# Riemannian Game Dynamics

When a platform or planner changes an incentive rule, it usually has to wait for trajectory data under that rule before knowing how the population will shift. PA-RmD keeps the payoff function as an explicit input and learns only the payoff-independent population response structure from historical trajectories, so it can predict the induced trajectory under a new payoff directly. On held-out payoffs in synthetic zero-sum cyclic and potential congestion games, and on held-out countries in a ten-country YouTube Trending panel, its one-step, full-rollout and final-state errors are lower than SINDy, Neural ODE, LEADS, CoDA and SIAR.

When a platform or planner changes an incentive rule, it usually has to wait for trajectory data under that rule before knowing how the population will shift. PA-RmD keeps the payoff function as an explicit input and learns only the payoff-independent population response structure from historical trajectories, so it can predict the induced trajectory under a new payoff directly. On held-out payoffs in synthetic zero-sum cyclic and potential congestion games, and on held-out countries in a ten-country YouTube Trending panel, its one-step, full-rollout and final-state errors are lower than SINDy, Neural ODE, LEADS, CoDA and SIAR.