<p>Hotelling’s Continuous Model: Consider Hotelling’s model, in which citizens are a continuum of voters on the interval <span class="math-container">$A = [−a, a]$</span>, with uniform
distribution <span class="math-container">$U (a)$</span>.</p>

<p>Show that for a general distribution <span class="math-container">$F (\cdot )$</span> over <span class="math-container">$[−a, a]$</span> the unique Nash
equilibrium is where each candidate chooses the policy associated with
the median voter.</p>

<p>I know that the median is <span class="math-container">$a^m=0$</span> but I don't understand what does a general distribution mean and what does "associated with median voter" means exactly. If somebody could clarify what this exercise asks me to do that would be great!</p>

<game-theory>
Hotelling’s Continuous Model - game theory
Slim Shady
# Hotelling’s Continuous Model - game theory

(Asked by: username_0 on 2020-05-08)

Hotelling’s Continuous Model: Consider Hotelling’s model, in which citizens are a continuum of voters on the interval $A = [−a, a]$, with uniform
distribution $U (a)$.

Show that for a general distribution $F (\cdot )$ over $[−a, a]$ the unique Nash
equilibrium is where each candidate chooses the policy associated with
the median voter.

I know that the median is $a^m=0$ but I don't understand what does a general distribution mean and what does "associated with median voter" means exactly. If somebody could clarify what this exercise asks me to do that would be great!

**Tags:** game-theory

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## 0 answers

