Dynamics of n-person Cournot games with asymmetric information and heterogeneous expectations

Abstract

This paper proposes an n-person Cournot game with asymmetric information and studies the stability of its Bayesian Nash equilibria. In such a game, a probability θ of high costs and a ratio γ of firms with incomplete information are introduced to express the asymmetric information. Furthermore, to relax rationality, we assume all firms with the same marginal costs always imitate each other in most periods except for sporadically using adaptive expectation. Theoretical analysis shows three important results. Firstly, in static n-person Cournot games, γ plays a negative role in the excess equilibrium output on asymmetric information as θ>0.5. However, γ has a positive influence if θ<0.5. Secondly, based on adaptive expectation, Bayesian Nash equilibria of dynamic n-person Cournot games are globally asymptotically stable. Thirdly, based on heterogeneous expectations, Bayesian Nash equilibria of dynamic n-person Cournot games are locally asymptotically stable under certain conditions of parameters. Besides, a larger θ or a smaller γ is more likely to cause bifurcations and chaos in oligopoly markets with asymmetric information by simulations.