Local stability and convergence factors of nonlinear duopoly games with different types of players

This study examines nonlinear duopoly games in the context of diseconomies of scale. The firms involved exhibit varied levels of rationality and can be classified as rational, boundedly rational, local monopoly approximation (LMA), or adaptive players. Using a systematic approach based on symbolic computation, we conduct a comprehensive analysis of the stability of these models. The results indicate that the equilibrium of these models is locally stable for all possible parameter values. We also compare the convergence factors of some models, which characterize the convergence speed of trajectories around the equilibrium. Insightfully, we find that for a heterogeneous duopoly market with one boundedly rational firm and one LMA firm, the convergence speed is determined by the efficiency-dominant (lower-cost) firm, regardless of whether the returns to scale are assumed to be decreasing or constant.