Econ 402 Fall 2016 Assignment 2 Based On Lecture 3amp 4 Due Wednesday 9 14 201

1 Each student has to submit their own solution. You can discuss the problem set with other students.

c) Derive the Nash equilibrium prices in the game played between the managers of the two divisions. What are the corresponding quantities and profits?

Question 3 – Revisiting Hotelling’s Model (4 pt) Two political parties, Left wing and Right wing compete in electoral elections. There is a continuum of voters uniformly distributed on the interval [0, 1] where 0 represents the leftmost view (extreme left) and 1 the rightmost. Each party can declare that their view is x where 1 ≥ ???? ≥ ???? and each voter votes to the party that declare that their views are closest to his views. For example, if a voter’s view is represented by 0.3, the left party chose 1/4 and the right party chose 1/2, this voter votes for the left party as 1/4 is closer to 0.3. If both parties choose the same spots they will split the votes between them. Each party’s objective is to have the highest percentage of voters voting for it. i) Describe the normal form of the game (players, strategies, payoffs). ii) Solve the game using (pure strategy) Nash equilibrium.

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