Before revision:  Analytical solutions are derived for the three problems: mean-variance portfolio problem (MVP) with constant risk aversion, MVP with a state-dependent risk aversion , and an investment/consumption problem with non-exponential discounting . Through these examples, we address the effects of roughness on equilibrium strategies .
After revision:  Analytical solutions are derived for the three problems: mean-variance portfolio problem (MVP) with constant risk aversion, MVP with a state-dependent risk aversion , and an investment/consumption problem with non-exponential discounting , we present that volatility roughness adjusts the equilibrium strategies considerably, up to 40\% in certain settings. Since rough volatility models capture the near-term downside risk by fitting the volatility skews, we interpret the adjustments as a hedge for this risk .