Price Vs Quantity in Duopoly Supergames With Close Substitutes

We model the non-cooperative choice between quantity and price in order to stabilize collusion, through two meta-games where each firm alternatively considers its payoff in the market supergame as directly related to its own or the rival's ability to collude. In the first setting, (i) if cartel profits are evenly split, 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; (ii) if Nash bargaining is adopted, price setting is dominant when substitutability is low, while no dominant strategy exists when substitutability is high, and the game has two asymmetric equilibria. In the second setting, the Nash equilibrium is unique and Pareto-efficient for the most part of the substitutability range, while again two asymmetric equilibria obtain when products are very close substitutes