CS 285 Fall 2010 –

1. (45 points) Big monkey (M ) and little monkey (m) live happily in the jungle, but they are often hungry. Both monkeys eat the fruit of a particular tree, which grows high above the ground. They both have two actions: “bang on tree” (B) and “climb to obtain the fruit” (C). Being more senior, big monkey gets to act first. Banging on the tree by big monkey yields 0.6 probability for the fruit to come down, but only 0.2 probability when performed by little monkey. However, big monkey requires 10 Kcal to bang on the tree, while little monkey need spend only 4 Kcal. Climbing up on the tree is certain to deliver the fruit, but costs 60 and 50 Kcal for the two monkeys, respectively. Also, if a fruit drops on the ground from banging on the tree, big monkey eats 60% of the fruit and little monkey eats 40%, but, when obtained through climbing, the monkey that got it eats 90% of it. If both monkeys choose to bang on the tree and the fruit does not come down, big monkey gets angry and can choose to punish little monkey for being lazy, which induces a cost of 10 Kcal to the former and 100 Kcal to the latter. Each fruit gives 80 Kcal to both monkeys and there is just one fruit on the tree.