# Hotelling-Downs Model with Multiple Parties – Consider the Hotelling-Downs model with four parties

November 24, 2016

2. Hotelling-Downs Model with Multiple Parties (30pts)

Consider the Hotelling-Downs model with four parties (A, B, C, and D) contending in the election. All parties are o?ce-seeking and maximize their own probabilities of winning the election. Suppose that the votersâ€™ ideal policies are distributed uniformly over the interval [0, 1]. Answer the questions on the following pages.

(1) Is the action pro?le where parties A and B choose the policy platform 1/4 and parties C and D choose the policy platform 3/4 a Nash equilibrium? Explain your answer. (15pts)

(2) Is the action pro?le where parties A and B choose the policy platform 1/3 and parties C and D choose the policy platform 2/3 a Nash equilibrium? Explain your answer. (15pts)

*Please explain in detail with logical steps. Will not give the press the accept button without concrete explanation*

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