Change the incentive rule and still forecast the crowd: PA-RmD separates payoff from response structure
Synopsis
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.
Interpretation
Population game dynamics can now be predicted by payoff design: given a payoff function unseen in training, the model directly outputs where it will push the population state. Earlier dynamics-learning methods fit only the motion realized under training payoffs, mixing the payoff-dependent incentive with the payoff-independent response rule, so a payoff change left no principled way to update the prediction. On held-out payoff functions in synthetic zero-sum cyclic and potential congestion games, PA-RmD under replicator dynamics reaches one-step errors of 1.29E-3 and 3.48E-4, below Neural ODE at 1.45E-2 and 1.62E-3, LEADS at 1.67E-2 and 1.63E-3, CoDA at 1.43E-2 and 1.63E-3, and SIAR at 5.03E-2 and 7.15E-3.
The construction writes population motion as a balance of two forces: a push from current payoffs and a cost of switching strategies. Riemannian game dynamics already describe motion as a payoff-driven gain minus a cost of motion; PA-RmD keeps that form but parameterizes the cost term as a matrix to be learned and shares it across all payoff functions. Training matches a finite-difference approximation of the time derivative against the predicted one-step displacement; the implementation parameterizes the matrix as a neural-network output plus the identity to keep it positive definite, and evaluates on zero-sum cyclic and potential congestion games with replicator, projection and multiplicative-weights response dynamics.
Perspective
Evaluation covers held-out payoff prediction on synthetic zero-sum cyclic and potential congestion games under replicator, projection and multiplicative-weights response dynamics, plus held-out-country prediction on a ten-country YouTube Trending panel with 122 aligned dates; the intended readers are researchers working on population game dynamics and mechanism design.
The theory relies on conditions including a response structure shared across payoffs and held-out payoff directions covered by training payoff directions; in the real data the population state is the category share of trending videos and payoffs are engagement proxies built from view counts, and the authors note the behavioral interpretation of these constructed quantities is limited because the data do not directly track creators' strategy revisions at individual or population level.