We are looking for a perception-perfect strategy with $s=(0,0,\dots)$ and $\hat s=(1,1,\dots)$
The agent may believe she will enrol tomorrow if:
$\begin{align} 0+\hat\beta\delta\left(-c_0-c_1+\frac\delta{1-\delta}b\right)&\le-c_0-c_1+\frac{\hat\beta}\delta1-\delta b\\ (1-\hat\beta\delta)(c_0+c_1)&\le\hat\beta\delta b \end{align}$
I know that the LHS refers to the utility the agent thinks she will get if she consumes tomorrow, but I don't know what the RHS is. Can anyone tell me what the RHS refers to?
This is from my economics lecture notes. This is in the context of beta-delta discounting, where $c_0+c_1$ is the cost of doing the task, and $b$ is the benefit from doing the action in all periods following the task.