Learning and the stability of cycles

We investigate the extent to which agents can learn to coordinate on stationary perfect-foresight cycles in a general-equilibrium environment. Depending on the value of a preference parameter, the limiting backward (direction of time reversed) perfect-foresight dynamics are characterized by steady-state, periodic, or chaotic trajectories for real money balances. We relax the perfect-foresight assumption and examine how a population of artificial, heterogeneous adaptive agents might learn in such an environment. These artificial agents optimize given their forecasts of future prices, and they use forecast rules that are consistent with steady-state or periodic trajectories for prices. The agents' forecast rules are updated by a genetic algorithm. We find that the population of artificial adaptive agents is able eventually to coordinate on steady state and low-order cycles, but not on the higher-order periodic equilibria that exist under the perfect-foresight assumption.