Price Equilibria in a Spatial Competition with Captive Buyers

TL;DR

This paper analyzes how captive buyers influence price equilibria in a spatial competition model with linear transportation costs and uniformly distributed informed consumers, extending Nakagawa's framework.

Contribution

It introduces a model with uniform informed consumers and linear transportation costs, classifies equilibrium types, and examines the effects of captive buyers on spatial competition.

Findings

No pure equilibrium exists in certain parameter regions.

Mixed strategy equilibria are characterized in those regions.

Captive buyers significantly impact the nature of price competition.

Abstract

This paper explores price competition with exogenous product differentiation in a spatial model similar to that of Nakagawa (2023). Nakagawa examines product differentiation within the framework of Varian (1980). Nakagawa integrates Varian's concept of uninformed consumers, who lack complete price information, into a spatial model based on Hotelling (1929). While Nakagawa placed informed consumers at the center of the Hotelling line and used quadratic transportation costs, our study employs a uniform distribution of informed consumers and linear transportation costs. This approach enables a more direct comparison with established spatial competition literature, particularly Osborne and Pitchik (1987). We classify equilibrium candidates and characterize the parameter regions corresponding to each equilibrium. There is no pure equilibrium in the region where we construct mixed strategy equilibria. Furthermore, we compare the expected profit in the equilibrium of our model with the findings of Osborne and Pitchik (1987). Finally, we discuss the impact of captive buyers on the nature of spatial competition.