Myopia and Discounting

We study perfectly patient agents who estimate the value of future events by generating noisy, unbiased simulations and combining those signals with priors to form posteriors. These posterior expectations exhibit as-if discounting: agents make choices as if they were maximizing a stream of known utils weighted by a discount function, D(t): This as-if discount function reflects the fact that estimated future utils are a combination of signals and priors, so average expectations are optimally shaded toward the mean of the prior distribution, generating behavior that partially mimics the properties of classical time preferences. When the simulation noise has variance that is linear in the event’s horizon, the as-if discount function is hyperbolic, D(t) = 1/(1 + αt). Our analysis includes a stripped-down Bayesian base case and two complementary, psychologically-enriched extensions: (i) the agent also uses the value of current rewards as an imperfect proxy for future rewards; (ii) the agent aggregates “building blocks” to construct a cognitively costly representation of the future, with predictive accuracy that improves as the number of building blocks increases. Our agents exhibit systematic preference reversals, but have no taste for commitment because they suffer from imperfect foresight, which is not a self-control problem. In our framework, agents exhibit less discounting if they have more domain-relevant experience, are more intelligent, or are encouraged to spend more time thinking about an intertemporal tradeoff. Agents who are unable to think carefully about an intertemporal tradeoff – e.g., due to cognitive load – exhibit more discounting. More myopia tends to coincide with more projection bias. In our framework, patience is unstable, fluctuating situationally with the accuracy of forecasting.