 A well-known sequential decision problem is the one facing Ulysses on his journey home to Ithaca in Homer’s great tale from antiquity. Ulysses must make a choice about the manner in which he will sail past an island inhabited by sweet-singing sirens. He can choose to sail unrestrained or else tied to the mast. In the former case, Ulysses will later have the choice, upon hearing the sirens, to either continue sailing home to Ithaca or to stay on the island indefinitely. In the latter case, he will not be free to make further choices and the ship will sail onwards to Ithaca past the sweet-singing sirens. The final outcome depends on what sequence of choices Ulysses makes. Ulysses’ decision problem is represented in tree (or extensive) form in  Figure 1  (where the two boxes represent choice points for Ulysses).