Discrete and continuous dynamics in nonlinear monopolies

A continuous time Cournot duopoly with delays

“…With regard to the issue of the functioning of markets with time-to-build technology, we recall the work of Matsumoto and Szidarovszky (2012) that studies a monopoly with bounded rationality. In order to include also problems related to the difficulty of adjusting production over time, we consider the modelling approach proposed by Berezowski (2001) and introduced in the economic literature by Matsumoto and Szidarovszky (2014). Specifically, we assume the existence of a friction in the production process so that the adjustment of quantities chosen by firm i at time t − τ i for time t is not perfectly achieved but it is subject to a feedback that acts in the opposite direction with respect to the instantaneous change in the quantity produced at the time t, that isẋ(t).…”

“…The starting point of the present paper, therefore, is the discrete time repeated Cournot duopoly of Bischi et al (1998), with the aim of studying it in continuous time with discrete delays. To this end, in this work we use the method proposed by Berezowski (2001) -and adopted by Matsumoto and Szidarovszky (2014) in the economic literature to describe complex dynamics in a monopoly market -by introducing a form of inertia to capture in a more realistic way the existence of frictions in the production process. The paper provides some findings about local and global bifurcations and chaotic dynamics that cannot be observed in both discrete time models and continuous time models without discrete delays.…”

On periodic and chaotic behavior in a two-dimensional monopoly model

“…Naimzada and Ricchiuti [10] propose to use a demand function (1) without inflection point to achieve a onedimensional map. Their model was generalized by Askar [9] and further by Matsumoto and Szidarovszky [8]. In these models the chaotic dynamic arises via a cascade of period-doubling bifurcations.…”

“…Most of the recent literature deals with simplified versions of the Puu model (8), cf. [8][9][10][11], and none of them analyzes the dynamic behavior of the Puu model in detail. Naimzada and Ricchiuti [10] propose to use a demand function (1) without inflection point to achieve a onedimensional map.…”

“…Puu [7,3] provides incomplete information on the existence of cycles of period 4 and the chaotic behavior of (8). Most of the recent literature deals with simplified versions of the Puu model (8), cf.…”