Equilibrium in Hotelling's Model of Spatial Competition

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Abstract
Using a partly analytical, partly computational approach we find and study a mixed strategy equilibrium in Hotelling's model of spatial competition (in which each of two firms chooses a location in a line segment, and a price). In the equilibrium we find, the firms randomize only over prices. They choose locations close to the quartiles of the market. The support of the equilibrium price strategy of each firm is the union of two short iintervals, and has an atom of approximate size 0.73 at the highest price. The equilibrium can be interpreted as one in which firms charge a relatively high price most of the time, and occaisionally hold a "sale".
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