The stability of Bayesian Nash equilibrium of dynamic Cournot duopoly model with asymmetric information

Few literatures apply complex oligopoly dynamics theory in games of incomplete information. This paper aims at analyzing dynamic behaviors of Bayesian game. A dynamic Cournot model with asymmetric information is proposed based on adaptive expectation and bounded rationality. Theoretical analysis draws two important conclusions: firstly, Bayesian Nash equilibrium of dynamic Cournot duopoly model with two players of adaptive expectation is always globally asymptotically stable. Secondly, Bayesian Nash equilibrium of dynamic Cournot duopoly model with players of adaptive expectation and gradient rule based on marginal profit is locally asymptotically stable only when parameters satisfy certain conditions. In our model, a firm of uncertain cost function is designed. A probability parameter θ of private type which differentiates high cost and low cost is introduced. Bifurcation, or even chaos with respect to θ, is performed by simulation which implies that large possibility of high-cost production yields easier chaos in duopoly market. High adjustment speeds of output form a three-dimensional strange attractors region. The unstable system's negative impact on equilibrium output and profit highlights the importance of system stability. Chaos control is in order to stabilize the equilibrium of the improved dynamic Cournot model with asymmetric information.