Equilibria in a Hotelling Model: First-Mover Advantage?

Abstract

We consider the presence of first-mover advantage or disadvantage in a duopoly model of product positioning in which firms are symmetric, except for order of entry. We study a generalization of the Hotelling model, in which a consumer's utility from a product depends on the location of product and consumer in product attribute space, a random utility term that captures idiosyncratic preferences, and the price of the product. Since the model is analytically intractable, we computationally study location equilibria, with prices decided simultaneously after locations have been chosen.

We analyze the equilibrium outcomes based on the sensitivity of a firm's profit to prices and locations. A first-mover advantage obtains when profits are highly sensitive to location but only moderately sensitive to price. In contrast, when the location sensitivity is low, a moderate price sensitivity results in a first-mover disadvantage. High price sensitivity leads to maximum differentiation in product attributes. Finally, low sensitivity to both price and location has both firms locating at the market center.

Keywords: Hotelling model, multinomial logit, first-mover advantage

JEL Classification: L11, D43, L13