Dynamics of a Duopoly Game with Heterogeneous Players and Time Delay

Abstract: In this work, the dynamics of a duopoly game with two heterogeneous players and time delay is investigated. It is assumed that one player adopts adaptive adjustment method and another considers time delay for marginal profit. A nonlinear dynamics is built and theoretical and numerical stability analysis is done for it. It is shown that time delay plays an important role in the system stability, an intermediate delayed rationality can delay the occurrence of complicated behaviors, and an intermediate delay can promote the system stability. The numerical simulations show that the system may lose stability through a period-doubling bifurcation or a Neimark-Sacker bifurcation.