Title: Beyond Last-Click: An Optimal Mechanism for Ad Attribution
Venue: NeurIPS 2025
Accepted: yes
Keywords: Ad Attribution

Mechanism Design

Accuracy

Dominant Strategy Incentive Compatible
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

Abstract

Accurate attribution for multiple platforms is critical for evaluating performancebased 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.

1 Introduction

Online advertising has become the dominant force in the global advertising landscape, with expenditures projected to exceed $790 billion in 2024-accounting for over 72% of total ad spend-and continuing to grow at a consistent rate of more than 10% annually. This substantial and growing capital investment calls for the development and application of robust methodologies to optimize budget allocation across diverse digital platforms.

Weian Li

Changyuan Yu

Baidu Inc.

Advertising attribution, the process of assigning credit for user conversions (such as app downloads or product purchases) to the platforms that contributed to 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-funnel 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 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's self-reported timestamps, making strategically timed reports both feasible and practically undetectable. 2

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 conversions 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 a 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 as a game-theoretic 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 1, with proofs in the full version.

∗

γ

=

2+

4

+

- √

4

).

We begin by analyzing the commonly used Last-Click Mechanism (LCM) and theoretically demonstrate that it is not DSIC. For LCM's performance, our findings reveal that, in the worst-case scenario,

6

2

6

√

3

√

3

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 are eligible for attribution, and the credit a platform receives depends solely on peer reports and prior probabilities-independent of its own report. Since a platform'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 fairness. We further prove that it 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-compatible 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 [13, 14, 23, 28, 29], Shapley value-based methods for fair allocation [1, 4, 24], and Markov models for channel transition influence [1, 15]. Furthermore, causal inference [6, 27] and deep learning [21, 18, 6, 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, 11]. While IC-based techniques have been widely applied in domains such as auctions [7], voting [9], 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 a 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 in a user's interaction sequence as the one that deserves credit. We focus on settings with at least two platforms, the minimal case where attribution ambiguity and manipulation arise. In practice, the number of platforms involved in a conversion is typically small-often no more than five.

2.1 Real-World Advertising Scenario

Consider the real-world online advertising scenario where a user interacts with ads from multiple platforms ( n ≥ 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 i ∈ [ n ] first detects a user click and records a log at the corresponding absolute click time t abs i . It then selects an absolute reported time r abs i ≥ t abs i , at which it submits the log to the advertiser. At some time t 0 ≥ max i ∈ [ n ] { t abs i } , the user converts, and the advertiser performs credit attribution based on reports received by t 0 -that is the set { r abs i | r abs i ≤ t 0 } . Crucially, while the advertiser observes the conversion time t 0 , platforms must decide when to report without knowing when the conversion will occur.

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 a game-theoretic model of the attribution process, capturing strategic platform behavior and informing mechanism design. To simplify analysis, we adopt a conversion-aligned timeline , setting the conversion time t 0 = 0 without loss of generality. Under this transformation, all click times are expressed relative to the conversion and lie in ( -∞ , 0] . Specifically, we define

where t i denotes the relative click time of platform i . Figure 1 illustrates this transformation: if two platforms record clicks at 10:40 a.m. and 10:50 a.m., and the conversion occurs at 11:00 a.m., their relative click times become t 1 = -20 and t 2 = -10 , with the conversion at time 0. Under the

conversion-aligned timeline, the relative click time t = ( t i ) i ∈ [ n ] -which depends on the unknown conversion time-is therefore unobservable to platforms. To capture this uncertainty, we model t i as a random variable drawn independently from a commonly known distribution, with cumulative distribution function (CDF) F i ( t ) and probability density function (PDF) f i ( t ) , supported on ( -∞ , 0] . This distribution may be interpreted as a prior belief based on platform-level statistics. Let F = { F i } i ∈ [ n ] denote the joint distribution from which the click time vector t is drawn.

To model strategic reporting, we assume each platform i ∈ [ n ] selects a non-negative reporting delay τ i ≥ 0 , resulting in a reported time r i = t i + τ i on the conversion-aligned timeline 3 . Since t i is unobservable when the platform commits to its strategy, the chosen delay τ i is applied uniformly across all realizations of t i . We denote the delay profile as τ = ( τ i ) i ∈ [ n ] , and the resulting reported time profile by r = ( r i ) i ∈ [ n ] = t + τ . Unless stated otherwise, all subsequent analysis is conducted on the conversion-aligned timeline.

2.3 Attribution Mechanism

We define an attribution mechanism M by its assignment rule M ( r ) := { x i ( r ) } i ∈ [ n ] , where x i ( r ) denotes the credit assigned to platform i given the reported time profile r . 4 A mechanism is said to be feasible if it satisfies the following constraints:

Constraints (1) and (2) bound individual credit and exclude post-conversion reports. Constraint (3) limits the expected credit, ensuring that the advertiser's overall budget is respected. 5

Given an attribution mechanism M , we define platform i ∈ [ n ] 's instantaneous utility under report profile r as the credit assigned to it by the mechanism: u i ( r ) = x i ( r ) . Given the distribution profile F and others' strategy τ -i , platform i selects its delay τ i to maximize its expected utility:

From the advertiser's perspective, an 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 ( τ i = 0 ) maximizes its utility u i ( r ) regardless of the realized true click times t = ( t i , t -i ) or the strategies τ -i chosen by other platforms 7 . That is, for all platforms i ∈ [ n ] , all true times t i ≤ 0 and t -i , all others' strategies τ -i , and any deviation delay τ ′ i > 0 :

It is easy to verify that DSIC is equivalent to a non-increasing allocation rule with respect to a platform'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 -i , the credit x i ( r i , r -i ) is non-increasing in its own report r i .

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 a mechanism M , given F as

where τ NE is the Nash equilibrium induced by F and M . Note that τ NE = 0 for a DSIC mechanism. Thus, given a known distribution F , the advertiser's optimization problem is formulated as:

Beyond defining accuracy with respect to a fixed F , we define the accuracy of mechanism M as

ACC ( M ) := inf ACC ( M ; F ) ,

capturing worst-case performance across F , serving as a evaluation for a mechanism's performance.

3 The Last-Click Mechanism

In this section, we conduct a rigorous analysis of 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 in both homogeneous and heterogeneous platform settings. Formally, the Last-Click Mechanism is defined as M LCM:

Definition 2 (Last-Click Mechanism) . Given the report profile r = ( r i ) i ∈ [ n ] , the Last-Click Mechanism is defined as M LCM = { x i ( r ) } i ∈ [ n ] . Specifically,

where S = { j ∈ [ n ] | r j ≤ 0 } is the set of platforms with effective reports. Ties are broken uniformly at random among the tied platforms.

Due to its simplicity and its intuitive principle of crediting the platform associated with the user's final click before conversion, LCM is widely adopted in practice. However, it is easy to see that platforms may benefit from strategically delaying their reports, making truthful reporting suboptimal. Therefore, LCM does not satisfy DSIC.

Proposition 1. The Last-Click Mechanism is not a DSIC mechanism.

3.1 Accuracy Analysis

Since LCM is not DSIC, it may assign credit to a platform that wasn't truly last, leading to inaccurate attribution. We therefore analyze its equilibrium accuracy in both homogeneous and heterogeneous platform settings, and derive accuracy bounds for both two-platform and n -platform cases. 8

We first consider the case with two homogeneous platforms and present our result in Theorem 2.

Theorem 2. When there are two homogeneous platforms with identical distribution F ( t ) , supported on ( -∞ , 0] , the accuracy of M LCM is exactly (2 -√ 2) 2 , and this bound is tight.

To prove Theorem 2, we first analyze the incentive constraint at a symmetric strategy profile ( τ 0 , τ 0 ) . By requiring that no platform benefits by unilaterally deviating from τ 0 to truthful reporting, we derive the necessary condition F ( -τ 0 ) ≥ 2 -√ 2 . Since LCM can only attribute correctly when both true click times are before -τ 0 , this yield a lower bound on accuracy of (2 -√ 2) 2 . We then construct a family of distributions f M ( t ) = c M ( e -t -1) , supported on [ -M, 0] , where c M is a normalization constant. We show that this game admits a unique symmetric Nash equilibrium, and as M →∞ , the accuracy converges to exactly (2 -√ 2) 2 .

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 ( t ) , supported on ( -∞ , 0] , the accuracy of M LCM is bounded as follows:

The lower bound is derived using an argument similar to the two-platform case, by examining the conditions 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 ) = -2 t supported on [ -1 , 0] .

Finally, we consider the heterogeneous case, where each platform may follow a different distribution F i ( t ) . Surprisingly, we show that the accuracy of the LCM can be arbitrarily low, even in a simple setting with just two heterogeneous platforms.

Theorem 4. When there are n heterogeneous platforms with distributions F i ( t ) , all supported on ( -∞ , 0] . the accuracy of M LCM can be arbitrarily small and approach to 0.

The proof relies on a key insight: a platform with a highly concentrated distribution (e.g., supported on ( C -ϵ, C + ϵ ) ) can easily manipulate its report to secure attribution credit. We construct an instance where one platform has such a concentrated distribution, while the others have click time supports strictly greater than it. In this scenario, we show that in equilibrium, the concentrated platform receives attribution with probability approaching 1, causing overall accuracy to approach 0.

4 The Peer-Validated Mechanism

In this section, we introduce the Peer-Validated Mechanism (PVM), a novel mechanism addressing the non-DSIC issue of LCM. Intuitively, if the credit assigned to a platform is independent of its own report, the mechanism is DSIC. Based on this idea, we propose the PVM as follows:

Definition 3 (Peer-Validated Mechanism) . Consider n platforms with the CDF { F i } i ∈ n and PDF { f i } i ∈ n supported on ( -∞ , 0] . Let r = ( r i ) i ∈ [ n ] be the reported time profile from n platforms. The Peer-Validated Mechanism assigns credit based on mutual validation among platforms, and is defined as M PVM = { x i ( r ) } i ∈ [ n ] , with

̸

where S = { j ∈ [ n ] | r j ≤ 0 } denotes platforms with eligible reports. β i = P ( i = arg max j { t j } ) = ∫ 0 -∞ f i ( t ) ∏ j = i F j ( t ) dt is the probability that platform i is the true last-click platform based on the prior. The validation threshold α ( i ) S is defined as the solution to ∏ j ∈ S \{ i } F j ( α ( i ) S ) = β i . 9

Roughly speaking, PVM assigns credit to platform i 's credit based on eligible reports from other platforms. When such peer reports exist, the mechanism compares them to a threshold α ( i ) S , which is chosen so that the probability of all peers' true click times being no later than α ( i ) S matches the prior β i that platform i is the true last. This validation process leverages instance-level information to make attribution decisions while preserving incentive compatibility. If no eligible peer reports are available, PVM falls back to allocating β i 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 ( r j > 0 ) are definitely misreports and thus excluded due to unmodeled behavior. Finally, the indicator I [ r i ≤ 0] ensures that attribution only goes to pre-conversion reports.

Since any reporting delay either disqualifies the platform itself or prevents others from being attributed, it is straightforward to verify that PVM satisfies feasibility and DSIC 10 , as formalized in Proposition 2.

Proposition 2. The Peer-Validated Mechanism is a DSIC mechanism.

̸

As PVM is DSIC, we focus on truthful reports ( r = t ). In this case, S = [ n ] , and we let α i denote the threshold used in x i ( · ) , defined by ∏ j = i F j ( α i ) = β i . The allocation rule then simplifies to

̸

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 5. 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 i ( t ) } i ∈ [ n ] that maximizes accuracy. This is a challenging task, as it involves optimizing over a set of functions simultaneously. However, if for any fixed expected attribution e i = E t [ x i ( t )] , we can characterize the most accurate DSIC rule that achieves it, then the problem reduces to optimizing over the expected attribution vector e = ( e i ) i ∈ [ n ] . The following lemma shows that such a characterization indeed exists.

Lemma 1. For platform i and a fixed expected attribution e i , there exists an optimal DSIC attribution rule for platform i w.r.t. accuracy, satisfying e i = E t [ x i ( t )] , that can be written as

̸

̸

where G i ( t ) = Π j = i F j ( t ) is the CDF of the random variable max j = i { t j } , and G i ( θ i ) = e i .

̸

̸

Herein, we give a proof sketch of Lemma 1. First, as any DSIC rule must be non-increasing in t i (Theorem 1), we claim that, to maximize accuracy, the optimal DSIC rule x i ( t i , t -i ) should be a constant when given t -i , so that larger values of t i , which more better indicate that platform i is last, are not penalized. Second, given a fixed expected attribution e i , the self-independent rule x i ( t -i ) should prioritize instances with smaller max j = i { t j } , where platform i is more likely to be last. This greedy strategy yields the threshold-form optimal DSIC rule in the lemma. When G i is somewhere flat, multiple thresholds may achieve e i , and combining them may yield non-threshold variants. Still, at least one such optimal rule exists.

Based on Lemma 1, the task reduces to finding the optimal ( e ∗ i ) i ∈ [ n ] . Since G i ( θ i ) = e i , the original optimization problem (4) can therefore be reformulated in terms of θ = ( θ i ) i ∈ [ n ] as follows:

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 5.

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 a DSIC mechanism can achieve.

Theorem 6. When there are n homogeneous platforms with identical distribution F ( t ) , supported on ( -∞ , 0] , the accuracy of M PVM is exactly equal to

In the homogeneous case, symmetry implies that all thresholds α i are equal, denoted by α , and satisfy F ( α ) n -1 = 1 /n . Therefore, PVM makes a correct attribution if either all reports are no greater than α , which occurs with probability (1 /n ) n/ ( n -1) , or exactly one report exceeds α , which occurs with probability 1 -(1 /n ) 1 / ( n -1) . These probabilities depend only on n , not on 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 a comparison with the Last-Click mechanism (presented in Table 2) to show that PVM is strictly superior.

In the rest, we consider the general heterogeneous-platform setting. We show a tight bound on accuracy for two-platform case (Theorem 7) and a lower bound for n -platform case (Theorem 8).

Theorem 7. When there are two heterogeneous platforms, the accuracy of M PVM is exactly equal to ACC ( M PVM ) = 19 / 27 ≈ 0 . 7037 .

To establish the result, we first formulate an 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 .

Theorem 8. When there are n heterogeneous platforms, the lower bound on the accuracy of M PVM is ACC ( M PVM ) = (19 / 27) ⌈ log 2 n ⌉ .

For n heterogeneous platforms, we design a binary-tree-based mechanism to derive a lower bound for PVM. Starting from the root node, which represents all n platforms, we recursively partition them into two disjoint subsets L and R of sizes ⌈ n/ 2 ⌉ and ⌊ n/ 2 ⌋ , respectively. Each subset is treated as a virtual platform, represented by the distribution of max i ∈ L { t i } or max i ∈ R { t i } . At each internal node, the attribution reduces to a problem between two heterogeneous platforms. Repeating this over ⌈ log 2 n ⌉ levels yields an overall accuracy lower bound of (19 / 27) ⌈ log 2 n ⌉ . Since PVM is guaranteed to perform at least as well as this mechanism, the same expression serves as a lower bound for its accuracy.

4.3 Fairness of PVM

Besides the DSIC and accuracy, PVM also satisfies a strong fairness property: the expected attribution E [ x i ] for each platform i exactly matches its true probability of contributing the last click, P ( i = arg max j { t j } ) . This alignment offers a principled basis for evaluating long-term platform effectiveness and simultaneously promotes trust in the mechanism's equity. To quantify this alignment and enable comparisons across mechanisms, we define the following metric:

Definition 4. The fairness score of mechanism M under the joint distribution F is defined as

Definition 5. A mechanism M is Fair if, for any joint distribution F , it holds that

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 ( α i ) i ∈ [ n ] under DSIC:

̸

̸

Proposition 3. The Peer-Validated Mechanism is Fair .

In contrast, the Last-Click Mechanism fails to meet this property.

Proposition 4. The Last-Click Mechanism is not Fair .

LCMfails the Fair property due to 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 zero in such settings.

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 n ∈ { 2 , 3 , 4 , 5 } identical platforms, all following the click time same distribution, repeated across four distributions derived

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 × 10 4 simulated user paths, repeated over 10 independent runs.

PVM consistently outperforms LCM in both accuracy and fairness across all settings. Table 4 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 ).

6 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-Validated Mechanism (PVM), a novel DSIC mechanism that allocates credit based on peer reports. We prove that PVM achieves optimal accuracy in homogeneous settings, offers provable guarantees in heterogeneous ones, and satisfies a strong fairness 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 incentive-compatible attribution systems. For instance, in machine learning-based models, excluding a platform's own report as an input feature ensures truthfulness, shifting the focus from detection to design.

Besides, PVM framework can be extended to settings with correlated click-time distributions while preserving the core peer-validation principle and the DSIC property. The validation rule generalizes from a scalar threshold ( α i ) to a multi-dimensional acceptance region D i over peer reports t -i , constructed greedily by including outcomes with the highest posterior probability that platform i was the true last click until P ( t -i ∈ D i ) = β i . A platform receives credit if and only if its peers' reports fall within D i . Under this modification, the homogeneous-case 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 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 lastclick probability, future work may explore mechanisms that further improve instance-level accuracy. Second, investigating correlated click-time distributions could enhance a mechanism's applicability in realistic scenarios. Next, a joint optimization framework modeling both advertiser and platform utilities, integrating attribution with budget allocation, represents a compelling direction. Finally, investigating repeated games with externalities-where platforms may strategically harm peers or misreport distributions to manipulate learned priors-could address dynamic interactions, potentially incorporating bidding strategies for a more comprehensive ecosystem model.

Acknowledgment

This work was supported by National Natural Science Foundation of China (No.62472428), Public Computing Cloud, Renmin University of China, the fund for building world-class universities (disciplines) of Renmin University of China.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nThe 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.\n\nQUESTIONS:\n# 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?\n\nLIMITATIONS:\nna", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\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?\n\nQUESTIONS:\nPlease refer to \"Weaknesses\". Explanations for weaknesses 2, 3, and 4 are expected.\n\nLIMITATIONS:\nThe 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.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\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.\n\nQUESTIONS:\n* 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?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\n### 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.\n\nQUESTIONS:\n1. 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.\n\nLIMITATIONS:\n* 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).", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}