A special learning process with time delay (Q2915555)

A special learning process in classical Cournot oligopolies is revisited; it has been introduced in [\textit{F. Szidarovszky} and \textit{J. B. Krawczyk}, PU.M.A., Pure Math. Appl. 15, No. 4, 453--468 (2004; Zbl 1136.91525)], and further examined in [\textit{G. I. Bischi} et al., Nonlinear oligopolies. Stability and bifurcations. Berlin: Springer (2010; Zbl 1182.91001)]. Without information delay, the system is always asymptotically stable showing that the beliefs of the firms about the price function converge to the true function as time goes to infinity. This stability however might be lost in the presence of fixed delay. The authors present a complete stability analysis of the delay model. They also discuss stability switches and the appearance of Hopf bifurcation. Conclusions, economic interpretations of the results, and further research directions are outlined in the final section.