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In this paper, we investigate two heterogeneous triopoly games where thedemand function of the market is isoelastic. The local stability and thebifurcation of these games are systematically analyzed using the symbolicapproach proposed by the author. The novelty of the present work is twofold. Onone hand, the results of this paper are analytical, which are different fromthe existing results in the literature based on observations through numericalsimulations. In particular, we rigorously prove the existence of double routesto chaos through the period-doubling bifurcation and through the Neimark-Sackerbifurcation. On the other hand, for the special case of the involved firmshaving identical marginal costs, we acquire the necessary and sufficientconditions of the local stability for both models. By further analyzing theseconditions, it seems that that the presence of the local monopolisticapproximation (LMA) mechanism might have a stabilizing effect for heterogeneoustriopoly games with the isoelastic demand.

Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand