In social dilemmas, the ability of individuals to coordinate their actions is crucial to reach group optima. Unless exacted by power or force, coordination in humans relies on a common understanding of the problem, which is greatly facilitated by communication. The lack of means of consultation about the nature of the problem and how to solve it may explain why multiagent coordination in nonhuman vertebrates has commonly been observed only when multiple individuals react instantaneously to a single stimulus, either natural or experimentally simulated, for example a predator, a prey, or a neighboring group. Here we report how vervet monkeys solved an experimentally induced coordination problem. In each of three groups, we trained a low-ranking female, the “provider,” to open a container holding a large amount of food, which the providers only opened when all individuals dominant to them (“dominants”) stayed outside an imaginary “forbidden circle” around it. Without any human guidance, the dominants learned restraint one by one, in hierarchical order from high to low. Once all dominants showed restraint immediately at the start of the trial, the providers opened the container almost instantly, saving all individuals opportunity costs due to lost foraging time. Solving this game required trial-and-error learning based on individual feedback from the provider to each dominant, and all dominants being patient enough to wait outside the circle while others learned restraint. Communication, social learning, and policing by high-ranking animals played no perceptible role.