TY - JOUR
T1 - A multiscale time model with piecewise constant argument for a boundedly rational monopolist
AU - Cavalli, Fausto
AU - Naimzada, A.
PY - 2016
Y1 - 2016
N2 - We present a dynamic model for a boundedly rational monopolist who, in a partially known environment, follows a rule-of-thumb learning process. We assume that the production activity is continuously carried out and that the costly learning activity only occurs periodically at discrete time periods, so that the resulting dynamical model consists of a piecewise constant argument differential equation. Considering general demand, cost and agent’s reactivity functions, we show that the behavior of the differential model is governed by a nonlinear discrete difference equation. Differently from the classical model with smooth argument, unstable, complex dynamics can arise. The main novelty consists in showing that the occurrence of such dynamics is caused by the presence of multiple (discrete and continuous) time scales and depends on size of the time interval between two consecutive learning processes, in addition to the agent’s reactivity and the sensitivity of the marginal profit.
AB - We present a dynamic model for a boundedly rational monopolist who, in a partially known environment, follows a rule-of-thumb learning process. We assume that the production activity is continuously carried out and that the costly learning activity only occurs periodically at discrete time periods, so that the resulting dynamical model consists of a piecewise constant argument differential equation. Considering general demand, cost and agent’s reactivity functions, we show that the behavior of the differential model is governed by a nonlinear discrete difference equation. Differently from the classical model with smooth argument, unstable, complex dynamics can arise. The main novelty consists in showing that the occurrence of such dynamics is caused by the presence of multiple (discrete and continuous) time scales and depends on size of the time interval between two consecutive learning processes, in addition to the agent’s reactivity and the sensitivity of the marginal profit.
KW - Boundedly rational monopolist
KW - bifurcation
KW - multiscale
KW - nonlinear difference equation
KW - piecewise continuous differential equations
KW - stability
KW - Boundedly rational monopolist
KW - bifurcation
KW - multiscale
KW - nonlinear difference equation
KW - piecewise continuous differential equations
KW - stability
UR - http://hdl.handle.net/10807/85358
U2 - 10.1080/10236198.2016.1202940
DO - 10.1080/10236198.2016.1202940
M3 - Article
SN - 1023-6198
SP - 1
EP - 10
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
ER -