Ergodic Herd Suppression via Distributional Feedback
Ramen Ghosh · HAL (Le Centre pour la Communication Scientifique Directe) · 2025
We study a sequential decision-making game in which agents choose actions based on private information and previous participants' observed behaviour. Without intervention, such systems often converge to herding equilibria or informational cascades, wherein long-run diversity collapses and rational agents imitate predecessors regardless of private signals. To mitigate this, we propose a distributional feedback mechanism that regulates the system based on the empirical ergodic distribution of agent actions. The regulator (e.g., a social planner or mechanism designer) introduces a penalty or incentive signal designed to align the long-run distribution with a target that encodes diversity or balance. We formulate the resulting control problem in the space of invariant measures and use optimal transport (Wasserstein geometry) to quantify deviation from the target. Our framework, which connects ideas from Bayesian learning, game theory, and ergodic control, provides a novel approach for steering large-agent systems away from collapse using minimal, decentralized intervention. This work has the potential to significantly impact the field as we provide theoretical results on the existence and structure of equilibrium distributions under feedback and validate the framework using simulations of stylized economic environments.