Stability of equilibrium price-production of dynamic duopoly Bertrand–Cournot game in a transnational supply chain with asymmetric information

Bounded rationality, asymmetric information and foreign trade are widespread in the economic market, and have been studied extensively in oligopoly games, but there are not many works discussing asymmetric information and bounded rationality in the supply chain hybrid game. In contrast with existing works, in our study, we innovatively construct a duopoly Bertrand–Cournot game model in a transnational supply chain with bounded rationality and asymmetric information. It is assumed that upstream firm 1 knows all the market information and adopts boundedly rational expectation, while downstream firm 2 only partially knows the market information and uses naïve expectation. Based on game theory and nonlinear dynamic theory, the complexity of the discrete system is analysed with respect to effective information, shareholding ratio and price sensitivity. Results reveal the following: (i) When the downstream firm knows little about the price information of the upstream firm, the market may be unstable or even chaotic; otherwise, it is conducive to the stability of the product market. (ii) When the shareholding ratio or the price sensitivity is relatively small, the market is more stable, and as they increase, the discrete price-production system goes through bifurcation and eventually falls into chaos. Our research has an important theoretical and practical significance for price-production supply chain competition in oligopoly markets.