Question 4 A village has two villagers with an income of 200 each. The village decides...

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Question 4 A village has two villagers with an income of £200 each. The village decides to take contributions to build a new commons. The commons can be of any size, and generates By utility for each of the villagers if the total contribution is y, where is a strictly positive real number. Contributions are also real numbers, bounded between 0 and 200. If villager 1 contributes ₁ and villager 2 contributes £2, then villager i's utility is 200 - x + ß (x₁ + x2). (a) What are the pure strategy Nash equilibria for each value of 3? [2 marks] (b) The mayor, an LSE trained economist who only values the total utility of the villagers, decides that she will only build the commons if total contributions exceed 80. That is, if x₁ + x2 < 80, then citizen i gets utility of 200- xi, and if x₁ + x2 ≥ 80, she gets 200-xi+ß (x₁ + x2). What is the logic behind the mayor's change? For what values of 3 would you expect an improvement from the change? Explain and justify your answers with game theoretic reasoning. [3 marks] Question 4 A village has two villagers with an income of £200 each. The village decides to take contributions to build a new commons. The commons can be of any size, and generates By utility for each of the villagers if the total contribution is y, where is a strictly positive real number. Contributions are also real numbers, bounded between 0 and 200. If villager 1 contributes ₁ and villager 2 contributes £2, then villager i's utility is 200 - x + ß (x₁ + x2). (a) What are the pure strategy Nash equilibria for each value of 3? [2 marks] (b) The mayor, an LSE trained economist who only values the total utility of the villagers, decides that she will only build the commons if total contributions exceed 80. That is, if x₁ + x2 < 80, then citizen i gets utility of 200- xi, and if x₁ + x2 ≥ 80, she gets 200-xi+ß (x₁ + x2). What is the logic behind the mayor's change? For what values of 3 would you expect an improvement from the change? Explain and justify your answers with game theoretic reasoning. [3 marks]

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a To find the pure strategy Nash equilibria we need to analyze the best response of each villager given the others contribution Lets consider the poss... View the full answer