Big Panda (BP) and Little Panda (LP) live on a deserted island in the South Pacific. Their food is the warifruit which grows only from the highest branches of the waritree. To get the fruit, one of the pandas must climb all the way up the tree, creep out on the precarious branch and shake vigorously until the fruit drops. Measurements show that a warifruit is worth 10 kilocalories (Kc) of energy. The cost to BP of climbing the tree is 2 Kc but is negligible (meaning 0 Kc) for LP. If both pandas climb the tree to get the fruit, BP takes most of the fruit and gets 7 Kc leaving LP only 3 Kc of fruit. If only LP climbs the tree, BP has eaten 9 Kc of the fruit by the time LP gets back down leaving him only 1 Kc. If BP climbs the tree, LP gets to eat 4 Kc of fruit before BP can climb down and get the other 6 Kc of fruit. If no pandas climb the tree, then they do not get the fruit, and both get 0 Kc.
(a) Assume BP decides first whether to climb the tree. LP observes this decision and then gets to choose. Draw the game tree for this sequential-move game.
(b) Find the rollback equilibrium. What is the rollback equilibrium outcome?