A big monkey and a small monkey eat coconuts which dangle high above the ground
ID: 1147395 • Letter: A
Question
A big monkey and a small monkey eat coconuts which dangle high above the ground on a coconut palm. One of them (at least) must climb the tree to shake a coconut fruit down. Then both can eat it. The one who does not climb has a head start in eating the fruit. If big monkey climbs the tree he incurs an energy cost of 2 kilocalories (Kc). Small monkey, being so small, does not incur any energy cost from climbing the tree. Suppose that one coconut can supply 10 Kc of energy and is divided between the two monkeys as follows: 2. Big monkey eats Small monkey eats 6 Kc 8 Kc 7 Kc 4 Kc 2 Kc 3 Kc If only big monkey climbs If only small monkey climbs If both monkeys climb Assuming decisions are made simultaneously and payoffs are net of energy costs, write this game in normal form being clear to state the players, strategies and payoffs. Does either player have a dominant strategy in this game? A weakly dominant strategy? Explain why or why not. What is/are the Nash equilibrium/equilibria of this game? After eating coconuts, small monkey gets larger and also incurs an energy cost of 2Kc for climbing the tree, just as big monkey does. Assuming the division of fruit remains unchanged as in the table above, redo parts a-c. a. b. c. d.Explanation / Answer
a. The game is played between the big monkey and the small monkey of climbing the tree to shake it off so that they may eat the fruit. If big monkey climbs the energy cost is 2 kc while small monkey doesn't incure any energy cost. one coconut supply 10kc of energy. From the table we can see that the more number of energy is consumed by the big monkey. The advantage is clearly seen in the case of big monkey.
b. In second statement, big monkey had a dominant strategy since it loses only 2-4 energy in each case.
The weak strategy is for small monkey irrespective of the fact that it is small in size and doesn't incure any energy cost for climbing the tree. It get a small energy supply after dividing among the both.
c. The Nash equilibrium of this game is it is especially helpful in two players game. Here both have different strategies. In this case formal analysis may become too long. This rule is not applicable where two players have different strategies. Here it dwpend on the action of climbing the tree who would be dominant first.
d. As per the given sitution the small monkey gets larger
In that case the situation would change
a. The energy would be lost of 2 kc on climbing the tree and it will have a disadvantage.
b. The small monkey will be in loss by already having least energy consumption and lost by climbing up the tree.
c. The Nash game will be in the a situation of interest of the players.
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