Dynamical analysis of a delayed monopoly game with a log-concave demand function

A delay monopoly game with bounded rationality is considered where the inverse demand function is a log-concave function. The stability/instability of the game when dynamics was driven by the gradient process is studied. We investigate delay effects on dynamics and demonstrate the stability switches from stability to instability. We find that the delay monopoly equilibrium undergoes a period-doubling bifurcation or Neimark–Sacker bifurcation when the parameters combinations cross the stability-switch curve.