Drawing on the empirical evidence that heterogeneity in inflation expectations is persistent and endogenously time-varying, we embed two inflation forecasting strategies—one based on costly ex ante perfect foresight, and the second based on costless ex ante extrapolative trend-following—in a macrodynamic model. Drawing also on the empirical evidence that inflation forecast errors may have to exceed some threshold before agents abandon their previously selected forecasting strategy, we describe agents as switching between forecasting strategies according to evolutionarily satisficing learning. Convergence to a long-run equilibrium consistent with output growth, unemployment and inflation at their natural levels may be achieved even if heterogeneity in inflation forecasting strategies (with predominance of the extrapolative foresight strategy) is an attractor of an evolutionarily satisficing dynamic perturbed by mutant agents. Thus, in keeping with the empirical evidence, heterogeneity in strategies to form inflation expectations (with prevalence of bounded rationality) can be a stable long-run equilibrium.