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.

Required:
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?

Question

03-09-2021
Business

Answered

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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.

Required:
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?

Sagot :

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Answer & Explanation:

a. The game tree for this sequential-move game is as follows:

"The image is attached below"

Therefore, if Big Panda climbs the tree the cost for him will be 2kilocalories, thus his payoff will reduce by 2Kc.

Similarly, if Little Panda climbs the tree there will be cost of 0Kc for climbing the tree.

b. When the rollback equilibrium is used, then Little panda will choose not to climb the tree corresponding to Big Panda's strategy for climbing the tree.

That is the payoff will be as:

If BP climbs the tree the payoff cost will be 4Kc, 4Kc

If BP don't climbs the tree the payoff cost will be 9Kc, 1Kc

In this case Big panda will chosoe not to climb the tree.

Therefore the rollback equilibrium will be equal to 9Kc, and 1Kc.

Sagot :

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