The "Collective Intelligence" (COIN) framework concerns the design of collectives of reinforcement-learning agents such that their interaction causes a provided "world" utility function concerning the entire collective to be maximized. Previously, we applied that framework to scenarios involving Markovian dynamics where no re-evolution of the system from counter-factual initial conditions (an often expensive calculation) is permitted. This approach sets the individual utility function of each agent to be both aligned with the world utility, and at the same time, easy for the associated agents to optimize. Here we extend that approach to systems involving non-Markovian dynamics. In computer simulations, we compare our techniques with each other and with conventional "team games" We show whereas in team games performance often degrades badly with time, it steadily improves when our techniques are used. We also investigate situations where the system’s dimensionality is effectively reduced. We show that this leads to difficulties in the agents’ ability to learn. The implication is that "learning" is a property only of high-enough dimensional systems.