Rationalizable Behavior in the Hotelling Model with Waiting Costs

TL;DR

This paper analyzes the Hotelling model with waiting costs, demonstrating how rationalizability predicts firm locations in models lacking pure Nash equilibria, with results on convergence and interval shrinking.

Contribution

It introduces the use of point rationalizability to predict firm locations in Hotelling models without pure Nash equilibria, highlighting convergence and interval dynamics.

Findings

Point rationalizability predicts firm locations in asymmetric two-firm models.

In symmetric three-firm models, rationalizable choices form a shrinking interval.

Convergence towards the center occurs as firms become more efficient at handling queues.

Abstract

This paper revisits the Hotelling model with waiting costs Kohlberg (1983), focusing on two specific settings where pure Nash equilibria do not exist: the asymmetric model with two firms and the symmetric model with three firms. In the asymmetric two-firm model, we show that the weaker concept of point rationalizability has strong predictive power, as it selects exactly two locations for both firms. As the two firms become more similar in their efficiency in handling queues of consumers, the two point rationalizable locations converge towards the center of the line. In the symmetric three-firm model, the set of point rationalizable choices forms an interval. This interval is shrinking in the inefficiency levels of the firms in handling queues of consumers.