Structural Analysis of Oligopoly Equilibria Based on Triangular Decomposition and Cylindrical Algebraic Decomposition

Huang, Bo and Li, Xiaoliang and Zhang, Ally Quan (2025) Structural Analysis of Oligopoly Equilibria Based on Triangular Decomposition and Cylindrical Algebraic Decomposition. In: Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation (ISSAC 2025) :. Association for Computing Machinery (ACM), New York. (In Press)

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Abstract

In this paper, we propose a novel symbolic computation algorithm for structural analysis of equilibrium outcomes of oligopoly games. Our approach does not require explicit solutions of demand and price functions or closed-form solutions of the first-order conditions. By leveraging the triangular decomposition, resultant, and cylindrical algebraic decomposition methods}, we efficiently address nonlinearities in demand systems, thereby extending the applicability of the backward induction method to a broader class of economic models. The algorithm enables automated, accurate comparisons across different competition frameworks, overcoming computational barriers posed by traditional methods.