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.