Price vs. quantity in oligopoly games

Price-setting and quantity-setting oligopoly games lead to extremely different outcomes in the market. One natural way to address this problem is to formulate a model in which some firms use price while the remaining firms use quantity as their decision variable. We introduce a mixed oligopoly game of this type and determine its equilibria. In addition, we consider an extension of this mixed oligopoly game through which the choice of the decision variables can be endogenized. We prove the emergence of the Cournot game.