Abstract: firms are bounded rationally in the market.So they make production decisions not only based on the marginal profit of current period but on the marginal profits of many continuous periods.The paper studies the influence of the delay on the system and finds that the stable region of Nash equilibrium is enlarged,which offers a realistic way to realize the control of the period doubling bifurcations.Meanwhile,when two parameters,adjusting speed and weighted factor,satisfy certain conditions,other complicated dynamical behaviors such as Hopf bifurcation will occur at the Nash equilibrium.Delayed decision rule can improve the system performance and has great influence on the market competition.

Key words: production decision, chaos, period doubling bifurcation, Hopf bifurcation