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Beyond Last-Click: An Optimal Mechanism for Ad Attribution
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Formulates ad attribution as a mechanism design problem and proposes the Peer-Validated Mechanism (PVM), a DSIC rule that attributes credit based on other platforms' reports, proving it optimal for homogeneous platforms and showing last-click is not DSIC and performs poorly.
Problem
Multi-platform ad attribution under last-click rules is vulnerable to strategic report timing, so platforms can misreport to capture credit; the field lacks a theoretical incentive-compatible attribution mechanism with accuracy guarantees.
Approach
A platform's credit depends only on other platforms' eligible reports (compared against a prior-calibrated threshold), so its own report cannot affect its own allocation, making the mechanism DSIC by design while matching the true last-click probability in expectation.
Key results
- PVM is DSIC and optimal among DSIC mechanisms in the homogeneous setting, with exact accuracy 1-(1-1/n)(1/n)^(1/(n-1)); for n=2 this is 0.75 versus LCM's worst-case upper bound of about 0.3431.
- For two heterogeneous platforms, PVM's exact worst-case accuracy is 19/27 (about 0.7037), whereas LCM's accuracy can approach 0.
- In simulations with n=5 homogeneous platforms, PVM improves accuracy over LCM by 0.3041 on average.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace LCM with PVM | Advertising attribution · Homogeneous platforms, n=2 | accuracy: (2-\sqrt{2})^2\approx0.3431 -> 3/4=0.75 | Helped |
| Replace LCM with PVM | Advertising attribution · Heterogeneous platforms, n=2 | accuracy: 0 -> 19/27\approx0.7037 | Helped |
| Replace LCM with PVM | Advertising attribution · Homogeneous platforms, n=2 | accuracy: 0.0404\pm0.0396 | Helped |
| Replace LCM with PVM | Advertising attribution · Homogeneous platforms, n=3, 4, and 5 | accuracy: 0.1583\pm0.0439; 0.2444\pm0.0580; 0.3041\pm0.0490 | Helped |
| Replace LCM with PVM | Advertising attribution · Heterogeneous platforms, n=2 (6 pairs) | accuracy: 0.0655\pm0.0283 | Helped |
| Replace LCM with PVM | Advertising attribution · Homogeneous platforms, n=2, 3, 4, and 5 | fairness: 0.0248\pm0.0089; 0.0157\pm0.0034; 0.0107\pm0.0047; 0.0111\pm0.0040 | Helped |
| Replace LCM with PVM | Advertising attribution · Heterogeneous platforms, n=2 (6 pairs) | fairness: 0.1320\pm0.0598 | Helped |
| Use PVM instead of LCM | Advertising attribution · Homogeneous platforms | accuracy: 1 - \left( 1 - \frac{1}{n} \right) \left( \frac{1}{n} \right)^{\frac{1}{n-1}} | Helped |
| Use PVM instead of LCM | Advertising attribution · Heterogeneous platforms | accuracy: (19/27)^{\lceil\log_2 n\rceil} | Helped |
| Use PVM instead of LCM | Advertising attribution · Any platform distribution | fairness: 1 | Helped |
| Use LCM | Advertising attribution · Any platform distribution | DSIC | Hurt |
Surprising findings
- Under heterogeneity, LCM's accuracy and fairness can be driven arbitrarily close to zero even with just two platforms.
Limitations
- Assumes independent click-time distributions; correlated extension only sketched.
- Models strategic delay only, not click spamming or injection.
- Full proofs deferred to a full version not included in the paper.
Experimental setup
Datasets: real-world ad conversion logs from four advertising platforms (used to fit click time distributions)
Benchmarks: simulated user paths fitted to real ad-conversion logs
Metrics: attribution accuracy fairness score
Baselines: Last-Click Mechanism
Builds on: last-click attribution Myerson-style incentive compatibility
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