Duopoly models with a joint capacity constraint

This paper extends two recent models of duopoly with a joint capacity constraint (Nie and Chen in Econ Model 29:1715-1721, 2012; Nie in J Econ 112(3):283-294, 2014) by relaxing their crucial assumption that the game has an equilibrium which is unique and interior. Instead, this paper tackles a more basic issue on when their assumption applies. Our investigation is undertaken by using the best-response curve analysis. Both standard duopoly and mixed duopoly are considered, and both simultaneous moves and sequential moves are investigated. We find that their assumption applies only when the constraint is sufficiently weak, otherwise the equilibrium is either non-unique or corner.