Analysis on the dynamics of a Cournot investment game with bounded rationality

In this work, a dynamic system of investment game played by two firms with bounded rationality is proposed. It is assumed that each firm in any period makes a strategy for investment and uses local knowledge to make investment strategy according to the marginal profit observed in the previous period. Theoretic work is done on the existence of equilibrium solutions, the instability of the boundary equilibriums and the stability conditions of the interior equilibrium. Numerical simulations are used to provide experimented evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium of the system can loose stability via flip bifurcation or Neimark-Sacher bifurcation and time-delayed feedback control can be used to stabilize the chaotic behaviors of the system.