  A possibly immortal agent tries to maximise its summed discounted rewards
over time, where discounting is used to avoid infinite utilities and encourage
the agent to value current rewards more than future ones. Some commonly used
discount functions lead to time-inconsistent behavior where the agent changes
its plan over time. These inconsistencies can lead to very poor behavior. We
generalise the usual discounted utility model to one where the discount
function changes with the age of the agent. We then give a simple
characterisation of time-(in)consistent discount functions and show the
existence of a rational policy for an agent that knows its discount function is
time-inconsistent.
