Equilibria in a Hotelling Model: First-Mover Advantage?

Abstract

We study a generalized Hotelling duopoly in which a consumer's net 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. Our model allows us to vary the relative impact of product attribute preferences (i.e., location) and idiosyncratic preferences on consumer utility. Since the model is analytically intractable, we computationally study equilibria under both simultaneous location and sequential location by the two .rms, with prices decided simultaneously after locations have been chosen. In our numerical analysis, the simultaneous game admits only symmetric equilibria. If product attribute preferences are weak (i.e., distance costs are unimportant) and idiosyncratic preferences are also weak, both .rms locate in the interior of the feasible location space. With strong product attribute preferences and weak idiosyncratic preferences, price competition is at its most intense, leading to maximal di.erentiation. As idiosyncratic preferences become more important, price competition is mitigated, leading to both .rms locating at the market center. In the sequential game, we .nd that when product attribute preferences are strong and idiosyncratic preferences are weak, the follower has a strong desire to avoid price competition and the leader experiences a .rst-mover advantage. However, if idiosyncratic preferences are also strong, price competition is somewhat weaker, and the leader cedes a location and pro.t advantage to the follower. If product attribute preferences and idiosyncratic preferences are both weak, maximal di.erentiation results, and entry order is irrelevant. Finally, when idiosyncratic preferences dominate, price competition is a non-issue, and both players locate at the market center. Once again, the order of entry does not matter.