This paper studies a game theoretic model where agents choose between two updating rules to predict a future endogenous variable. Agents rationally choose between these predictors based on relative performance. Conditions for evolutionary stability and stability under learning are found for the Nash solutions and corresponding parameter equilibria. Stability conditions are contingent upon parameter values and the initial distribution of heterogeneity. However, when the cost of using the more advanced updating rule is sufficiently large, all agents will asymptotically use the more parsimonious, or Minimum State Variable (MSV), updating rule.