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(a) Solve for person i's expected resource payout as a function of the probability that she encounters someone altruistic, PA. Do this twice: once when i is altruistic and once when i is selfish. (b) Graph your solutions from above. Is there a stable equilibrium outcome? If so, what is it?

(a) Solve for person i's expected resource payout as a function of the probability that she encounters someone altruistic, PA. Do this twice: once when i is altruistic and once when i is selfish. (b) Graph your solutions from above. Is there a stable equilibrium outcome? If so, what is it?

Principles of Microeconomics
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 6PA
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2. How might altruistic behavior come about? Consider the following simple game: • There are two types of people: altruistic (A) and selfish (S). "Luck" randomly assigns people either 10 or 0 units worth of productive resources (e.g., some people are born into a rich family and others into a poor family). So, for any random encounter between two people, one person has 10 resources and the other has 0 Altruistic individuals always volunteer half of their resources with the other person if the latter has zero. Altruist people never fight Selfish people never volunteer half of their resources with the other person if the latter has zero • When two selfish people encounter one another they will always fight, as the one with zero will demand half of what the one with 10 has (who refuses to share). Fighting costs each 3 units of resources The game can be summarized as follows, where the #s w/i each cell summarize the average payout that a particular player would receive given their role in that particular scenario. i A A (i=5, j = 5) S (i= 7.5, j = 2.5) Using a framework similar to the "Hawks v. following: S (i = 2.5, j = 7.5) (i=2,j=2) Doves" example in class, please do the (a) Solve for person i's expected resource payout as a function of the probability that she encounters someone altruistic, PA. Do this twice: once when i is altruistic and once when i is selfish. (b) Graph your solutions from above. Is there a stable equilibrium outcome? If so, what is it?
Transcribed Image Text:2. How might altruistic behavior come about? Consider the following simple game: • There are two types of people: altruistic (A) and selfish (S). "Luck" randomly assigns people either 10 or 0 units worth of productive resources (e.g., some people are born into a rich family and others into a poor family). So, for any random encounter between two people, one person has 10 resources and the other has 0 Altruistic individuals always volunteer half of their resources with the other person if the latter has zero. Altruist people never fight Selfish people never volunteer half of their resources with the other person if the latter has zero • When two selfish people encounter one another they will always fight, as the one with zero will demand half of what the one with 10 has (who refuses to share). Fighting costs each 3 units of resources The game can be summarized as follows, where the #s w/i each cell summarize the average payout that a particular player would receive given their role in that particular scenario. i A A (i=5, j = 5) S (i= 7.5, j = 2.5) Using a framework similar to the "Hawks v. following: S (i = 2.5, j = 7.5) (i=2,j=2) Doves" example in class, please do the (a) Solve for person i's expected resource payout as a function of the probability that she encounters someone altruistic, PA. Do this twice: once when i is altruistic and once when i is selfish. (b) Graph your solutions from above. Is there a stable equilibrium outcome? If so, what is it?
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