Endogenous Timing in a Mixed Duopoly and Private Duopoly - ‘Capacity- then-Quantity’ Game

We consider a game of endogenous timing of sequential choice of capacity and quantity with observable delay in a mixed duopoly and a private duopoly under two possible time structures. In mixed duopoly, we find that a simultaneous play at the capacity stage or at the quantity stage can never be supported as subgame perfect Nash equilibrium (SPNE); whereas a simultaneous play at each stage turns out to be the unique SPNE in a private duopoly. In mixed duopoly there is multiplicity of equilibria and all SPNEs require sequentiality at the capacity as well as quantity stage. These equilibrium outcomes are invariant with respect to the endogenous time structures. In this context, we also show that the public firm never chooses over (excess) capacity in mixed duopoly, while the private firm never chooses under capacity in both mixed and private duopoly.