Equilibrium in the Canonical Stackelberg Triopoly via Response Functions and Fixed Point Theory
Functional Analysis
2026-04-30 v1
Abstract
We analyze a canonical extension of the Stackelberg duopoly to a sequential framework, where each firm strategically anticipates the reactions of all subsequent players. In a triopoly (three-firm) settings, we obtain existence and uniqueness of market equilibrium via a reformulation of the equilibrium conditions that draws on coupled fixed-point theory. Even with linear demand, convergence of myopic best-response dynamics is not guaranteed. A recursive equilibrium formulation enables the analysis of the limiting case as the number of participants grow.
Keywords
Cite
@article{arxiv.2604.26487,
title = {Equilibrium in the Canonical Stackelberg Triopoly via Response Functions and Fixed Point Theory},
author = {Anton Badev and Martin Pavlov and Boyan Zlatanov},
journal= {arXiv preprint arXiv:2604.26487},
year = {2026}
}