A stochastic version of a Stackelberg–Nash–Cournot equilibrium model

We consider a stochastic version of the Stackelberg–Nash–Cournot model proposed by Murphy et al. In the first stage, the leader chooses and announces his production level taking into account the reaction of the followers. The decision of the leader is taken when market demand is uncertain. In the second stage, the followers, knowing the leader's output, react to this level according to the Cournot assumption. At this stage, demand is known. We study the extension of the Murphy et al. model and give a numerical illustration of this model using the European gas market.