The model is a two-country overlapping generations economy with boundedly rational agents who update their decision rules using a version of the stochastic replicator dynamic. The results show that stationary rational expectations equilibria of this model are unstable under this type of evolutionary adaptation. The paper also derives a two-period-ahead forecast of the values of average fractions of savings placed in each of the two currencies. This forecast is used in decisionmaking of a rational agent who has a full knowledge of the evolutionary economy. The performance of the rational agent is compared to the performance of boundedly rational agents, based on the average utility received over time. Results show that the difference between utilities earned by rational and boundedly rational agents is small. In addition, the average utility of the best-performing boundedly rational agents is higher than the average utility of the rational agents.