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On click-fraud under pro-rata revenue sharing rule

Hao Yu

TL;DR

The study analyzes click-fraud under pro-rata revenue sharing, introducing a non-cooperative model with a fraud-technology cap $\lambda_0$ that bounds undetectable fake streams. It proves that honesty is a strict dominant strategy when fraud tech is weak and identifies a unique, bounded fraud equilibrium when fraud tech is strong, with low-real-share artists cheating while the total fake streams remain bounded. To mitigate fraud without abandoning pro-rata, it proposes a parametric weighted rule $R_i^{pw}(\alpha)$ that interpolates toward user-centric, increasing fraud-deterrence as $\alpha$ decreases, and derives conditions for achieving fraud-free equilibrium under technological constraints. The analysis also discusses Spotify's qualification policy and its potential unintended effects, offering practical guidance on policy design and revenue-sharing rule selection to balance efficiency, fairness, and fraud resilience.

Abstract

Click-fraud is commonly seen as a key vulnerability of pro-rata revenue sharing on music streaming platforms, whereas user-centric is largely immune. This paper develops a tractable non-cooperative model in which artists can purchase fraud activity that generates undetectable fake streams up to a technological limit. We show that pro-rata can be fraud-robust: when fraud technology is weak, honesty is a strict dominant strategy, and an efficient fraud-free equilibrium obtains. When fraud technology is strong, a unique fraud equilibrium arises, yet aggregate fake streams remain bounded. Although fraud is inefficient, the resulting redistribution may improve fairness in some cases. To mitigate fraud without abandoning pro-rata, we introduce a parametric weighted rule that interpolates between pro-rata and user-centric, and characterize parameter ranges that restore a fraud-free equilibrium under technology constraint. We also discuss implications of Spotify's modernized royalty system for fraud incentives.

On click-fraud under pro-rata revenue sharing rule

TL;DR

The study analyzes click-fraud under pro-rata revenue sharing, introducing a non-cooperative model with a fraud-technology cap that bounds undetectable fake streams. It proves that honesty is a strict dominant strategy when fraud tech is weak and identifies a unique, bounded fraud equilibrium when fraud tech is strong, with low-real-share artists cheating while the total fake streams remain bounded. To mitigate fraud without abandoning pro-rata, it proposes a parametric weighted rule that interpolates toward user-centric, increasing fraud-deterrence as decreases, and derives conditions for achieving fraud-free equilibrium under technological constraints. The analysis also discusses Spotify's qualification policy and its potential unintended effects, offering practical guidance on policy design and revenue-sharing rule selection to balance efficiency, fairness, and fraud resilience.

Abstract

Click-fraud is commonly seen as a key vulnerability of pro-rata revenue sharing on music streaming platforms, whereas user-centric is largely immune. This paper develops a tractable non-cooperative model in which artists can purchase fraud activity that generates undetectable fake streams up to a technological limit. We show that pro-rata can be fraud-robust: when fraud technology is weak, honesty is a strict dominant strategy, and an efficient fraud-free equilibrium obtains. When fraud technology is strong, a unique fraud equilibrium arises, yet aggregate fake streams remain bounded. Although fraud is inefficient, the resulting redistribution may improve fairness in some cases. To mitigate fraud without abandoning pro-rata, we introduce a parametric weighted rule that interpolates between pro-rata and user-centric, and characterize parameter ranges that restore a fraud-free equilibrium under technology constraint. We also discuss implications of Spotify's modernized royalty system for fraud incentives.
Paper Structure (19 sections, 12 theorems, 69 equations)

This paper contains 19 sections, 12 theorems, 69 equations.

Table of Contents

  1. Introduction
  2. Model
  3. Analysis
  4. Fraud-free equilibrium under weak fraud technology
  5. Fraud equilibrium under strong fraud technology
  6. Fairness comparison
  7. Discussion on alternative methods
  8. Parametric weighted rule
  9. Spotify's modernized royalty system
  10. Concluding remarks
  11. Proofs
  12. Proof of Lemma \ref{['lem:index2']}
  13. Proof of Lemma \ref{['lem:index12']}
  14. Proof of Theorem \ref{['thm:index4']}
  15. Proof of Proposition \ref{['prop:index1']}
  16. ...and 4 more sections

Key Result

Lemma 1

$t_i = 0$ is a strict dominant strategy of artist $i$ if and only if $\lambda_0 \leq \overline{\lambda}[1+\xi h(d_i)]$, where

Theorems & Definitions (13)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Proposition 1
  • Corollary 1
  • Corollary 2
  • Definition 1
  • Proposition 2
  • Corollary 3
  • ...and 3 more