Dynamic stochastic games are the workhorse for studying the feedback loop between firms’ decisions and industry evolution, but computing equilibria for counterfactual analysis remains hard: both the state space and the expectation over successor states grow exponentially in the number of players. We combine forward simulation, projection methods, and deep neural networks to compute equilibria in games with many players. Equilibrium conditions are cast as a functional equation. Value and policy functions are replaced by deep neural networks and training proceeds by stochastic gradient descent over states drawn from the ergodic distribution using an all-in-one expectation operator. In a capacity accumulation game and an entry/exit game, we compute accurate equilibria with up to 128 firms.