On local stability of Cournot models with simultaneous and sequential decisions

In this paper, two classes of discrete myopic adjustment dynamics are mainly considered under some fairly general and reasonable assumptions in an oligopolistic industry where all firms produce a homogeneous product. Hosomatsu’s lemma is firstly generalized in the sense that a necessary and sufficient condition for stability in a variety of discrete systems is derived for a much larger range of the parameter setting. By virtue of this key finding, asymptotical stability under one Cournot adjustment dynamic follows immediately, where all firms update their outputs simultaneously at each period. However, if adjustment-decisions are made sequentially so that the latter firms are able to recognize newly-adjusted outputs of the former in each period, it turns out that this revised dynamic is “more stable”. That is, under sequential decision the convergence to equilibrium behavior can be achieved more easily.

► We generalize Hosomatsu’s lemma.
► We provide stability conditions for two dynamic models.
► We show sequential decision acts as a stabilizing factor.