The stability, bifurcation and chaos of a duopoly game in the market of complementary products with mixed bundling pricing

This paper constructs a non-competitive duopoly price model with mixed bundling pricing in complementary product market. The system is modeled by nonlinear difference equations. The existence of Nash equilibrium point and its stability are studied. The effects of complementarity degree and discount of bundling on the stability are investigated. The effects of the price adjustment parameters on the producer surplus are also investigated, especially when the parameters are used with the discount of bundling. The results show: increasing the degree of complementarity or the discount of bundling can enlarge the stable region of the system. Firms can get higher producer surplus with suitable discount of bundling in stable state than in unstable state of the market.