Simple and complex adjustment dynamics in Cournot duopoly models

We are investigating microeconomic foundations of Cournot duopoly games such that the reaction functions are unimodal. We demonstrate that cost functions incorporating an interfirm externality lead to a system of coupled logistic equations. In the situation where agents take turns, we observe periodic and complex behavior. A closer analysis reveals some well-known local bifurcations. In a more general situation, where agents move simultaneously, we observe global bifurcations which typically occur in two-parameter families of two-dimensional endomorphisms.