuable input for an advertiser's downstream goal of optimizing ROI. Our work focuses on creating this foundational layer of truthful reporting.\n\nWe agree that the idea of a multi-level game involving strategic interplay—such as strategic time reporting by platforms and strategic attribution by advertisers—is fascinating. **A full, joint-optimization game that models both advertiser and platform utilities while integrating the attribution and budget allocation processes represents a compelling direction for future research.** This convinces us that the field of ad attribution is rich with open questions, and we hope our foundational work can serve as a catalyst for such studies.\n\n## Q5: Noise Robustness\nPVM provides a robust foundation upon which engineering solutions can be built to address these issues:\n- **Jittered Impressions:** Under a mechanism like LCM, platforms introduce large, minute-scale strategic delays to alter the click sequence. PVM’s DSIC property eliminates these strategic errors. The only remaining temporal noise is millisecond-level “jitter” from network latency. This minor, random noise is highly unlikely to change which platform was the true last click, making PVM's outcome robust to this issue.\n- **Delayed Reports:** We interpret this concern as the risk that operational delays could corrupt data and lead to inaccurate estimates of the click-time distributions that PVM relies on. This, in fact, highlights a key advantage of our design. **PVM’s DSIC property incentivizes platforms to eliminate strategic delays, ensuring the collected data is fundamentally honest.** This provides a clean baseline. Over time, an advertiser can statistically model and filter out these non-strategic latencies to better estimate the true distributions. This creates **a positive feedback loop**: better $F_i$ estimates lead to more precise PVM thresholds. Such a learning process is impossible under LCM, where strategic and operational delays are indistinguishable.\n- **Soft Conversions:** This is an excellent point and a standard challenge in practical attribution.  We view it as an issue of business logic that must be defined before the mechanism is applied. An advertiser must first establish a clear, consistent rule for what event constitutes the conversion $t_0$. PVM's logic can be readily applied to any consistently defined conversion event."}, {"review_id": "cUloveqCVB", "reviewer": "Reviewer_jUsn", "summary": "The paper studies a theoretical model for ad attribution. The goal if to attribute a conversion to the last click before this conversion, but to do this, we need to rely on the reports of click times from a number of self-interested platforms. The natural and commonly-used LCM mechanism that simply attributes the contribution to the last reported click is not incentive compatible: platforms might have an incentive to delay their report. The paper proposes a dominant-strategy incentive-compatible mechanism called PVM for this problem, assuming known priors on the time between clicks on each platform and the conversion (and if I understand correctly, assuming that these time delays are independent). The mechanism credits a platform if the other platforms report times that are earlier than some thresholds, ignoring the platform's own report (beyond checking that the click is reported before the conversion). Obviously if platforms report their times truthfully, the LCM is perfectly accurate in picking the last click and PVM is sometimes inaccurate. But interestingly, the paper shows that if platforms act strategically, then in an equilibrium, LCM can be much less accurate in picking the last click than PVM. In fact, they show that PVM is the most accurate incentive compatible mechanism. The paper also shows a fairness property of PVM and evaluates the accuracy and fairness of PVM compared to LCM in numerical experiments for small sizes.", "questions": "* Do you need the assumption that F_i's are independent?\n* Why do thresholds always exist? Are they unique? What happens if they don't exist or are not unique?\n* Can anything be said in a setting without priors or with inaccurate priors?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n+ Interesting and novel theoretical solution for a non-standard mechanism design problem.\n+ It is quite interesting (and perhaps surprising) that the authors can show the optimality of PVM wrt accuracy.\n+ From a technical point of view, the paper is significantly novel and is not a simple application of known methods.\n\nWeaknesses:\n- Assumptions of the model are not properly discussed. Mainly:\n  - It is assumed that there are known priors commonly known by everyone. What if that is not the case?\n  - It seems that the paper assumes that the F_i distributions are independent, but this is not clearly stated. Also, I don't think this is a reasonable assumption, since the conversion delay times on different platforms are clearly correlated with the conversion time and therefore are intercorrelated. I'd understand if an unrealistic assumption like this might be necessary to obtain theoretical results, but this needs to be properly discussed.\n  -  Do thresholds alpha_S^i always exist? Are they unique?  I guess some form of regularity might be necessary for the existence and uniqueness of these thresholds.\n- While the results are interesting from a theoretical point of view, I don't expect any practical application (mainly because of the unrealistic assumptions).\n- Minor: the title of the paper is a bit misleading. The paper does not go beyond the last-click attribution. It proposes a better mechanism for last-click attribution in a strategic environment.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for your constructive feedback! We are grateful that you recognized our work's **significant technical novelty** and the **\"surprising\" accuracy optimality** of our PVM mechanism. For the concerns you raised about our model's assumptions, our responses are summarized below, with detailed replies provided further on.\n\n## Summary of Responses and Planned Revisions\n\n| Question | Summarized Response | Revision |\n|-|-|-|\n| Need for Independent Assumption | **Our PVM framework is extensible to the general correlated case, preserving its core desirable properties.** We focused on the independent case because it is **sufficient** to present our foundational results, while also offering maximum **clarity** and the strongest analytical bounds. | We will add a discussion to the **Conclusion** to clarify our independence assumption. |\n| Threshold Existence and Uniqueness | The thresholds' existence and uniqueness are guaranteed under standard regularity conditions on the priors, and the mechanism is easily adapted for any theoretical edge cases. | We will clarify in a new **footnote** along with the handling of theoretical edge cases |\n| Settings Without Priors or with Inaccurate Priors | PVM's DSIC property addresses the **\"cold-start”** problem of unknown or inaccurate priors by allowing platforms to begin with arbitrary priors, collect honest data (from platforms) over time, and gradually learn accurate priors. | We will revise the **Model and Preliminaries** section to better explain the motivation for choosing a DSIC mechanism, ensuring its benefits are clear to a broader audience. |\n| Practical Value Concern | The practical value lies in a twofold contribution: (1) providing a **theoretical diagnosis** of the root cause of strategic reporting delays, and (2) offering **a concrete design principle for future attribution mechanisms.** | We will expand the **Future Work part in Conclusion** section  to discuss the practical implications of our work and suggest paths toward real-world implementation. |\n\n## Q1: The Need for Independence Assumption\n\nWe apologize if the statement of our independence assumption was not sufficiently prominent. We do state it on line 117, but we will ensure it is highlighted more explicitly.\n\n**Our PVM framework can be extended to settings with correlated click-time distributions.** The core peer-validation principle is preserved, ensuring the mechanism remains DSIC, but the validation rule is generalized:\n\n- **Mechanism Modification**: Instead of using a single threshold ($\\alpha_i$), the mechanism would define a multi-dimensional \"acceptance region\" $D_i$ for the vector of peer reports $t_{-i}$. To maximize accuracy, this region $D_i$ is constructed by a greedy algorithm: we iteratively add the peer-report outcomes $t_{-i}$ that yield the highest posterior probability that platform i was the true last click (i.e., $P(t_i > \\max\\{t_{-i}\\} | t_{-i})$ is highest). This process continues until the total probability of $t_{-i}$ falling within this region equals the prior probability that i is the last click ($\\beta_i$). A platform $i$ receives credit if and only if its peers' reports $r_{-i}$ fall within this precomputed region $D_i$.\n\n- **Impact on Results**: Under this modification, our conclusions in the homogeneous setting remain unchanged, as the proof is based on the symmetric structure. In the heterogeneous setting, the conclusions for LCM also remain unchanged, as its accuracy and fairness have already approached zero and thus cannot degrade further. The primary change is PVM's performance in the heterogeneous setting, where the accuracy guarantee becomes a weaker (but still valuable) $1/n$ lower bound. While this is still strictly superior to LCM's worst-case accuracy of 0, it lacks the tighter bound derived under the independence assumption.\n\nWhile our PVM framework can be extended to the correlated case, our primary goal with this paper was to introduce our peer-validation framework in the clearest possible setting. We believe our paper makes a twofold contribution: providing the first theoretical model for strategic misreporting under the new \"no-redirect\" paradigm, and introducing our novel peer-validated mechanism as a robust solution. **The independence assumption provides an ideal setting to demonstrate these contributions, as it is sufficient to fully characterize the strategic problem while showcasing PVM's superiority with a simpler mechanism, more elegant proofs, and stronger analytical bounds.** Intuitively, this can be viewed from a backward-looking perspective: given a conversion, the advertiser forms an estimate for each platform's time lag, and the uncertainties in these separate estimates are modeled as independent. We sincerely thank the reviewer for raising this point, as it has helped us realize the importance of making this reasoning explicit. We will add a discussion on this methodological choice to the Conclusion to make the paper stronger.\n\n## Q2: The Existence and Uniqueness of PVM Thresholds\n\nThank you for this excellent question regarding the technical conditions for our thresholds. The thresholds $\\alpha_i$ exist and are unique under standard regularity conditions, and the mechanism can be straightforwardly adapted for edge cases.\n\nAs defined in our paper, the threshold $\\alpha_i$ is the solution to $G_i(\\alpha_i) = \\beta_i$, where $G_i(t) = \\Pi _{j\\neq i} F_j(t)$ is the cumulative distribution function (CDF) of the maximum click time among platform $i$'s peers, and $\\beta_i$ is the prior probability that $i$ is the true last click.\n\n- **Standard Case (Existence and Uniqueness)**: If $G_i(t)$ is continuous and strictly increasing. In this standard case, for any $\\beta_i$ in $(0,1)$, a unique solution $\\alpha_i$ is guaranteed to exist by the Intermediate Value Theorem.\n\n- **Special Case 1 (Flat CDF)**: If $G_i(t)$ has a flat region, and $\\beta_i$ falls within this flat range, the threshold $\\alpha_i$ would not be unique. However, a flat region in $G_i(t)$ implies that the probability of the maximum peer click time occurring within that specific interval is zero ($P(\\max\\{t_{-i\\}} \\in [a,b]) = 0$). Therefore, any threshold $\\alpha_i$ chosen within this flat interval will yield the exact same attribution outcome. The choice is arbitrary and has no impact on the mechanism's performance. We acknowledge this possibility in our proof sketch for Lemma 1.\n\n- **Special Case 2 (Discontinuous CDF)**: In the rare event that $G_i(t)$ could have a jump discontinuity at a point $\\theta$ such that $G_i(\\theta-) < \\beta_i < G_i(\\theta)$, a single threshold $\\alpha_i$ would not exist. This scenario implies a non-zero probability that $\\max\\{t_{-i}\\} = \\theta$. The mechanism can be modified to handle this by using a probabilistic assignment: if $\\max\\{\\boldsymbol{t}_{-i}\\} = \\theta$, we assign credit to platform $i$ with a specific probability $p$ such that the expected attribution remains $\\beta_i$. However, we consider this case to be of limited practical relevance, as click times are typically modeled as continuous random variables.\n\n## Q3: Settings Without Priors or with Inaccurate Priors\n\nWe see the settings without priors or with inaccurate priors as a **cold-start problem**. This is precisely why we pursued a DSIC mechanism--- **Learning Priors via a Virtuous Cycle**.\n\nEven if an advertiser starts with inaccurate priors (or no priors at all), PVM's DSIC property solves the ''cold-start'' problem by allowing platforms to start with arbitrary priors. Since DSIC ensures truthful reporting, the data collected (from platforms) over time is honest, allowing advertisers to learn the correct distribution and improve their priors. This allows them to iteratively learn and refine their estimates of the true click-time distributions over time.\n\n**This creates a powerful virtuous cycle:** truthful data leads to more accurate priors, which in turn makes the PVM mechanism more precise and effective. **In contrast, a non-DSIC mechanism like LCM offers no such path**; it consistently provides biased data, making it impossible for the advertiser to ever learn the true distributions. Under LCM, platforms are instead incentivized to continuously develop new ways to game the system, leading to a negative spiral.\n\n## Concern: Practical Value of Our Theoretical Work\n\nIn response to the question of practical application, we believe our theoretical work offers value on two distinct levels: **(1) providing a foundational diagnosis of the root cause of strategic misreporting in the new \"no-redirect\" conversion paradigm, and (2) offering a concrete design principle (\"peer-validation\") for future systems.**\n\nFirst, our work frames the issue of misreporting. We show it is not a simple monitoring problem to be solved with better detection, but rather a fundamental incentive flaw in the widely-used Last-Click Mechanism. This shifts the focus of any practical solution away from a costly **\"cat-and-mouse game\"** of enforcement and towards the core need for incentive-compatible design.\n\nThis diagnosis leads to our second insight: a concrete and transferable design principle of \"peer-validation.\" This principle is highly practical. **For instance, in a modern system using a neural network for attribution, our key engineering guideline to ensure truthfulness (DSIC) is that a platform's credit must be calculated without using its own reported timestamp as an input feature.** This is a clear, actionable takeaway for practitioners developing the next generation of robust, ML-based models. \n\nWe believe this work serves as a valuable starting point for designing trustworthy attribution mechanisms in the new \"no-redirect\" paradigm, and we hope it will inspire more research in this critical and evolving area."}, {"review_id": "zgrxSLJbOv", "reviewer": "Reviewer_nsc8", "summary": "This paper provides a new perspective on the advertising attribution problem by rethinking it through the lens of mechanism design, with a particular focus on the strategic aspects of reported click time. It reformulates the problem and theoretically demonstrates the limitations of the widely used Last-Click Mechanism (LCM). The authors propose a novel mechanism, the Peer-Validated Mechanism (PVM), which does not rely on the click time reported by the platform itself, and conduct a theoretical analysis of its properties. Additionally, the paper introduces a notion of fairness specific to this setting and provides an estimation for it.", "questions": "Please refer to \"Weaknesses\". Explanations for weaknesses 2, 3, and 4 are expected.", "limitations": "The elaboration of social impact is missing. The article designs a mechanism that might be applied in the real society. The ineffectiveness of self-reported information in increasing their own benefits for participants in this attribution mechanism may lead to irrational reporting, causing chaos.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. This perspective is novel — it reformulates the Ad attribution problem into a mechanism design problem from the angle of reported click time, under which the problem becomes clean.\n2. Within the authors’ problem setting, the theoretical analysis of PVM is well-executed, including the elegant proof of the optimality of PVM for homogeneous platforms and a detailed derivation in the accuracy analysis.\n\nWeaknesses:\n1. This paper has some issues with its presentation. \n- First, concerning citations: they should be placed appropriately where claims are made. For instance, citations supporting the mention of various methods in the second paragraph of the Introduction should be provided there, rather than all being clustered in the Related Work section.\n- There is a discrepancy in Table 1: the reported accuracy for the LCM differs from the value given in Theorem 3.\n- The wording around line 65 creates the impression that this is the first theoretical analysis of the problem. However, while you present a new modeling approach, theoretical analyses from other perspectives have been conducted previously.\n- Regarding Figure 2.2, it seems rather pointless. If a figure is truly necessary, it would be better to include an introductory teaser figure at the beginning, explaining the basics of ad attribution and illustrating how the two mechanisms (LCM and PVM) work.\n2. The problem formulation in this paper appears problematic.\n- If advertisements use external links (as is now the mainstream practice), the ad provider can obtain the authentic timestamp at the moment of the click. Since this issue is easily resolvable, it raises doubts about the meaningfulness of this specific modeling assumption. The statement at line 33 (\"a platform may delay the reporting...\") likely requires a citation to substantiate the claim that platforms actually engage in this behavior.\n- To my knowledge, the more common attacks in this context are click spamming and click injection. While click injection (which falls under the category of hijacking) is beyond the current scope of discussion, your model also fails to address the click spamming problem. For instance, a platform could report a click once when it occurs, and then report the same click again minutes later. This behavior wouldn't reduce its own revenue but would unfairly diminish the attributed revenue of other platforms (this also relates to normalization issues, which will be discussed later).\n3. Problem Formulation: Normalization Issue.\n- In Section 2.3, the constraint in Equation (3) is somewhat unsatisfying. This expectation-based constraint is arguably too weak. Crucially, unlike the LCM, it does not guarantee that the total credit sums to exactly 1 for each individual conversion. Under this condition, if the advertiser’s total budget is fixed, then any action by a platform that reduces the attributed revenue of others would inherently increase its own revenue. Consequently, the Peer-Validated Mechanism appears not necessarily DSIC in this specific sense.\n4. The PVM exhibits excessive reliance on the conversion time distribution function $F_i(t)$.\n- In the PVM design, $\\alpha$ and $\\beta$ are critical parameters whose values entirely depend on accurate knowledge of $F_i(t)$. This requirement for $F_i$ constitutes an overly strong informational assumption. Although the authors claim it is a \"commonly known distribution\" at line 116, this distribution is fundamentally unknowable under the paper’s core premise that \"advertisers cannot obtain authentic click times\".\n- The computation of $\\alpha$ and $\\beta$ is highly sensitive to the precision of $F_i(t)$ due to its multiplicative nature. Coarse estimates of $F_i(t)$ may be insufficient for reliable implementation.\n- Moreover, the $F_i$ across platforms are likely correlated, yet the paper models each platform’s click time using a univariate distribution over time without justification. This interdependence remains unaddressed.\n- Conversely, if one does possess the prior distributions $F_i$ and knowledge of which platforms participated in a conversion, could an allocation rule be designed that directly assigns credit (disregarding reported timestamps entirely) while preserving desirable incentive properties?", "was_revised": true, "final_justification": "From the perspective of a one-shot game, the work is commendable. I give a borderline accept since the limitations cannot be ignored.", "rebuttal": "Thank you for your detailed review. We sincerely appreciate your recognition of our **novel perspective**, **well-executed theoretical analysis**, and the **elegant proof**. We will address the typos you mentioned in Weakness 1 and have summarized our overall responses to the other concerns below, with detailed replies provided further on. **Apologies for the brevity, but due to space limitations, a more detailed rebuttal on strategic feasibility can be found in our responses to Reviewer Fr9B and Tb4U, while the discussion on the independence of $F_i$ is addressed in our response to Reviewer nsc8.**\n## Summary of Responses and Planned Revisions\n| Question | Sub-question| Summarized Response | Planned Revisions |\n|-|-|-|-|\n| W2 Problem Formulation | Strategic Delayed Feasibility | We focus on the scenario where the landing page is out of the advertiser's control (e.g., app stores). The strategic feasibility for platforms to delay click reports arises from **the infeasibility of third-party verification via MMP redirection**, due to **a shift in tracking practices since 2020**, driven by **new privacy regulations** (e.g., GDPR, ATT) and **advertiser concerns** (e.g., protection of proprietary user data). | Revise **Introduction** to clarify problem context and add industry citations.  |\n|  | Other Click Attacks  | PVM removes the incentive for a rational agent to \"spam\", as this action offers no personal gain under our utility model.|-|\n| W3 Normalization Issue | Expectation-based Constraint| This is a deliberate choice reflecting **the practical goal of long-term budget control** while allowing for mechanism design flexibility. |-|\n| | DSIC Claim| The DSIC holds under the standard self-interested agent model $(u_i=x_i)$. The insightful point about a fixed budget is **a compelling future research direction exploring **repeated games with externalities**.                                                             | We will add a discussion to **the Future Work part in Conclusion** on modeling the problem as a repeated game with externalities. |\n| W4 Prior Issue | Knowledge of Prior  |PVM's DSIC property addresses the \"cold-start” problem of unknown or inaccurate priors by allowing platforms to begin with arbitrary priors, collect honest data (from platforms) over time, and gradually learn accurate priors.| We will revise the **Model and Preliminaries** section to better explain the benefits of DSIC, ensuring it is clearer to a broader audience.|\n|   | Independence Assumption| **Our PVM framework is extensible to the general correlated case, preserving its core desirable properties.** We focused on the independent case because it is **sufficient** to present our foundational results, while also offering maximum **clarity** and the strongest analytical bounds.     | We will add a discussion to the **Conclusion** to clarify our independence assumption. |\n|    | Possible Prior-Only Mechanism | While the prior-only mechanism you suggest is incentive-compatible, it is **suboptimal** in accuracy.  | -   |    |\n\n## W2:  Problem Formulation\nThis is not just a theoretical issue. **As a leading company in the industry, we have direct insights from our proprietary data.**\n### (W2.1) Strategic Delayed Feasibility\n\nThe user conversion process could be classified into 2 scenarios based on the landing page:\n- **Advertiser-controlled landing pages**: For example, when a company runs ads on Facebook and directs users to its own website. In this case, the advertiser can easily record the true click timestamp. **However, this is not the focus of our paper**.\n- **Advertiser-uncontrolled landing pages**: This includes cases like app developers advertising their apps (with the landing page being an app store) or merchants promoting products on third-party platforms (e.g., Amazon). Here, advertisers cannot record click timestamps by themselves because they don’t control the landing page.\n\nIn cases with advertiser-uncontrolled landing pages, advertisers often use **Mobile Measurement Partners (MMPs)**, like AppsFlyer, to track user interactions. The process involves **redirecting** users through a MMP's URL before reaching the landing page. When a user clicks on an ad, he/she first goes to the MMP's URL, which logs the timestamp and metadata, then is redirected to the final landing page. This allows the MMP to independently track the click and provide the data to the advertiser.\n\n**However, recent changes in platform policies and advertiser priorities have made redirect-based verification harder to implement**:\n\n- **Platform-Side Prohibition on Third-Party Redirection**: Regulations like GDPR (2018), China’s PIPL (2021), and Apple’s ATT (2021) limit redirection paths to protect user privacy and prevent unsafe redirects. As a result, many app stores and ad platforms now require users to go directly to landing pages, cutting out third-party servers.\n- **Advertiser-Side Constraints**: (**Data Privacy**) Many advertisers are increasingly protective of their proprietary user data and are unwilling to share it with external parties like MMPs. (**Redirect Impact on UX**) Even when redirects are allowed and data privacy is not a concern, many platforms display warning messages—like **“Are you sure you want to visit this link?”**—that disrupt the user experience and hurt conversion. (**Cost of Redirect Solutions**) Implementing redirects, whether through MMPs or in-house systems, is costly, making it less attractive.\n\nDue to these changes, external-link-based verification is no longer viable for many advertisers, leaving them dependent on unverified platform-reported data.   **Based on our unpublished research, this method of attribution through platform-reported click data is the dominant approach for app download ads, accounting for at least 70% of cases.** \n\nFurthermore, using third-party verification becomes a costly **\"cat-and-mouse game\"** of detection versus fraud, as it doesn’t address the underlying platform incentive to misreport. **In contrast, PVM addresses the root cause by using mechanism design (DSIC) to make honesty the most profitable strategy.**\n\n### (W2.2) Other Click Attacks \nPVM resists click spamming for the same reason as the normalization issue. In LCM, platforms are incentivized to spam by being rewarded for the last reported click. However, under PVM, platforms have no such incentive, as their reward depends on peer reports, not their own. Therefore, spamming has no impact on their payoff, regardless of how much they spam.\n\n## W3: Normalization Issue\n\n### (W3.1) Expectation Constraint \nThe expectation-based normalization ($E[\\sum x_i]\\leq 1$) was a deliberate one, motivated by **the practical objective of ensuring the advertiser's budget is respected on average over many conversions.** This approach provides the necessary **long-term budget control that advertisers require**, while allowing for the flexibility needed to design a powerful incentive-compatible mechanism.\n### (W3.2) DSIC Claim\nPVM is DSIC under our standard utility model ($u_i = x_i$), where agents are rational and self-interested, meaning their utility depends only on their own payoff. In this model, platforms are indifferent to the payoffs of their peers.\n\nThe idea of a fixed advertiser budget is insightful, as it leads to a new research direction: **a repeated game with externalities**. In this setting, platforms would be incentivized to hurt their peers’ performance to capture a larger share of the fixed budget. **This is a sophisticated challenge, as such externalities can compromise the incentive properties of even canonical truthful mechanisms like VCG.** However, we believe **it is a compelling direction for future research, and it further convinces us that strategic behavior in ad attribution is a rich field with significant value**.\n\n## W4: Click Time Distribution Issues\n\n### (W4.1) Knowledge of Prior\n**The \"unknowable prior\" is exactly why DSIC is important.**  PVM's DSIC property solves the 'cold-start' problem by allowing platforms to start with arbitrary priors. Since DSIC ensures truthful reporting, the data collected (from platforms) over time is honest, allowing advertisers to learn the correct distribution and improve their priors. \n\n### (W4.2) Independence Assumption\nOur PVM framework **can be extended to settings with correlated click-time distributions**:\n- **Mechanism Modification**: Instead of a single threshold ($\\alpha_i$), the mechanism defines a multi-dimensional \"acceptance region\" $D_i$ based on peer reports $t_{-i}$. This region is constructed by a greedy algorithm that adds the peer-report outcomes with the highest probability that platform $i$ was the true last click. A platform receives credit if its peers' reports fall within this region.\n- **Impact on Results**: Our conclusions in the homogeneous setting remain unchanged, as the proof is based on the symmetric structure. In the heterogeneous setting, LCM's performance remains unchanged, as its accuracy is already near zero. The main change is PVM's accuracy guarantee, which becomes a weaker $1/n$ lower bound.\n\nAlthough we can extend PVM to correlated settings, the focus of this paper is on introducing the peer-validation framework and presenting two key contributions: **the first theoretical model for strategic misreporting** in the \"no-redirect\" paradigm, and **a peer-validated mechanism** as a robust solution. **The independence assumption is sufficiently to fully characterize the problem, while also making PVM’s superiority clearer through a simpler mechanism and stronger analytical bounds.** We will discuss this choice in the Conclusion to strengthen the paper. \n\n### (W4.3) Possible Prior-Only Mechanism\nA prior-only mechanism is DSIC but suboptimal for our objective (Equation 4). In contrast, **PVM is the optimal DSIC mechanism in the homogeneous setting and superior to LCM**, as shown both theoretically and experimentally."}, {"review_id": "gNm3wffndt", "reviewer": "Reviewer_Tb4U", "summary": "The paper provides a mechanism design perspective on the last click attribution mechanism in online advertising. \nIt frames the situation of click reporting as a mechanism design problem where platforms have incentive to misreport their times of interaction with the user in order to get the attribution.\nA prior on the times of interaction is assumed (Bayesian model). The Accuracy of the mechanism is defined as a performance metrics.\nAfter showing that the Last Click mechanism is not incentive compatible, the paper introduces an alternative, PVM (peer-validated mechanism) that satisfies this property. The paper then consider the homogeneous case (iid) to refine the results on accuracy. \nThe paper finishes with some consideration on fairness and a very short simulation section.", "questions": "# Major question\n\nCan you please provide more details on where the situation described in the paper occurs in practice?\nMaybe   providing examples of what you call a platform would help me better contextualize.\n\n\n# Minor questions\n\nDo you have real-life example of such strategy being applied somewhere (l37)\n\nIn practice, what is the mechanism by which a platform declares a click, and what  can the advertiser  checks on the platform declaration ? \n\nCan the mechanism be adapted in the case where multiple conversions or clicks per platform occur?", "limitations": "na", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper is quite original as it presents a mechanism design problem where the hidden information is not related to the agents' preferences. The topic of last-click attribution is indeed an important one, as it is a heuristic known for having many failure modes. For instance, an RTB bidder is incentivised to overbid when it knows it lost the attribution. The introduction of measures of fairness and accuracy seems novel in this context. The peer validated mechanism the authors identified is simple and optimal. Also, it seems that  since it is non-increasing, it is DSIC, which implies that even if the advertiser do not have the right priors at cold-start, it will be able to learn them from the generated data. \n\n\nI have some strong reservation on this paper, because the situation that motivates the analysis is  not  how things work in practice. I hope I missed something, in which case a clarification from the authors should change my evaluation.\nThe blocking issue to me is the following sentence, that motivates most of the document: \"In particular, a platform may delay the reporting of a user’s click to appear later in the user’s interaction sequence and thereby capture the conversion credit.\"\nIn practice, when a user clicks on a link, they are redirected to the advertiser's website. The http call to the advertiser page contains a field called http referer that indicates the origin of the click (the platform). The advertiser hence knows how the user landed on the the advertiser's site. \nYou can find out more here: https://en.wikipedia.org/wiki/HTTP_referer\nThe platform does not have any control on that.", "was_revised": true, "final_justification": "The authors addressed my major concern on the paper relevancy on real life situation. \nI am therefore increasing my score (by 2).", "rebuttal": "Thank you for your thoughtful review. We are grateful that you recognized our work as **\"quite original\"**, our PVM mechanism as **\"simple and optimal\"**, and that **its DSIC property addresses the cold-start problem**. We are especially grateful for your **crucial question regarding practical feasibility**, which has helped us realize the need to better clarify the modern industry context for this problem.  We also emphasize that our work is not just a theoretical issue. **As a leading company in the industry, we have direct insights from our proprietary data.**  Our responses to this are summarized in the table below, with detailed explanations to follow.\n\n##  Summary of Responses and Planned Revisions\n|Question| Summarized Response|Revision|\n|-|-|-|\n| **Major Question**: The Practical Context and Platform Examples | Our work addresses a growing challenge faced by advertisers, such as app developers and e-commerce merchants, who use major platforms like Facebook, Google, and TikTok to direct users to **landing pages they do not control** (e.g., app stores, Amazon). For this group, the external-link verification you described is not feasible, and the traditional alternative—third-party redirects (MMPs)—is collapsing due to **new privacy policies** and **business concerns**. | We will update the **Introduction** to highlight the recent shift in tracking paradigms and the resulting challenges of platform misreporting. |\n| Real-Life Example | Two common examples of this scenario are **app downloads** and **e-commerce platforms**. | We will update the **Introduction** to better illustrate real-life scenarios. |\n| Ad Click Declaration and Verification Mechanisms | Advertisers match the **\"Device Fingerprint\"** collected after a user conversion (e.g., when a user first opens their app) with the click reports from the ad platform, which also include the fingerprint. **While this confirms that a user clicked, it does not allow the advertiser to independently verify when the click actually occurred, forcing them to rely on the platform's reporting time.** This information gap creates the opportunity for strategic manipulation, which our paper addresses. | We will update the **Introduction** to better illustrate the attribution procedure. |\n| Adapting the Mechanism for Multiple Clicks or Conversions per Platform | PVM can be applied to these scenarios **with minimal modification**. | - |\n\n\n\n## Q1 Major Question: The Practical Context and Platform Examples\n\nIn some scenarios—for instance, a brand like Nike directing ad traffic to its **own brand site**—verification via external links is straightforward.\n\n**Our work, however, focuses on the more complex and increasingly prevalent scenario where advertisers do not control the landing page**. A key example is a game developer advertising on TikTok whose landing page is the Apple App Store. In our model, the \"platforms\" are the major ad networks where these advertisers place their ads, primarily Facebook, Instagram, Google Ads, and TikTok Ads.\n\nThe critical feature of this scenario is that the advertiser does not control the final landing page—key examples being app developers linking to the App Store or e-commerce merchants to a marketplace like Amazon. **This is precisely why the external-link verification method you described is not viable for them: they cannot deploy their own tracking pixels on these third-party platforms and thus have no independent way to verify the true click timestamp.**\n\nHistorically, this verification gap for uncontrolled landing pages was filled by third-party **Mobile Measurement Partners (MMPs)**, such as AppsFlyer. These services track user interactions through **redirection**. When a user clicks on an ad, he/she are first directed through a MMP's URL, which logs the timestamp and metadata, before being redirected to the final landing page. This process allows the MMP to track the click and provide click data to the advertiser.\n\nHowever, recent changes in **platform policies** and evolving **advertiser priorities** have made redirect-based verification increasingly **difficult to implement**.\n\n**(1) Platform-Side Prohibition of Third-Party Redirection**\n\nBefore 2020, MMPs like AppsFlyer and Adjust commonly used redirection to track ad clicks, capturing important data (e.g., the IDFA) before redirecting users to their landing pages. However, this practice has become increasingly restricted due to growing privacy concerns. **Regulations such as the General Data Protection Regulation (GDPR, 2018), China's Personal Information Protection Law (PIPL, 2021), and Apple's App Tracking Transparency (ATT, 2021) have significantly limited redirection paths.** These regulations primarily aim to protect user privacy and prevent third-party services from redirecting users to potentially unsafe websites. As a result, platforms like the Apple App Store, along with ad platforms such as Meta and Google Ads, now require users to be directed directly to the landing page, eliminating the ability to route user data through third-party servers. Consequently, advertisers can no longer rely on MMPs for click tracking.\n\n**(2) Advertiser-Side Constraints**\n\nEven in cases where redirects are not explicitly banned, advertisers are increasingly moving away from them due to several key factors:\n\n- **Protection of Proprietary Data**: Many advertisers are highly protective of their user data and reluctant to share it with external parties, even when such third-party solutions are not explicitly prohibited.\n- **Impact of Redirects on Conversion Rates**: Even when redirects are permitted, the growing prevalence of disruptive pop-up warnings has become a major concern. Many platforms, though not completely banning redirects, now display confirmation prompts (e.g., **\"Are you sure you want to visit this link?\"**) that create friction in the user experience, thereby discouraging users from completing their intended actions.\n- **High Costs of Redirect Solutions**: Whether using third-party MMPs or developing an in-house solution, implementing redirects incurs significant costs, making these solutions less attractive to advertisers.\n\nAs a result of these developments, **the ability to use external links for  verification has been severely diminished**. Consequently, a large number of advertisers are left increasingly reliant on unverified, platform-reported data, making the strategic delay of timestamps a meaningful and urgent issue.  **Based on our unpublished research, this method of attribution through platform-reported click data is the dominant approach for app download ads, accounting for at least 70% of cases.** \n\nFurthermore, even if third-party verification were still possible, the traditional approach becomes a costly **\"cat-and-mouse game\"** between detection and fraud, as it does not address the platforms' inherent incentive to misreport data. **In contrast, PVM tackles the problem at its core by using mechanism design (DSIC), ensuring that honesty becomes the most profitable strategy for all involved parties.**\n\n## Q2 Real-Life Examples\n\nTwo common examples of this scenario are app downloads and e-commerce platforms:\n\n- **App Downloads**: When a user clicks on an ad for an app, he/she is sent directly to the App Store (e.g., Google Play or Apple’s App Store). Since platforms no longer allow redirects and the app store page is not controlled by the advertiser, the advertiser cannot use a MMP to track the exact timing of the click. This creates a situation where the advertiser cannot verify the attribution independently, and the platform can manipulate the timing of click reporting to affect attribution.\n- **E-commerce Platforms**: Similarly, when users click on ads for products on advertising platform (e.g., Facebook), they are sent directly to an e-commerce platform (e.g., Amazon). Just like in the app download scenario, since redirects are not allowed by Facebook or Amazon, MMPs cannot track clicks for advertiser.\n\n## Q3 Ad Click Declaration and Verification Mechanisms\n\nWhen a user clicks an ad on a platform like Facebook or TikTok, the ad platform instantly captures a detailed **Device Fingerprint**. This includes key information such as the Device Advertising ID (e.g., IDFA or GAID, if permitted), IP address, and a User-Agent string. The platform then sends this data packet directly to the advertiser's server (maybe with some strategic delay).\n\nLater, if the user converts (e.g., by opening the newly downloaded app for the first time), the advertiser's SDK in the app collects the same type of Device Fingerprint from the device. By matching the fingerprint from this new conversion to the previously received click reports, the advertiser can then attribute the installation.\n\n**However, while this matching process can verify that a specific user clicked, it provides the advertiser with no way to independently verify when that click truly occurred.** This information asymmetry, and the resulting potential for strategic timestamp manipulation, is precisely the problem we address in our paper.\n\n## Q4 Adapting the Mechanism for Multiple Clicks or Conversions per Platform\n\nPVM can be straightforwardly adapted to handle both scenarios. The key principle is that PVM operates on a per-conversion basis, considering the last click from each platform.\n\n- **Multiple Clicks**: When a single platform serves multiple ads to a user before one conversion, the standard last-click attribution principle is applied before PVM is invoked. Specifically, for each platform, only the timestamp of its final click prior to the conversion is considered a candidate for attribution. PVM then operates on this set of candidate last clicks (one from each participating platform).\n- **Multiple Conversions**: In scenarios where a platform contributes to multiple conversions, we apply PVM to each conversion independently. This ensures that each conversion event is attributed correctly."}]

Author rebuttal:

Meta-review: This paper studies the strategic aspects of the last click attribution mechanism and shows a new mechanism that behaves much better when players are strategic and can misreport the click time to their advantage. The authors engaged with the reviewers to clarify some misconceptions, and the scores are overall positive.
Decision: Accept (poster)