Discrete beliefs space and equilibrium: a cautionary note

Bounded rationality requires assumptions about ways in which rationality is con-
strained and agents form their expectations. Evolutionary schemes have been used to model beliefs dynamics, with agents choosing endogenously among a limited number of beliefs heuristics according to their relative performance. This work shows that arbitrarily constraining the beliefs space to a finite (small) set of possibilities can generate artificial equilibria that can be stable under evolutionary dynamics. Only when "enough" heuristics are available are beliefs in equilibrium not artificially constrained. I discuss these findings in light of an alternative approach to modelling beliefs dynamics, namely, adaptive learning.