c.ass. Sup- 2. Consider the following sequential variant of the public goods game w pose that there are 2 consumers, 1 and 2. First consumer 1 chooses a quantity ₁ ≥ 0 to provide of the public good. After observing 1's choice, 2 chooses a quantity 2 ≥ 0 to provide. When the price of the public good is p, 1's payoff is u₁(1, 2) = a√√x₁ + x₂-p²₁ where a > 0 and 2's payoff is u₂(x₁, x2) = √√x1 + x2 − px2. (a) Suppose that a = 1. Show that this game has a Nash equilibrium in which 1 contributes a positive amount. Solution: There are many such Nash equilibria. One is for 1 to contribute and for 2 to contribute 0 regardless of how much 1 contributes.
c.ass. Sup- 2. Consider the following sequential variant of the public goods game w pose that there are 2 consumers, 1 and 2. First consumer 1 chooses a quantity ₁ ≥ 0 to provide of the public good. After observing 1's choice, 2 chooses a quantity 2 ≥ 0 to provide. When the price of the public good is p, 1's payoff is u₁(1, 2) = a√√x₁ + x₂-p²₁ where a > 0 and 2's payoff is u₂(x₁, x2) = √√x1 + x2 − px2. (a) Suppose that a = 1. Show that this game has a Nash equilibrium in which 1 contributes a positive amount. Solution: There are many such Nash equilibria. One is for 1 to contribute and for 2 to contribute 0 regardless of how much 1 contributes.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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