# Horizontal Product Differentiation in Varian's Model of Sales

## TL;DR

This paper extends Varian's sales model by explicitly including firms' location choices in a Hotelling spatial competition framework, revealing symmetric mixed strategy equilibria and the persistence of monopoly profit levels despite product differentiation.

## Contribution

It introduces a spatial competition model with explicit location choices in Varian's framework, demonstrating equilibrium existence and profit equivalence to monopoly outcomes.

## Key findings

- Existence of symmetric mixed strategy equilibria.
- Equilibrium involves randomized location and pricing strategies.
- Expected profits match maximum monopoly profits.

## Abstract

We consider the explicit introduction of firms' choice of location to Varian's model of sales for a two-stage spatial competition model based on a standard Hotelling's linear city model. This model is the formalization of Varian's model of sales in the context of Hotelling's spatial competition. We obtain three main results. First, we show that there exists a subgame perfect equilibrium in which each firm chooses a symmetric mixed strategy equilibrium profile. This equilibrium includes symmetric location pairs and asymmetric location pairs. Second, the equilibrium behaviors in our model are randomized at both location and price stages. Third, we show that expected profits in a subgame perfect equilibrium are equal to the maximum monopoly profit from an uninformed market. Thus, even when product differentiation is explicitly introduced into a Varian-type model, Varian's implication can be retained; the opportunity for profit in an informed market is lost with competition.