Exercise 17.11 [101x3-mdp-exercise]

Consider the $101 \times 3$ world shown in Figure grid-mdp-figure(b). In the start state the agent has a choice of two deterministic actions, Up or Down, but in the other states the agent has one deterministic action, Right. Assuming a discounted reward function, for what values of the discount $\gamma$ should the agent choose Up and for which Down? Compute the utility of each action as a function of $\gamma$. (Note that this simple example actually reflects many real-world situations in which one must weigh the value of an immediate action versus the potential continual long-term consequences, such as choosing to dump pollutants into a lake.)