Nonlinear Cournot oligopoly games with isoelastic demand function: The effects of different behavior rules

The analysis of asymptotical convergence for the oligopoly game has always been important to characterize the firms’ long-term behavior. In the nonlinear oligopoly competition possibly involving chaotic fluctuations, non-convergent trajectories are particularly undesirable since the resulting behavior will become unpredictable. In this paper, consistent with a traditional assumption that the firms update their outputs simultaneously, we at first construct an adjustment process and discuss the convergence to the equilibrium for a nonlinear Cournot duopoly game with the isoelastic demand function. We indicate that the tendency to instability does rise with the number of firms and the adjustment speeds. In particular, we alter this assumption from simultaneous decisions to sequential decisions so that the latter firms are able to observe the former ones at every time periods. We finally arrive at a conclusion that the unique equilibrium is convergent as long as the adjustment speeds are less than a fixed threshold, no matter what the number of the firms. Our findings show that the firms with sequential decisions can achieve the equilibrium more easily.