Question

This morning, Odysseus can choose to sail toward the island of the Sirens (T) or away from it (A). If he sails away, then there is no further choice to be made and his payoffs are (0,0), where the first number is how he values the outcome now, and the second number is how he will value the outcome this afternoon. If he chooses T this morning, he will be near the island this afternoon and will hear the siren song. At that point, he will choose whether to sail past (P) the island safely or sail toward (T) the island, dashing the ship into the rocks. The payoffs are (10,10) if he sails past and (-10,20) if he dashes the ship into the rocks, where again the first number in each pair is how he values the outcome this morning, and the second is how he will value it this afternoon.

1. Write down the extensive form of this game. What action does Odysseus take this morning if he uses backward induction to make his decision? Explain.

2. Now add a new stage at the beginning of the game in which Odysseus decides whether or not to have his crew commit to lashing him to the mast (and plugging their ears) this afternoon. If he is lashed to the mast, he is rendered unable to select (T) in the afternoon. Otherwise the game is as above. Write down the extensive form of this new game and solve it by backward induction. Explain

Answer 1