Price vs Quantity in Duopoly Supergames with Close Substitutes

We model the non-cooperative choice between quantity and price in order to stabilize collusion with horizontally differentiated goods, through two meta-games where each firm alternatively considers its payoff in the market supergame as directly related to its own or the rivals ability to collude. In the first setting, firms collude in prices irrespective of the degree of differentiation, so that initially a Prisoners Dilemma is observed, while for very close substitutes the outcome is Pareto-efficient. In the second setting, the Nash equilibrium is unique and Pareto-efficient for the most part of the substitutability range, while two asymmetric equilibria obtain when products are very close substitutes.