English

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}
}