Abstract
In this paper, we consider the nonlinear discrete-time dynamic model proposed by Bischi and Baiardi (Chaos Solitons Fractals 79:145-156, 2015a). The model considers players with adaptive adjustment mechanisms towards the best reply and a form of inertia in adopting such mechanism. Moreover, we formulate an extension of the original model, where endogenous market size is considered. Through numerical simulations, we show that multiple attractors may exist in the presence of homogeneous agents and the emergence of non-synchronized trajectories both in the short (on-off intermittency) and long (global riddling) run. Therefore, the article highlights that strategic contexts exist in which the players’ knowledge of the market and the adoption of the best reply do not always allow the use of the representative agent’s rhetoric to describe the dynamics of the model.
Highlights
In recent years the economic theory has become increasingly interested in the study of contexts characterized by the presence of heterogeneous agents both in the macroeconomic, microeconomic, and financial spheres
3 The problems of synchronization and chaotic synchronization In Bischi and Baiardi (2015a) the authors complement the analysis provided in Farris et al (2005) stressing the dynamic consequences of heterogeneities highlighting the way in which non-identical players, whose behaviors are characterized by different effectiveness and inertia parameters, influence the equilibrium points, their stability and bifurcations, as well as the global dynamic scenarios of the model
We considered the map proposed by Bischi and Baiardi (2015a), which is based on the market share attraction model considered in Farris et al (2005)
Summary
In recent years the economic theory has become increasingly interested in the study of contexts characterized by the presence of heterogeneous agents both in the macroeconomic, microeconomic, and financial spheres. We aim to show two main issues: (i) even in the presence of homogeneous agents, non-synchronized and complex behaviors can be observed due to the presence of multiple equilibria, and (ii) a low degree of heterogeneity may significantly affect the dynamics of the model among players due to existence of non-topological (Milnor) attractors. This last point shows that using the rhetoric of the representative agent to describe marketing dynamics may be misleading.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
