Abstract
We analyze a triopoly game model with fully heterogeneous players when the demand function is isoelastic. The three players were considered to be bounded rational, adaptive, and naïve. Existing equilibrium points and their locally asymptotic stability conditions are studied. Complexity of the dynamical system is examined by means of numerical simulations, such as period cycles, bifurcation diagrams, strange attractors and sensitive, dependence on initial conditions. This paper extends the result of Tramontana (2010) who considered a heterogeneous duopoly with isoelastic demand function. Comparisons with respect to the heterogeneous triopoly model of Elabbasy et al. (2009) assuming linear demand function are performed.
Highlights
Oligopolistic market is a universal market mechanism, in which a trade is controlled by a small number of firms producing the same or homogeneous products
The analysis showed that the delay case increases the domain of stability, and firms using delayed bounded rationality have a higher chance of reaching a Nash equilibrium point
We propose a fully heterogeneous bounded rational, adaptive, and naıve expectations triopoly game model with nonlinear demand function and linear cost functions
Summary
Oligopolistic market is a universal market mechanism, in which a trade is controlled by a small number of firms producing the same or homogeneous products. After that the similar conclusion was shown by Ahmed and Agiza for a isoelastic demand function and, again, constant marginal costs They demonstrated that with four players the Cournot equilibrium is neutrally stable and with five and higher becomes unstable 5. In 9, , Agiza and Elsadany investigated dynamics of a duopoly game with bounded rational and naıve adaptive assuming linear inverse demand function and linear cost functions. Models with heterogeneous players were studied in 19, 20 In these two papers, triopoly with different expectations were used, namely bounded, rational, adaptive, and naıve expectations.
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