I am an econ undergrad trying to understand how to maximize this payoff function, which includes binary components. I want to solve this equation using backwards induction, so I want to maximize the given function with respect to A (A is continous on the interval [0,1]), but I am quite confused how to differentiate a function with binary components.
Here the R portion of the function is a binary indicator that is either 0 or 1.
Any advice or pointing me in the right direction would be greatly appreciated.