1 Part B: Written Q1. Games / Mini-Max: The Potato Game (14 pts) Aldo and Becca are playing the game below, where the left value of each node is the number of potatoes that Aldo gets, and the right...

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1 Part B: Written Q1. Games / Mini-Max: The Potato Game (14 pts) Aldo and Becca are playing the game below, where the left value of each node is the number of potatoes that Aldo gets, and the right value of each node is the number of potatoes that Becca gets (i.e. Aldo: left, Becca: right). Unlike prior scenarios where having more potatoes results in more utility, Becca and Aldo will have a more complex view of what makes a “good” distribution of potatoes. Becca will use the following thought process to decide which move to take:  Among all choices where she gets at least as many potatoes as Aldo, she’ll pick the one that maximizes Aldo’s number of potatoes (very nice!).  If there are no choices where she gets at least as many potatoes as Aldo, she’ll simply maximize her own potato count (ignoring Aldo’s value). Aldo will do the same thing, but substituting “he” for “she”, “her” for “his”, and “Becca” for “Aldo”. The rules above effectively tell us how Becca (and Aldo) rank the utility of any set of choices. i. (4 pts) Fill in the blanks below with the choice that each player would make at each stage. Assume that both Aldo and Becca are trying to maximize their own utility as described above. 2 ii. (4 pts) Assume that Aldo and Becca know that the sum at any leaf node is no more than 12. Cross out the edges to any nodes that can be pruned (if none can be pruned then write “no pruning possible” in above tree). iii. (4 pts) Suppose that Becca attempts to minimize Aldo’s utility instead of maximizing her own utility, and that Aldo knows this, and tries to maximize his own utility -- considering Becca’s strategy. Repeat part ii. There is no need to cross out edges that are pruned. iv. (2 pts) Suppose that Becca chooses uniformly randomly, and Aldo knows this and tries to maximize his own utility -- considering Becca’s strategy. Which move will Aldo make to maximize his expected utility, assuming he treats Becca as a chance node: left, middle, or right? If there is not enough information, pick “Not Enough Information”.  Left  Right  Middle  Not enough information