In a certain town, 5 people are preparing for dinner. Each person decides for themselves whether they will have vegetable soup or a slice of apple strudel. The apple strudel can only be made if they gather apples, which are located in a hard-to-reach area full of walnut trees. Assume that at least three residents are needed to gather the apples. Each person can gather vegetables for soup themselves, as they are located in a garden that each resident has in front of their house. Additionally, assume that only those who participated in gathering the apples evenly distribute the apple strudel. (a) Find all pure Nash equilibria if each resident prefers 1/5 of an apple strudel to vegetable soup. (b) Find all pure Nash equilibria if each resident prefers 1/4 of an apple strudel to vegetable soup, but prefers vegetable soup to 1/5 of an apple strudel.
In a certain town, 5 people are preparing for dinner. Each person decides for themselves whether they will have vegetable soup or a slice of apple strudel. The apple strudel can only be made if they gather apples, which are located in a hard-to-reach area full of walnut trees. Assume that at least three residents are needed to gather the apples. Each person can gather vegetables for soup themselves, as they are located in a garden that each resident has in front of their house. Additionally, assume that only those who participated in gathering the apples evenly distribute the apple strudel.
(a) Find all pure Nash equilibria if each resident prefers 1/5 of an apple strudel to vegetable soup.
(b) Find all pure Nash equilibria if each resident prefers 1/4 of an apple strudel to vegetable soup, but prefers vegetable soup to 1/5 of an apple strudel.
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