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Working Paper-
ISCTE
Lisbon University Institute
Complex Dynamics in Simple
Vivaldo M. Mendes
Cournot Duopoly Games
Diana A. Mendes
Working Paper - 10/08
- Lisbon University Institute
Orlando Gomes
Complex Dynamics in Simple Cournot Duopoly
Games
Diana A. Mendes
Vivaldo M. Mendes†
Orlando Gomes‡
Abstract
The main aim of this paper is to analyse the dynamics of nonlinear
discrete-time maps generated by duopoly games with heterogeneous
and quadratic cost functions, in which players do not form expeta-
tions about the rival’s actions accordingto the ratioal expectations hy-
pothesis. We discusse here two cases. In the rst one we introduce
games with boundedly rational players and in the second one games
with adaptive expectations. The dynamics are mainly analysed by
numerical simulations. There are always multiple equilibria, and the
signicance of the Nash equilibria is pointed out.
1 Introduction
The complexity of oligopoly models may arise from a large set of sources.
It may come from the particular form of expectations formation related to
the rival actions that is considered in the model, or from the kind of cost
structures that are taken into consideration, or, nally, whether the demand
function is linear or not. In this paper we assume that the market demand
function is linear and that cost structures are nonlinear and heterogeneous.
What happens to the dynamics of the Cournot model if the rms form
expectations not according to the rational expectations hypothesis?
What happens if both rms are bounded rational? By bounded rational
rms, we have in mind that rms usually do not have a complete knowledge
of the market, and hence they try to use partial information based on the
local estimates of the marginal prot. At each time period , each rm
increases (decreases) its production at the period (+ 1) if the marginal
prot is positive (negative). This kind of expectations