Abstract
The aim of this paper is to analyze a classical duopoly model introduced by Puu in 1991 when lower bounds for productions are added to the model. In particular, we prove that the complexity of the modified model is smaller than or equal to the complexity of the seminal one by comparing their topological entropies. We also discuss whether the dynamical complexity of the new model is physically observable.
Highlights
In this paper we study a model which is a modification of the well-known duopoly model introduced by Puu as follows
The second one, which will be analyzed in the subsection, is to study when such topological chaoticity can be observed in numerical simulations and we will show that, in all the examples we have considered, it never appears
We analyze the dynamics of the model from three points of view, topological, physical, and numerical
Summary
In this paper we study a model which is a modification of the well-known duopoly model introduced by Puu as follows (see [1]). Where qi, i = 1, 2, are the outputs of each firm and p is the price and ci, i = 1, 2, are the constant marginal costs. Under these assumptions, we see that both firms maximize their profits, given by Πi = qi/(q1 + q2) − ciqi, i = 1, 2, if q1. Any reasonable production cost function increases with output; so producing nothing is the best choice for lowering costs. We propose a new model which keeps the idea of a minimal firm production as follows: fc1,ε max {√. We will introduce notion of topological entropy that we will use to analyze it and, we will show the result of our analysis for this model
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