Technology Sharing Cartels and Industrial Structure under a Rule of Thumb

We analyse the effect of learning by doing on firm performances when profit maximization follows a rule of thumb. Three regimes are compared: the technology sharing cartels, the oligopoly with spillovers, the proprietary regime. We show the dynamic implications on the industrial structure when firm production plan is revisited period by period.Oligopoly, Cartel, Industrial Structure, Learning, Dynamic Behaviour, Rule of Thumb

Controlling Chaos Through Local Knowledge

We propose an duopoly game where quantity-setting firms have incomplete information about the demand function. In each time step, they solve a profit maximization problem assuming a linear local approximation of the demand function. In particular, we construct an example using the well known duopoly Puu's model with isoelastic demand function and constant marginal costs. An explicit form of the dynamical system that describes the time evolution of the duopoly game with boundedly rational players is given. The main result is the global stability of the system.Cournot duopoly, incomplete information, isoelastic demand function, time evolution, boundedly rational players.

Double route to chaos in an heterogeneous triopoly game

We move from a triopoly game with heterogeneous players (E.M.Elabassy et al., 2009. Analysis of nonlinear triopoly game with heterogeneous players. Computers and Mathematics with Applications 57, 488-499). We remove the nonlinearity from the cost function and introduce it in the demand function. We also introduce a different decisional mechanism for one of the three competitors. A double route to complex dynamics is shown to exist, together with the possibility of multistability of different attractors, requiring a global analysis of the dynamical system.Triopoly game; Heterogeneous players; Global analysis

Strategic interactions and heterogeneity in a overlapping generations model with negative environmental externalities

We analyze an overlapping generations model where individuals’ welfare depends on the stock of a free access environmental good E and on the consumption C of a private good. We assume that the production process of the private good depletes the natural resource but that specific investments alleviate these damages. In such context, we show that strategic behaviour and heterogeneity in preferences may be a source of complex dynamics.Heterogeneous agents; environmental externalities; overlapping generations models.

multiple attractors and nonlinear dynamics in an overlapping generations model with environment

This paper develops a one-sector productive overlapping generations model with environment where a CES technology is assumed. Relying on numerical and geometrical approaches, various dynamic properties of the proposed model are explored: the existence of the phenomenon of multistability or the coexistence of different attractors was demonstrated. Finally, we describe a nontypical global bifurcation which determines the appearance of an attracting cycle

Endogenous Reactivity in a Dynamic Model of Consumer's Choice

We move from a boundedly rational consumer model (Naimzada and Tramontana, 2008, 2010) characterized by a gradient-like decisional process in which, under particular parameters conditions, the asymptotical convergence to the optimal choice does not happen but it does under a least squared learning mechanism. In the present paper, we prove that even a less sophisticated learning mechanism leads to convergence to the rational choice and also prove that convergence is ensured when both learning mechanisms are available. The stability results that we obtain give more strength to the rational behavior assumption of the original model; in fact, the less demanding is the learning mechanism ensuring convergence to the rational behavior, the higher is the probability that even quite naive consumers will learn the composition of their optimum consumption bundles

An evolutionary model with best response and imitative rules

We formulate an evolutionary oligopoly model where quantity setting players produce following either the static expectation best response or a performance-proportional imitation rule. The choice on how to behave is driven by an evolutionary selection mechanism according to which the rule that brought the highest performance attracts more followers. The model has a stationary state that represents a heterogeneous population where rational and imitative rules coexist and where players produce at the Cournot–Nash level. We find that the intensity of choice, a parameter representing the evolutionary propensity to switch to the most profitable rule, the cost of the best response implementation as well as the number of players have ambiguous roles in determining the stability property of the Cournot–Nash equilibrium. This marks important differences with most of the results from evolutionary models and oligopoly competitions. Such differences should be referred to the particular imitative behavior we consider in the present modeling setup. Moreover, the global analysis of the model reveals that the above-mentioned parameters introduce further elements of complexity, conditioning the convergence toward an inner attractor. In particular, even when the Cournot–Nash equilibrium loses its stability, outputs of players little differ from the Cournot–Nash level and most of the dynamics is due to wide variations of imitators’ relative fraction. This describes dynamic scenarios where shares of players produce more or less at the same level alternating their decision mechanisms

Oligopoly Games with Local Monopolistic Approximation

We propose a repeated oligopoly game where quantity setting firms have incomplete knowledge of the demand function of the market in which they operate. At each time step they solve a profit maximization problem by using a subjective approximation of the demand function based on a local estimate its partial derivative, computed at the current values of prices and outputs, obtained through market experiments. At each time step they extrapolate such local approximation by assuming a linear demand function and ignoring the effects of the competitors outputs. Despite a so rough approximation, that we call "Local Monopolistic Approximation" (LMA), the repeated game may converge to a Nash equilibrium of the true oligopoly game, i.e. the game played under the assumption of full information. An explicit form of the dynamical system that describes the time evolution of oligopoly games with LMA is given for arbitrary differentiable demand functions, provided that the cost functions are linear or quadratic. Sufficient conditions for the local stability of Nash Equilibria are given. In the particular case of an isoelastic demand function, we show that the repeatead game based on LMA always converges to a Nash equilibrium, both with linear and quadratic cost functions. This stability result is compared with "best reply" dynamics, obtained under the assumption of isoelastic demand (fully known by the players) and linear costs.Oligopoly games, bounded rationality, subjective demand, Nash equilibrium, dynamical systems, stability

Complex Dynamics in an Evolutionary General Equilibrium Model

We propose an exchange economy evolutionary model with discrete time, in which there are two utility-maximizing groups of agents which differ in the preference structure. Assuming an evolutionary mechanism based on the relative utility values realized by the two kinds of agents, we analytically and numerically investigate the existence of equilibria, their stability, and possible phenomena of coexistence between groups, mainly in terms of the heterogeneity degree in the preference structure. We find that our system has two trivial equilibria, at which just one of the two groups is present, and possibly a nontrivial equilibrium, characterized by the coexistence of the two groups of agents. Such nontrivial equilibrium may be stable, attracting all trajectories, or unstable. In the latter case, interesting, periodic, or chaotic, dynamics arise. We prove that the nontrivial equilibrium emerges via a transcritical bifurcation and loses stability via a flip bifurcation, after which the coexistence between groups is oscillatory in nature, presenting a regular or irregular behavior. In order to better investigate the role of the heterogeneity degree parameter, we perform a bifurcation analysis considering different scenarios, characterized by a balanced or unbalanced endowment distribution of the two goods