Monkey Business III

For those of you who haven't attempted Monkey Business and Monkey Business II , this is the 3rd question in the series.

Big Monkey (BM) and Little Monkey(LM) are both searching for food. After searching frantically, they finally stumble upon a banana tree. To their dismay, there is only ONE banana left on the tree. Herein lies the problem. To get to the fruit, one of them must climb the tree, and shake vigorously until the fruit is dislodged and falls to the ground below. For all its worth, each banana provides 10 kilocalories (Kc) of energy, but the penalty for running up and shaking the fruit loose costs 2 Kc. for BM and 0 Kc for LM. Moreover, if both of them climb the tree, shake the fruit loose, then climbs down and eat the fruit, BM gets 7Kc and LM gets 3Kc; if only BM climbs the tree, while LM waits below for the fruit to fall, BM gets 6Kc and LM gets 4 Kc.; if only LM climbs the tree, BM gets 9kc and LM gets 1 Kc. as most of the banana is gone by the time LM gets down to retrieve his share. What IF BM and SM choose simultaneously or equivalently, where each chooses an action without seeing what the other has chosen. Which of these statements are true?

A. Big Monkey's payoff is 4.5Kc

B. Small Monkey's payoff is 2Kc

C. The mixed strategy equilibrium is with probability of 0.5

D. All of the above

Assumptions: 1).Both choose at the same time 2). Monkeys are always energy maximizers. 3). Monkeys are aware of costs-benefits of their actions. 4). Monkeys are smart