On the Power of Strategic Corpus Enrichment in Content Creation Games

TL;DR

This work addresses instability in content-ranking games caused by strategic publisher behavior. It introduces corpus enrichment with a small set of fixed dummy documents to transform a Colonel Blotto–type ranking game into one with pure Nash equilibria and convergent best-response dynamics, while preserving the use of classical ranking functions. The authors present two schemes—uniform and generalized corpus extension—establishing tight bounds on the number of added documents and proving equilibrium existence; uniform extension also guarantees convergence of best-response dynamics under broad conditions, whereas the generalized approach may fail to converge in some cases. The results yield stable, welfare-maximizing ecosystems where original publishers prevail, offering practical mediator strategies and computational tools for best-response computations, with clear tradeoffs between augmentation efficiency and social welfare. Overall, the paper bridges game-theoretic stability with practical ranking systems, extending Blotto-style insights to modern content recommendation contexts.

Abstract

Search and recommendation ecosystems exhibit competition among content creators. This competition has been tackled in a variety of game-theoretic frameworks. Content creators generate documents with the aim of being recommended by a content ranker for various information needs. In order for the ecosystem, modeled as a content ranking game, to be effective and maximize user welfare, it should guarantee stability, where stability is associated with the existence of pure Nash equilibrium in the corresponding game. Moreover, if the contents' ranking algorithm possesses a game in which any best-response learning dynamics of the content creators converge to equilibrium of high welfare, the system is considered highly attractive. However, as classical content ranking algorithms, employed by search and recommendation systems, rank documents by their distance to information needs, it has been shown that they fail to provide such stability properties. As a result, novel content ranking algorithms have been devised. In this work, we offer an alternative approach: corpus enrichment with a small set of fixed dummy documents. It turns out that, with the right design, such enrichment can lead to pure Nash equilibrium and even to the convergence of any best-response dynamics to a high welfare result, where we still employ the classical/current content ranking approach. We show two such corpus enrichment techniques with tight bounds on the number of documents needed to obtain the desired results. Interestingly, our study is a novel extension of Borel's Colonel Blotto game.

Figures (5)

• Figure 1: Illustration of different equilibrium profiles in the game $G_t=\langle 2, 5, 0.5, t \rangle$ for varying $t$ values.
• Figure 2: Possible fair and unfair improvement steps in the game $G=\langle 2, 4, 1, 0.4 \rangle$, with the player that deviates marked in red.
• Figure 3: Illustration of different equilibrium profiles in the game $G_{\vec{t}}=\langle 2, 4, 1, \vec{t}\rangle$ for varying $\|\vec{t}\|_1$ values.
• Figure 4: Improvement cycle in the game $G=\langle 2, 6, 1, (\frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, 0, 0)\rangle$, with deviations marked in red at each step.
• Figure 5: Estimated value of $\|t\|_1$ by different values of $p$.

Theorems & Definitions (41)

• Lemma 2.0
• Theorem 3.1: Haya1arxiv
• Theorem 4.1
• Theorem 4.2
• Corollary 4.2
• Definition 1: Social Welfare
• Lemma 4.2
• Definition 2: Deviation Equity
• Definition 3: Fair Player
• Theorem 5.1