Decision Trees: Homework
Mathematics 170
due November 12, 2004
1. Mathematics and Politics, pg. 17, problem 1.
2. Suppose you are trying to explain the optimal strategy for bidding in
the dollar auction with stakes s= 3, assuming that both players use the
conservative convention. You point out that if the bankroll is b= 3,
then the optimal strategy is to bid 1 and the other player will pass;
however if the bankroll is b= 4, the optimal strategy is different (see
problem 1 above).
Your listener does not understand the difference. “Surely,” says he,
“if the optimal strategy involves never actually going past 3, then the
bankroll doesnt affect the outcome.” Explain to him why this is not
the case, without using the decision tree (he gets lost in the symbols)
or O’Neill’s Theorem (he doesn’t trust this O’Neill character anyway).
In other words, just explain in plain English where the distinction
arises.
3. Mathematics and Politics, pg. 18, problem 4a. (The notation is defined
in the middle of page 18, and refers to the definitions on the bottom of
17 and top of 18.)
4. Suppose you are playing the dollar auction with stakes s= 3. Your
bankroll is b= 3; however, player twos bankroll is b= 4. In other
words, you can bid at most 3 but player two can bid up to 4. Draw the
decision tree. What is your optimal strategy?
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