An economical model for dumping by dumping in a Cournot model

We consider an international trade economical model where two firms of different countries compete in quantities and can use three different strategies: (i) repeated collusion, (ii) deviation from the foreigner firm followed by punishment by the home country and then followed by repeated Cournot, or (iii) repeated deviation followed by punishment. In some cases (ii) and (iii) can be interpreted as dumping.We compute the profits of both firms for each strategy and we characterize the economical parameters where each strategy is adopted by the firms.