# Stackelberg Independence

## TL;DR

This paper examines the conditions under which the Stackelberg quantity leadership model's independence property holds, showing it is fragile and often fails with realistic market complexities.

## Contribution

It identifies the precise assumptions needed for Stackelberg independence and demonstrates its failure under common market deviations.

## Key findings

- Stackelberg independence holds under linear demand and constant marginal costs.
- Small deviations from linear demand can eliminate the informativeness of leaders' actions.
- The property fails with non-linear demand, differentiated goods, and externalities.

## Abstract

The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. I show that under the standard assumptions, leaders' actions are informative about market conditions and independent of leaders' beliefs about the arrivals of followers. However, this Stackelberg independence property relies on all standard assumptions being satisfied. It fails to hold whenever the demand function is non-linear, marginal cost is not constant, goods are differentiated, firms are non-identical, or there are any externalities. I show that small deviations from the linear demand assumption may make the leaders' choices completely uninformative.