Equilibrium World Models

Abstract

We introduce \emph{Equilibrium World Models} (EWMs), a deep-learning method for globally solving dynamic stochastic models that feature rare disasters, binding constraints, and counterfactual states. Standard unsupervised neural-network-based solvers impose equilibrium conditions only on states generated by their own simulated policy. Their solutions can therefore be self-confirming: accurate on the simulated path, but untested off it, sensitive to initialization, and costly when expectations must be recomputed at each step. EWMs change the computational representation, not the economics. They enforce the model's exact equilibrium conditions on a broader, model-generated distribution of ordinary, rare, stressed, and counterfactual states. They carry the continuation with a learned surrogate, but certify the resulting policy strictly against the true equilibrium conditions. We provide an error decomposition, an off-path residual bound, and a convergence result linking self-confirming solutions to rational-expectations equilibria. We demonstrate EWMs through a sequence of test cases that isolate the main pathologies of classical deep-learning solvers and then scale them to richer economies. In a rare-disaster Brock--Mirman laboratory, coverage reduces disaster-region residuals by an order of magnitude. In a high-dimensional international real-business-cycle model, classical deep-learning solvers fail from all random starts, whereas EWMs converge from nearly all and evaluate continuations up to two orders of magnitude less often. When actions move transition measures, EWMs use action-conditioned continuations to recover the relevant policy margin. In a heterogeneous-agent economy with aggregate risk, EWMs compress the numerical representation of the wealth distribution by at least 25x while imposing exact full-distribution rational-expectations conditions.