Stackelberg Independence*

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.

Optimal sequential contests

“…Admati and Perry (1991) and Bonatti and Hörner (2011) showed similar 2 Daughety (1990) used such a model to show that an oligopoly where players are divided between two periods is more concentrated but also closer to competitive equilibrium than an oligopoly where all players move at once. Hinnosaar (2021) provides a literature review and shows that the linear oligopoly model has unique properties that fail when the demand is not linear. 3 Recently, Ely, Georgiadis, Khorasani, and Rayo (2022) studied feedback design in a continuous-time model where the designer wants to prolong participation for as long as possible and contestants do not observe their successes.…”

“…22 Daughety (1990) used such a model to show that an oligopoly where players are divided between two periods is more concentrated but also closer to competitive equilibrium than an oligopoly where all players move at once. Hinnosaar (2021) provides a literature review and shows that the linear oligopoly model has unique properties that fail when the demand is not linear. …”