Dynamics in Two-sided Attention Markets: A Non-Convex Optimization View

How do attention markets — where creators compete for engagement, users choose what to consume, and platforms mediate via recommender systems — behave in the long run? Existing theory addresses each side in isolation, leaving open whether the coupled dynamics of user choice, platform ranking and creator strategy converge to a coherent outcome at all. For a dynamic model of attention markets encompassing heterogeneous creator costs, multinomial logit user choice and a spectrum of ranking schemes, we show that this three-way feedback loop is equivalent to mirror descent or its delayed-gradient variant on a global potential function. This potential decomposes into four interpretable socioeconomic forces: content quality, fairness, production efficiency and diversity, whose balance is directly shaped by the platform's ranking policy. This characterization provides a theoretical foundation for designing healthier creator ecosystems by identifying key policy parameters that govern these trade-offs. Moreover, non-convexity of the potential, intensified by social influence and popularity-based ranking, explains the path-dependent and winner-take-all outcomes observed on real-world platforms.