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On the Power of Strategic Corpus Enrichment in Content Creation Games
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Shows that adding a small number of fixed dummy documents (corpus enrichment) to a classical ranking game among content creators yields pure Nash equilibria and best-response convergence to high-welfare outcomes, modeling the game as a Colonel Blotto variant.
Problem
Content ranking games among competing content creators lack pure Nash equilibria under classical distance-based rankers, so the ecosystem can be unstable and best-response dynamics may cycle.
Approach
Instead of changing the ranking algorithm, the mediator adds a small set of static dummy documents that act as per-query score thresholds; with the right design (uniform or non-uniform thresholds) this yields pure equilibria, welfare-maximizing outcomes, and convergence of best-response dynamics under fairness, with tight bounds on the number of added documents.
Key results
- Uniform corpus enrichment guarantees a pure Nash equilibrium with at most n added documents (n = number of publishers), regardless of number of queries m.
- Under uniform enrichment, best-response dynamics with fair players converge to a pure equilibrium with rate O(min{m, n^2}).
- Generalized non-uniform thresholds can reduce the needed dummy documents; e.g., in the G<4,5,1> example only one document is needed versus three under uniform thresholds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add uniform-threshold static documents | Multiple-Queries Ranking Game · Arbitrary n, m, p | pure equilibrium existence: without corpus extension, a pure Nash equilibrium exists iff p ≤ 1/max{⌈2 · m/n − 1⌉, 1}; with uniform enrichment, |T|≤ | Helped |
| Add uniform-threshold static documents under the stated conditions | Multiple-Queries Ranking Game · Uniform corpus enrichment, fair best-response dynamics | best-response convergence: no more than n steps when m mod n=0; O(min{m, n^2}) otherwise | Helped |
| Replace uniform thresholds with query-specific thresholds (ablation) | Corpus-enriched ranking game · G⟨4, 5, 1⟩ | number of added documents: three documents -> one document | Helped |
| Replace uniform thresholds with query-specific thresholds (ablation) | Corpus-enriched ranking game · Generalized corpus enrichment | best-response convergence | Hurt |
| Replace uniform thresholds with query-specific thresholds (ablation) | Corpus-enriched ranking game · Generalized corpus enrichment | social welfare maximization | Hurt |
Surprising findings
- With non-uniform thresholds, best-response dynamics may fail to converge even though a pure equilibrium exists.
Limitations
- Best-response convergence is only guaranteed under a fairness assumption on tie-breaking deviations and for restricted peak value ranges.
- Generalized enrichment does not guarantee convergence of best-response dynamics.
- Only original publishers are selected as winners; allowing higher-quality dummy documents to win is left for future work.
Experimental setup
Metrics: pure Nash equilibrium existence social welfare publisher exposure number of added documents
Builds on: Colonel Blotto game multiple-queries ranking game (Ben-Porat and Tennenholtz)
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