The complex dynamics of a multi-product mixed duopoly model with partial privatization and cross-ownership

Abstract

The aim of privatization is to break the monopoly of public firm and ensure the effective competition. Selling a stake of public firm to private firm is the prevailing international practice. This paper proposes a multi-product mixed duopoly game model with partial privatization and cross-ownership, in which a public firm and a private firm coexist. The creative 3-D bifurcation diagram is used to investigate the dynamic characteristics of the high-dimension model. Some useful results are gained: The output adjustment strategy of public firm influences the system complex dynamics more violently than private firm’s output strategy; larger privatization level of public firm can help stabilize the market; especially, quite different with other researches, larger multi-product substitution level is advantageous to promote the stability of the market. The results of the study provide reference for policy-making of government and enterprises in this kind of duopoly mixed market.