Summary: We consider a discounted stochastic game of common-property capital accumulation with nonsymmetric players, bounded one-period extraction capacities, and a transition law satisfying a general strong convexity condition. We show that the infinite-horizon problem has a Markov-stationary (subgame-perfect) equilibrium and that every finite-horizon truncation has a unique Markovian equilibrium, both in consumption functions which are continuous and nondecreasing and have all slopes bounded above by 1. Unlike previous results in strategic dynamic models, these properties are reminiscent of the corresponding optimal growth model.